Simulation Study 2
Parameter Bias
R. Noah Padgett
2022-01-07
Last updated: 2022-02-13
Checks: 5 1
Knit directory: Padgett-Dissertation/
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# Load packages
source("code/load_packages.R")
source("code/load_utility_functions.R")
# environment options
options(scipen = 999, digits=3)
# results folder
res_folder <- paste0(w.d, "/data/study_2")
# read in data
source("code/load_extracted_data.R")Parameter Bias
The true values (those used to simulated the data) are defined below.
true_params <- list(
lambda = 0.9 # factor loadings
, tau = NULL # item thresholds
, theta = 1 + 0.9**2 # total variance of latent response variables
, beta_lrt = 1.5 # intercept for response time
, sigma_lrt = 1/0.25 # precision of obs. RT
, sigma_s = 1/0.1 # precision of Latent Speed Variable
, sigma_st = -sqrt(0.1)*0.23 # covariance between factors
, rho = 0.1 # relationship between PID and response time
, omega = NULL # factor reliability
)
# Item Thresholds
# Tau depends on N_cat, N_items
getTau <- function(N_cat, N_items, lambda=0.9, seed=1){
set.seed(seed)
if(N_cat == 2){
tau <- matrix(
runif(N_items, -0.5, 0.5),
ncol=N_cat - 1,
nrow=N_items,
byrow=T
)
tau = -tau
}
if(N_cat > 2 & N_cat < 7){
tau <- matrix(ncol=N_cat-1, nrow=N_items)
for(c in 1:(N_cat-1)){
if(c == 1){
tau[,1] <- runif(N_items, -1, -0.33)
}
if(c > 1){
tau[,c] <- tau[,c-1] + runif(N_items, 0.25, 1)
}
}
}
if(N_cat == 7){
tau <- matrix(ncol=N_cat-1, nrow=N_items)
for(c in 1:(N_cat-1)){
if(c == 1){
tau[,1] <- runif(N_items, -2, -1.33)
}
if(c > 1){
tau[,c] <- tau[,c-1] + runif(N_items, 0.33, 1.0)
}
}
}
tau = tau*lambda
return(tau)
}
# ex. N_cat=2 & N_items=5
getTau(2, 5) [,1]
[1,] 0.2110
[2,] 0.1151
[3,] -0.0656
[4,] -0.3674
[5,] 0.2685getTau(2, 10) [,1]
[1,] 0.2110
[2,] 0.1151
[3,] -0.0656
[4,] -0.3674
[5,] 0.2685
[6,] -0.3586
[7,] -0.4002
[8,] -0.1447
[9,] -0.1162
[10,] 0.3944getTau(2, 20) [,1]
[1,] 0.21104
[2,] 0.11509
[3,] -0.06557
[4,] -0.36739
[5,] 0.26849
[6,] -0.35855
[7,] -0.40021
[8,] -0.14472
[9,] -0.11620
[10,] 0.39439
[11,] 0.26462
[12,] 0.29110
[13,] -0.16832
[14,] 0.10431
[15,] -0.24286
[16,] 0.00207
[17,] -0.19586
[18,] -0.44272
[19,] 0.10797
[20,] -0.24970# ex. N_cat=5 & N_items=5
getTau(3, 5) [,1] [,2]
[1,] -0.740 0.0915
[2,] -0.676 0.1870
[3,] -0.555 0.1165
[4,] -0.352 0.2973
[5,] -0.778 -0.5117getTau(3, 10) [,1] [,2]
[1,] -0.740 -0.3759
[2,] -0.676 -0.3314
[3,] -0.555 0.1342
[4,] -0.352 0.1319
[5,] -0.778 -0.0337
[6,] -0.358 0.2027
[7,] -0.330 0.3790
[8,] -0.502 0.3930
[9,] -0.521 -0.0391
[10,] -0.863 -0.1130getTau(3, 20) [,1] [,2]
[1,] -0.740 0.11603
[2,] -0.676 -0.30741
[3,] -0.555 0.11031
[4,] -0.352 -0.04260
[5,] -0.778 -0.37301
[6,] -0.358 0.12736
[7,] -0.330 -0.09632
[8,] -0.502 -0.01843
[9,] -0.521 0.29140
[10,] -0.863 -0.40801
[11,] -0.776 -0.22539
[12,] -0.794 -0.16383
[13,] -0.486 0.07242
[14,] -0.668 -0.31769
[15,] -0.436 0.34769
[16,] -0.600 0.07633
[17,] -0.467 0.29384
[18,] -0.302 -0.00402
[19,] -0.671 0.04267
[20,] -0.431 0.07141# ex. N_cat=5 & N_items=5
getTau(5, 5) [,1] [,2] [,3] [,4]
[1,] -0.740 0.0915 0.456 1.016
[2,] -0.676 0.1870 0.531 1.241
[3,] -0.555 0.1165 0.805 1.700
[4,] -0.352 0.2973 0.782 1.263
[5,] -0.778 -0.5117 0.233 0.983getTau(5, 10) [,1] [,2] [,3] [,4]
[1,] -0.740 -0.3759 0.4801 1.030
[2,] -0.676 -0.3314 0.0368 0.666
[3,] -0.555 0.1342 0.7991 1.357
[4,] -0.352 0.1319 0.4417 0.792
[5,] -0.778 -0.0337 0.3716 1.155
[6,] -0.358 0.2027 0.6883 1.365
[7,] -0.330 0.3790 0.6131 1.374
[8,] -0.502 0.3930 0.8761 1.174
[9,] -0.521 -0.0391 0.7729 1.486
[10,] -0.863 -0.1130 0.3418 0.844getTau(5, 20) [,1] [,2] [,3] [,4]
[1,] -0.740 0.11603 0.8952 1.736
[2,] -0.676 -0.30741 0.3544 0.778
[3,] -0.555 0.11031 0.8638 1.399
[4,] -0.352 -0.04260 0.5557 1.005
[5,] -0.778 -0.37301 0.2095 0.874
[6,] -0.358 0.12736 0.8852 1.284
[7,] -0.330 -0.09632 0.1444 0.692
[8,] -0.502 -0.01843 0.5287 1.271
[9,] -0.521 0.29140 1.0107 1.293
[10,] -0.863 -0.40801 0.2846 1.100
[11,] -0.776 -0.22539 0.3220 0.776
[12,] -0.794 -0.16383 0.6425 1.434
[13,] -0.486 0.07242 0.5931 1.052
[14,] -0.668 -0.31769 0.0725 0.523
[15,] -0.436 0.34769 0.6204 1.167
[16,] -0.600 0.07633 0.3685 1.196
[17,] -0.467 0.29384 0.7323 1.541
[18,] -0.302 -0.00402 0.5711 1.059
[19,] -0.671 0.04267 0.7145 1.464
[20,] -0.431 0.07141 0.5710 1.444# ex. N_cat=5 & N_items=5
getTau(7, 5) [,1] [,2] [,3] [,4] [,5] [,6]
[1,] -1.64 -0.801 -0.3800 0.217 1.078 1.61
[2,] -1.58 -0.709 -0.3055 0.424 0.849 1.15
[3,] -1.45 -0.759 -0.0478 0.847 1.537 2.06
[4,] -1.25 -0.576 -0.0474 0.479 0.851 1.67
[5,] -1.68 -1.344 -0.5829 0.183 0.641 1.14getTau(7, 10) [,1] [,2] [,3] [,4] [,5] [,6]
[1,] -1.64 -1.219 -0.3581 0.2296 1.022 1.61
[2,] -1.58 -1.172 -0.7472 -0.0887 0.598 1.41
[3,] -1.45 -0.743 -0.0533 0.5413 1.310 1.87
[4,] -1.25 -0.724 -0.3510 0.0583 0.689 1.13
[5,] -1.68 -0.917 -0.4590 0.3369 0.953 1.29
[6,] -1.26 -0.661 -0.1313 0.5688 1.342 1.70
[7,] -1.23 -0.501 -0.1956 0.5804 0.891 1.38
[8,] -1.40 -0.506 0.0212 0.3833 0.968 1.58
[9,] -1.42 -0.894 -0.0731 0.6603 1.399 2.10
[10,] -1.76 -0.997 -0.4947 0.0503 0.765 1.31getTau(7, 20) [,1] [,2] [,3] [,4] [,5] [,6]
[1,] -1.64 -0.779 0.0128 0.86022 1.419 2.11
[2,] -1.58 -1.151 -0.4635 0.01053 0.737 1.25
[3,] -1.45 -0.765 0.0045 0.57831 1.117 1.58
[4,] -1.25 -0.880 -0.2492 0.24827 0.741 1.64
[5,] -1.68 -1.220 -0.6038 0.08564 0.839 1.52
[6,] -1.26 -0.728 0.0445 0.49712 0.916 1.34
[7,] -1.23 -0.925 -0.6142 -0.02865 0.697 1.07
[8,] -1.40 -0.874 -0.2892 0.46990 0.840 1.43
[9,] -1.42 -0.599 0.1394 0.48717 0.932 1.79
[10,] -1.76 -1.261 -0.5458 0.27902 0.662 1.32
[11,] -1.68 -1.088 -0.5031 -0.00164 0.440 1.33
[12,] -1.69 -1.035 -0.2187 0.58449 0.917 1.66
[13,] -1.39 -0.791 -0.2299 0.27610 0.960 1.47
[14,] -1.57 -1.159 -0.7145 -0.21622 0.609 1.17
[15,] -1.34 -0.540 -0.2003 0.38398 1.151 1.54
[16,] -1.50 -0.800 -0.4428 0.39217 1.170 1.47
[17,] -1.37 -0.591 -0.1036 0.71456 1.286 2.01
[18,] -1.20 -0.840 -0.2301 0.30211 0.846 1.21
[19,] -1.57 -0.837 -0.1413 0.62447 1.410 1.98
[20,] -1.33 -0.786 -0.2439 0.63237 1.294 1.98# factor reliability
# depends on N_items & simulated lambda value
getOmega <- function(lambda, N_items){
(lambda*N_items)**2/((lambda*N_items)**2 + N_items)
}
# ex. N_items = 5
getOmega(0.9, 5)[1] 0.802getOmega(0.9, 10)[1] 0.89getOmega(0.9, 20)[1] 0.942The code below loops through the posterior summaries to compute the relative bias for each parameter.
# compute relative bias
mydata <- mydata %>%
# use posterior median & mean for comparison
mutate(
post_median_rb_est = (post_q50 - true_value)/true_value*100,
post_mean_rb_est = (post_mean - true_value)/true_value*100,
post_median_bias_est = post_q50 - true_value,
post_mean_bias_est = post_mean - true_value,
# compute convergence
converge = ifelse(Rhat - 1.10 < 0, 1, 0)
) %>%
filter(converge == 1)
# Update condition labels for plotting
mydata$condition_lbs <- factor(
mydata$condition,
levels = 1:24,
labels = c(
"nCat=2, nItem= 5, N= 500",
"nCat=2, nItem= 5, N=2500",
"nCat=2, nItem=10, N= 500",
"nCat=2, nItem=10, N=2500",
"nCat=2, nItem=20, N= 500",
"nCat=2, nItem=20, N=2500",
"nCat=5, nItem= 5, N= 500",
"nCat=5, nItem= 5, N=2500",
"nCat=5, nItem=10, N= 500",
"nCat=5, nItem=10, N=2500",
"nCat=5, nItem=20, N= 500",
"nCat=5, nItem=20, N=2500",
"nCat=3, nItem= 5, N= 500",
"nCat=3, nItem= 5, N=2500",
"nCat=3, nItem=10, N= 500",
"nCat=3, nItem=10, N=2500",
"nCat=3, nItem=20, N= 500",
"nCat=3, nItem=20, N=2500",
"nCat=7, nItem= 5, N= 500",
"nCat=7, nItem= 5, N=2500",
"nCat=7, nItem=10, N= 500",
"nCat=7, nItem=10, N=2500",
"nCat=7, nItem=20, N= 500",
"nCat=7, nItem=20, N=2500"
)
)
# columns to keep
keep_cols <- c("condition","condition_lbs", "iter", "N", "N_items", "N_cat", "parameter_group", "rb_est", "rb_est_paragrp")Summaring Relative Bias
Factor Loadings (\(\lambda\))
param = "FACTOR LOADING"
rb <- mydata %>%
filter(parameter_group == "lambda")
# tabular summary of relative bias
rb_tbl <- rb %>%
group_by(condition, N_cat, N_items, N) %>%
summarise(N_converge = n(),
true = mean(true_value),
avg_median_est = mean(post_q50),
avg_mean_est = mean(post_mean),
Post_Median_RB_Mean = mean(post_median_rb_est),
Post_Median_RB_SD = sd(post_median_rb_est),
Post_Mean_RB_Mean = mean(post_mean_rb_est),
Post_Mean_RB_SD = sd(post_mean_rb_est),
Post_Median_AB = mean(post_median_bias_est),
Post_Mean_AB = mean(post_mean_bias_est))`summarise()` has grouped output by 'condition', 'N_cat', 'N_items'. You can override using the `.groups` argument.kable(rb_tbl, format="html", digits=3) %>%
kable_styling(full_width = T) %>%
scroll_box(width="100%",height = "100%")| condition | N_cat | N_items | N | N_converge | true | avg_median_est | avg_mean_est | Post_Median_RB_Mean | Post_Median_RB_SD | Post_Mean_RB_Mean | Post_Mean_RB_SD | Post_Median_AB | Post_Mean_AB |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 1 | 2 | 5 | 500 | 341 | 0.9 | 0.670 | 0.728 | -25.6 | 39.10 | -19.13 | 40.15 | -0.230 | -0.172 |
| 2 | 2 | 5 | 2500 | 327 | 0.9 | 0.752 | 0.764 | -16.5 | 20.51 | -15.09 | 20.84 | -0.148 | -0.136 |
| 3 | 2 | 10 | 500 | 846 | 0.9 | 0.774 | 0.810 | -14.0 | 35.80 | -10.00 | 36.90 | -0.126 | -0.090 |
| 4 | 2 | 10 | 2500 | 900 | 0.9 | 0.775 | 0.781 | -13.9 | 15.00 | -13.18 | 15.15 | -0.125 | -0.119 |
| 5 | 2 | 20 | 500 | 1898 | 0.9 | 0.808 | 0.829 | -10.2 | 29.68 | -7.88 | 30.46 | -0.092 | -0.071 |
| 6 | 2 | 20 | 2500 | 1945 | 0.9 | 0.776 | 0.779 | -13.8 | 12.02 | -13.45 | 12.09 | -0.124 | -0.121 |
| 7 | 5 | 5 | 500 | 388 | 0.9 | 0.768 | 0.787 | -14.7 | 25.26 | -12.51 | 26.54 | -0.132 | -0.113 |
| 8 | 5 | 5 | 2500 | 456 | 0.9 | 0.766 | 0.769 | -14.9 | 10.93 | -14.58 | 10.99 | -0.134 | -0.131 |
| 9 | 5 | 10 | 500 | 920 | 0.9 | 0.779 | 0.786 | -13.5 | 19.00 | -12.65 | 19.29 | -0.121 | -0.114 |
| 10 | 5 | 10 | 2500 | 965 | 0.9 | 0.768 | 0.770 | -14.6 | 8.07 | -14.45 | 8.09 | -0.132 | -0.130 |
| 11 | 5 | 20 | 500 | 1890 | 0.9 | 0.785 | 0.790 | -12.8 | 16.41 | -12.25 | 16.53 | -0.115 | -0.110 |
| 12 | 5 | 20 | 2500 | 1933 | 0.9 | 0.770 | 0.771 | -14.4 | 6.82 | -14.31 | 6.83 | -0.130 | -0.129 |
| 13 | 3 | 5 | 500 | 433 | 0.9 | 0.772 | 0.800 | -14.2 | 30.01 | -11.06 | 31.22 | -0.128 | -0.100 |
| 14 | 3 | 5 | 2500 | 474 | 0.9 | 0.762 | 0.767 | -15.4 | 13.83 | -14.83 | 13.99 | -0.138 | -0.133 |
| 15 | 3 | 10 | 500 | 980 | 0.9 | 0.780 | 0.792 | -13.3 | 23.64 | -11.96 | 24.07 | -0.120 | -0.108 |
| 16 | 3 | 10 | 2500 | 995 | 0.9 | 0.759 | 0.761 | -15.7 | 9.91 | -15.46 | 9.96 | -0.141 | -0.139 |
| 17 | 3 | 20 | 500 | 1987 | 0.9 | 0.788 | 0.795 | -12.5 | 19.11 | -11.65 | 19.37 | -0.112 | -0.105 |
| 18 | 3 | 20 | 2500 | 2000 | 0.9 | 0.757 | 0.758 | -15.9 | 8.29 | -15.74 | 8.32 | -0.143 | -0.142 |
| 19 | 7 | 5 | 500 | 389 | 0.9 | 0.797 | 0.813 | -11.4 | 24.56 | -9.69 | 25.41 | -0.103 | -0.087 |
| 20 | 7 | 5 | 2500 | 207 | 0.9 | 0.777 | 0.779 | -13.7 | 9.72 | -13.42 | 9.76 | -0.123 | -0.121 |
| 21 | 7 | 10 | 500 | 424 | 0.9 | 0.793 | 0.799 | -11.9 | 17.05 | -11.18 | 17.23 | -0.107 | -0.101 |
| 22 | 7 | 10 | 2500 | 451 | 0.9 | 0.776 | 0.777 | -13.8 | 7.70 | -13.66 | 7.72 | -0.124 | -0.123 |
| 23 | 7 | 20 | 500 | 879 | 0.9 | 0.793 | 0.796 | -11.9 | 15.28 | -11.51 | 15.38 | -0.107 | -0.104 |
| 24 | 7 | 20 | 2500 | 700 | 0.9 | 0.776 | 0.777 | -13.8 | 6.53 | -13.67 | 6.54 | -0.124 | -0.123 |
# visualize RB estimates
p1 <- ggplot() +
stat_summary(
data = rb,
aes(x = condition, y = post_median_rb_est,
group = condition),
fun.data = cust.boxplot,
geom = "boxplot"
) +
geom_point(data = rb_tbl,
aes(x = condition, y = Post_Median_RB_Mean),
color = "black") +
geom_abline(intercept = -10,
slope = 0,
linetype = "dashed") +
geom_abline(intercept = 10,
slope = 0,
linetype = "dashed") +
lims(y = c(-100, 100)) +
coord_flip() +
labs(
title = paste0("Relative Bias for ", param, " posterior median"),
subtitle = "Plot includes RB estimate for each parameter estimate (boxplot) and\n average RB esimate (black dot)",
caption = "Note. Dashed lines represent +/-10% relative bias"
) +
theme_bw() +
theme(panel.grid = element_blank())
p2 <- ggplot() +
stat_summary(
data = rb,
aes(x = condition, y = post_median_bias_est,
group = condition),
fun.data = cust.boxplot,
geom = "boxplot"
) +
geom_point(data = rb_tbl,
aes(x = condition, y = Post_Median_AB),
color = "black") +
geom_abline(intercept = 0,
slope = 0,
linetype = "dashed")+
coord_flip() +
labs(
title = paste0("Average Bias for ", param, " posterior median"),
subtitle = "Plot includes AB estimate for each parameter estimate (boxplot) and\n average AB esimate (black dot)",
caption = "Note. Dashed line represent 0 bias"
) +
theme_bw() +
theme(panel.grid = element_blank())
p1 + p2Warning: Removed 15 rows containing non-finite values (stat_summary).
Item Thresholds (\(\tau\))
param = "Item Thresholds"
rb <- mydata %>%
filter(parameter_group == "tau")
# tabular summary of relative bias
rb_tbl <- rb %>%
group_by(condition, N_cat, N_items, N) %>%
summarise(N_converge = n(),
true = mean(true_value),
avg_median_est = mean(post_q50),
avg_mean_est = mean(post_mean),
Post_Median_RB_Mean = mean(post_median_rb_est),
Post_Median_RB_SD = sd(post_median_rb_est),
Post_Mean_RB_Mean = mean(post_mean_rb_est),
Post_Mean_RB_SD = sd(post_mean_rb_est),
Post_Median_AB = mean(post_median_bias_est),
Post_Mean_AB = mean(post_mean_bias_est))`summarise()` has grouped output by 'condition', 'N_cat', 'N_items'. You can override using the `.groups` argument.kable(rb_tbl, format="html", digits=3) %>%
kable_styling(full_width = T) %>%
scroll_box(width="100%",height = "100%")| condition | N_cat | N_items | N | N_converge | true | avg_median_est | avg_mean_est | Post_Median_RB_Mean | Post_Median_RB_SD | Post_Mean_RB_Mean | Post_Mean_RB_SD | Post_Median_AB | Post_Mean_AB |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 1 | 2 | 5 | 500 | 478 | 0.031 | 0.031 | 0.033 | -8.28 | 129.2 | -6.41 | 132.0 | 0.000 | 0.002 |
| 2 | 2 | 5 | 2500 | 491 | 0.032 | 0.029 | 0.029 | -2.28 | 56.4 | -1.66 | 56.7 | -0.003 | -0.002 |
| 3 | 2 | 10 | 500 | 985 | -0.046 | -0.041 | -0.041 | -2.85 | 112.5 | -1.55 | 114.1 | 0.005 | 0.005 |
| 4 | 2 | 10 | 2500 | 1000 | -0.046 | -0.050 | -0.050 | -3.30 | 46.6 | -3.16 | 46.7 | -0.004 | -0.004 |
| 5 | 2 | 20 | 500 | 2000 | -0.050 | -0.056 | -0.056 | 6.40 | 1480.3 | 8.90 | 1493.2 | -0.006 | -0.006 |
| 6 | 2 | 20 | 2500 | 2000 | -0.050 | -0.053 | -0.053 | -15.94 | 746.1 | -15.52 | 746.7 | -0.003 | -0.003 |
| 7 | 5 | 5 | 500 | 1943 | 0.299 | 0.301 | 0.303 | -3.81 | 46.7 | -3.19 | 47.1 | 0.002 | 0.004 |
| 8 | 5 | 5 | 2500 | 1997 | 0.303 | 0.284 | 0.284 | -8.11 | 19.6 | -8.03 | 19.7 | -0.019 | -0.019 |
| 9 | 5 | 10 | 500 | 3980 | 0.281 | 0.281 | 0.282 | -6.67 | 91.3 | -6.44 | 91.6 | 0.000 | 0.000 |
| 10 | 5 | 10 | 2500 | 3998 | 0.284 | 0.274 | 0.274 | -9.11 | 42.7 | -9.07 | 42.6 | -0.010 | -0.010 |
| 11 | 5 | 20 | 500 | 7970 | 0.278 | 0.290 | 0.291 | -22.63 | 433.6 | -22.57 | 433.9 | 0.012 | 0.013 |
| 12 | 5 | 20 | 2500 | 7990 | 0.279 | 0.269 | 0.269 | -16.54 | 170.1 | -16.53 | 170.3 | -0.010 | -0.010 |
| 13 | 3 | 5 | 500 | 977 | -0.288 | -0.165 | -0.167 | 58.04 | 115.6 | 59.29 | 116.4 | 0.123 | 0.121 |
| 14 | 3 | 5 | 2500 | 1000 | -0.292 | -0.172 | -0.173 | 54.39 | 96.7 | 54.54 | 96.8 | 0.120 | 0.119 |
| 15 | 3 | 10 | 500 | 1997 | -0.266 | -0.151 | -0.152 | -50.96 | 224.2 | -50.63 | 224.7 | 0.114 | 0.113 |
| 16 | 3 | 10 | 2500 | 2000 | -0.266 | -0.153 | -0.153 | -48.43 | 182.5 | -48.33 | 182.5 | 0.113 | 0.113 |
| 17 | 3 | 20 | 500 | 4000 | -0.293 | -0.184 | -0.184 | -67.29 | 672.9 | -66.92 | 673.2 | 0.109 | 0.108 |
| 18 | 3 | 20 | 2500 | 4000 | -0.293 | -0.185 | -0.185 | -52.74 | 443.1 | -52.69 | 443.1 | 0.108 | 0.108 |
| 19 | 7 | 5 | 500 | 2854 | 0.055 | 0.085 | 0.086 | -11.43 | 75.1 | -10.96 | 75.8 | 0.030 | 0.031 |
| 20 | 7 | 5 | 2500 | 1483 | 0.049 | 0.049 | 0.049 | -11.29 | 29.5 | -11.21 | 29.4 | 0.000 | 0.000 |
| 21 | 7 | 10 | 500 | 2971 | 0.045 | 0.073 | 0.074 | -6.00 | 95.5 | -5.74 | 95.8 | 0.028 | 0.028 |
| 22 | 7 | 10 | 2500 | 2989 | 0.044 | 0.054 | 0.054 | -8.05 | 47.1 | -8.01 | 47.2 | 0.010 | 0.010 |
| 23 | 7 | 20 | 500 | 5933 | 0.035 | 0.077 | 0.077 | 7.31 | 724.4 | 7.78 | 728.1 | 0.042 | 0.042 |
| 24 | 7 | 20 | 2500 | 4538 | 0.037 | 0.045 | 0.045 | -2.09 | 293.1 | -2.09 | 292.9 | 0.008 | 0.008 |
# visualize RB estimates
p1 <- ggplot() +
stat_summary(
data = rb,
aes(x = condition, y = post_median_rb_est,
group = condition),
fun.data = cust.boxplot,
geom = "boxplot"
) +
geom_point(data = rb_tbl,
aes(x = condition, y = Post_Median_RB_Mean),
color = "black") +
geom_abline(intercept = -10,
slope = 0,
linetype = "dashed") +
geom_abline(intercept = 10,
slope = 0,
linetype = "dashed") +
lims(y = c(-100, 100)) +
coord_flip() +
labs(
title = paste0("Relative Bias for ", param, " posterior median"),
subtitle = "Plot includes RB estimate for each parameter estimate (boxplot) and\n average RB esimate (black dot)",
caption = "Note. Dashed lines represent +/-10% relative bias"
) +
theme_bw() +
theme(panel.grid = element_blank())
p2 <- ggplot() +
stat_summary(
data = rb,
aes(x = condition, y = post_median_bias_est,
group = condition),
fun.data = cust.boxplot,
geom = "boxplot"
) +
geom_point(data = rb_tbl,
aes(x = condition, y = Post_Median_AB),
color = "black") +
geom_abline(intercept = 0,
slope = 0,
linetype = "dashed")+
coord_flip() +
labs(
title = paste0("Average Bias for ", param, " posterior median"),
subtitle = "Plot includes AB estimate for each parameter estimate (boxplot) and\n average AB esimate (black dot)",
caption = "Note. Dashed line represent 0 bias"
) +
theme_bw() +
theme(panel.grid = element_blank())
p1 + p2Warning: Removed 7514 rows containing non-finite values (stat_summary).
Latent Response Variance (\(\theta\))
param = "Latent Response Variance"
rb <- mydata %>%
filter(parameter_group == "theta")
# tabular summary of relative bias
rb_tbl <- rb %>%
group_by(condition, N_cat, N_items, N) %>%
summarise(N_converge = n(),
true = mean(true_value),
avg_median_est = mean(post_q50),
avg_mean_est = mean(post_mean),
Post_Median_RB_Mean = mean(post_median_rb_est),
Post_Median_RB_SD = sd(post_median_rb_est),
Post_Mean_RB_Mean = mean(post_mean_rb_est),
Post_Mean_RB_SD = sd(post_mean_rb_est),
Post_Median_AB = mean(post_median_bias_est),
Post_Mean_AB = mean(post_mean_bias_est))`summarise()` has grouped output by 'condition', 'N_cat', 'N_items'. You can override using the `.groups` argument.kable(rb_tbl, format="html", digits=3) %>%
kable_styling(full_width = T) %>%
scroll_box(width="100%",height = "100%")| condition | N_cat | N_items | N | N_converge | true | avg_median_est | avg_mean_est | Post_Median_RB_Mean | Post_Median_RB_SD | Post_Mean_RB_Mean | Post_Mean_RB_SD | Post_Median_AB | Post_Mean_AB |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 1 | 2 | 5 | 500 | 250 | 1.81 | 1.63 | 1.87 | -9.86 | 37.55 | 3.127 | 46.48 | -0.179 | 0.057 |
| 2 | 2 | 5 | 2500 | 310 | 1.81 | 1.60 | 1.66 | -11.40 | 16.23 | -8.439 | 17.21 | -0.206 | -0.153 |
| 3 | 2 | 10 | 500 | 756 | 1.81 | 1.71 | 1.88 | -5.68 | 32.22 | 3.674 | 37.81 | -0.103 | 0.066 |
| 4 | 2 | 10 | 2500 | 887 | 1.81 | 1.62 | 1.65 | -10.66 | 11.96 | -9.057 | 12.37 | -0.193 | -0.164 |
| 5 | 2 | 20 | 500 | 1844 | 1.81 | 1.72 | 1.83 | -4.72 | 26.70 | 1.397 | 29.74 | -0.086 | 0.025 |
| 6 | 2 | 20 | 2500 | 1941 | 1.81 | 1.61 | 1.63 | -10.85 | 9.46 | -9.902 | 9.64 | -0.196 | -0.179 |
| 7 | 5 | 5 | 500 | 366 | 1.81 | 1.64 | 1.73 | -9.39 | 21.81 | -4.619 | 25.77 | -0.170 | -0.084 |
| 8 | 5 | 5 | 2500 | 452 | 1.81 | 1.60 | 1.61 | -11.81 | 8.47 | -11.042 | 8.61 | -0.214 | -0.200 |
| 9 | 5 | 10 | 500 | 908 | 1.81 | 1.63 | 1.67 | -9.83 | 15.24 | -7.650 | 15.98 | -0.178 | -0.138 |
| 10 | 5 | 10 | 2500 | 964 | 1.81 | 1.60 | 1.60 | -11.84 | 6.23 | -11.435 | 6.28 | -0.214 | -0.207 |
| 11 | 5 | 20 | 500 | 1876 | 1.81 | 1.64 | 1.66 | -9.50 | 13.20 | -8.019 | 13.56 | -0.172 | -0.145 |
| 12 | 5 | 20 | 2500 | 1932 | 1.81 | 1.60 | 1.60 | -11.76 | 5.25 | -11.498 | 5.28 | -0.213 | -0.208 |
| 13 | 3 | 5 | 500 | 402 | 1.81 | 1.68 | 1.80 | -7.28 | 26.35 | -0.301 | 30.88 | -0.132 | -0.005 |
| 14 | 3 | 5 | 2500 | 465 | 1.81 | 1.59 | 1.62 | -11.89 | 10.86 | -10.744 | 11.23 | -0.215 | -0.194 |
| 15 | 3 | 10 | 500 | 976 | 1.81 | 1.65 | 1.72 | -8.71 | 20.05 | -5.268 | 21.45 | -0.158 | -0.095 |
| 16 | 3 | 10 | 2500 | 993 | 1.81 | 1.58 | 1.59 | -12.49 | 7.65 | -11.918 | 7.76 | -0.226 | -0.216 |
| 17 | 3 | 20 | 500 | 1986 | 1.81 | 1.65 | 1.69 | -8.87 | 15.77 | -6.593 | 16.50 | -0.161 | -0.119 |
| 18 | 3 | 20 | 2500 | 2000 | 1.81 | 1.58 | 1.59 | -12.77 | 6.29 | -12.384 | 6.34 | -0.231 | -0.224 |
| 19 | 7 | 5 | 500 | 374 | 1.81 | 1.68 | 1.75 | -7.13 | 21.88 | -3.121 | 24.43 | -0.129 | -0.056 |
| 20 | 7 | 5 | 2500 | 205 | 1.81 | 1.61 | 1.62 | -11.17 | 7.52 | -10.543 | 7.62 | -0.202 | -0.191 |
| 21 | 7 | 10 | 500 | 420 | 1.81 | 1.65 | 1.69 | -8.71 | 13.99 | -6.860 | 14.50 | -0.158 | -0.124 |
| 22 | 7 | 10 | 2500 | 451 | 1.81 | 1.61 | 1.61 | -11.27 | 5.98 | -10.919 | 6.03 | -0.204 | -0.198 |
| 23 | 7 | 20 | 500 | 861 | 1.81 | 1.65 | 1.67 | -8.93 | 12.52 | -7.658 | 12.80 | -0.162 | -0.139 |
| 24 | 7 | 20 | 2500 | 700 | 1.81 | 1.61 | 1.61 | -11.28 | 5.04 | -11.037 | 5.06 | -0.204 | -0.200 |
# visualize RB estimates
p1 <- ggplot() +
stat_summary(
data = rb,
aes(x = condition, y = post_median_rb_est,
group = condition),
fun.data = cust.boxplot,
geom = "boxplot"
) +
geom_point(data = rb_tbl,
aes(x = condition, y = Post_Median_RB_Mean),
color = "black") +
geom_abline(intercept = -10,
slope = 0,
linetype = "dashed") +
geom_abline(intercept = 10,
slope = 0,
linetype = "dashed") +
lims(y = c(-100, 100)) +
coord_flip() +
labs(
title = paste0("Relative Bias for ", param, " posterior median"),
subtitle = "Plot includes RB estimate for each parameter estimate (boxplot) and\n average RB esimate (black dot)",
caption = "Note. Dashed lines represent +/-10% relative bias"
) +
theme_bw() +
theme(panel.grid = element_blank())
p2 <- ggplot() +
stat_summary(
data = rb,
aes(x = condition, y = post_median_bias_est,
group = condition),
fun.data = cust.boxplot,
geom = "boxplot"
) +
geom_point(data = rb_tbl,
aes(x = condition, y = Post_Median_AB),
color = "black") +
geom_abline(intercept = 0,
slope = 0,
linetype = "dashed")+
coord_flip() +
labs(
title = paste0("Average Bias for ", param, " posterior median"),
subtitle = "Plot includes AB estimate for each parameter estimate (boxplot) and\n average AB esimate (black dot)",
caption = "Note. Dashed line represent 0 bias"
) +
theme_bw() +
theme(panel.grid = element_blank())
p1 + p2Warning: Removed 31 rows containing non-finite values (stat_summary).
Response Time Intercepts (\(\beta_{lrt}\))
param = "RT Intercepts"
rb <- mydata %>%
filter(parameter_group == "beta_lrt")
# tabular summary of relative bias
rb_tbl <- rb %>%
group_by(condition, N_cat, N_items, N) %>%
summarise(N_converge = n(),
true = mean(true_value),
avg_median_est = mean(post_q50),
avg_mean_est = mean(post_mean),
Post_Median_RB_Mean = mean(post_median_rb_est),
Post_Median_RB_SD = sd(post_median_rb_est),
Post_Mean_RB_Mean = mean(post_mean_rb_est),
Post_Mean_RB_SD = sd(post_mean_rb_est),
Post_Median_AB = mean(post_median_bias_est),
Post_Mean_AB = mean(post_mean_bias_est))`summarise()` has grouped output by 'condition', 'N_cat', 'N_items'. You can override using the `.groups` argument.kable(rb_tbl, format="html", digits=3) %>%
kable_styling(full_width = T) %>%
scroll_box(width="100%",height = "100%")| condition | N_cat | N_items | N | N_converge | true | avg_median_est | avg_mean_est | Post_Median_RB_Mean | Post_Median_RB_SD | Post_Mean_RB_Mean | Post_Mean_RB_SD | Post_Median_AB | Post_Mean_AB |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 1 | 2 | 5 | 500 | 402 | 1.5 | 1.50 | 1.51 | 0.091 | 4.01 | 0.618 | 3.91 | 0.001 | 0.009 |
| 2 | 2 | 5 | 2500 | 401 | 1.5 | 1.51 | 1.51 | 0.547 | 2.53 | 0.694 | 2.49 | 0.008 | 0.010 |
| 3 | 2 | 10 | 500 | 927 | 1.5 | 1.48 | 1.49 | -1.067 | 3.09 | -0.817 | 3.10 | -0.016 | -0.012 |
| 4 | 2 | 10 | 2500 | 974 | 1.5 | 1.51 | 1.51 | 0.559 | 1.75 | 0.630 | 1.74 | 0.008 | 0.009 |
| 5 | 2 | 20 | 500 | 1986 | 1.5 | 1.48 | 1.48 | -1.312 | 2.46 | -1.194 | 2.47 | -0.020 | -0.018 |
| 6 | 2 | 20 | 2500 | 1999 | 1.5 | 1.50 | 1.50 | 0.299 | 1.32 | 0.332 | 1.32 | 0.004 | 0.005 |
| 7 | 5 | 5 | 500 | 464 | 1.5 | 1.51 | 1.51 | 0.533 | 3.69 | 0.805 | 3.63 | 0.008 | 0.012 |
| 8 | 5 | 5 | 2500 | 488 | 1.5 | 1.52 | 1.52 | 1.423 | 2.09 | 1.467 | 2.09 | 0.021 | 0.022 |
| 9 | 5 | 10 | 500 | 984 | 1.5 | 1.50 | 1.50 | -0.303 | 2.76 | -0.199 | 2.75 | -0.005 | -0.003 |
| 10 | 5 | 10 | 2500 | 1000 | 1.5 | 1.51 | 1.51 | 0.569 | 1.33 | 0.595 | 1.33 | 0.009 | 0.009 |
| 11 | 5 | 20 | 500 | 1995 | 1.5 | 1.49 | 1.49 | -0.819 | 2.62 | -0.771 | 2.62 | -0.012 | -0.012 |
| 12 | 5 | 20 | 2500 | 2000 | 1.5 | 1.51 | 1.51 | 0.389 | 1.09 | 0.401 | 1.09 | 0.006 | 0.006 |
| 13 | 3 | 5 | 500 | 480 | 1.5 | 1.50 | 1.51 | 0.353 | 3.97 | 0.692 | 3.90 | 0.005 | 0.010 |
| 14 | 3 | 5 | 2500 | 494 | 1.5 | 1.52 | 1.52 | 1.428 | 2.21 | 1.513 | 2.20 | 0.021 | 0.023 |
| 15 | 3 | 10 | 500 | 996 | 1.5 | 1.50 | 1.50 | 0.051 | 3.06 | 0.205 | 3.05 | 0.001 | 0.003 |
| 16 | 3 | 10 | 2500 | 1000 | 1.5 | 1.51 | 1.51 | 0.753 | 1.53 | 0.789 | 1.52 | 0.011 | 0.012 |
| 17 | 3 | 20 | 500 | 2000 | 1.5 | 1.49 | 1.49 | -0.779 | 2.40 | -0.716 | 2.40 | -0.012 | -0.011 |
| 18 | 3 | 20 | 2500 | 2000 | 1.5 | 1.50 | 1.50 | 0.064 | 1.23 | 0.085 | 1.23 | 0.001 | 0.001 |
| 19 | 7 | 5 | 500 | 482 | 1.5 | 1.50 | 1.51 | 0.281 | 3.37 | 0.520 | 3.35 | 0.004 | 0.008 |
| 20 | 7 | 5 | 2500 | 237 | 1.5 | 1.52 | 1.52 | 1.226 | 1.72 | 1.246 | 1.72 | 0.018 | 0.019 |
| 21 | 7 | 10 | 500 | 497 | 1.5 | 1.50 | 1.50 | -0.144 | 2.49 | -0.054 | 2.49 | -0.002 | -0.001 |
| 22 | 7 | 10 | 2500 | 497 | 1.5 | 1.51 | 1.51 | 0.447 | 1.25 | 0.471 | 1.25 | 0.007 | 0.007 |
| 23 | 7 | 20 | 500 | 999 | 1.5 | 1.49 | 1.49 | -0.799 | 2.24 | -0.755 | 2.23 | -0.012 | -0.011 |
| 24 | 7 | 20 | 2500 | 760 | 1.5 | 1.50 | 1.50 | 0.172 | 1.07 | 0.180 | 1.07 | 0.003 | 0.003 |
# visualize RB estimates
p1 <- ggplot() +
stat_summary(
data = rb,
aes(x = condition, y = post_median_rb_est,
group = condition),
fun.data = cust.boxplot,
geom = "boxplot"
) +
geom_point(data = rb_tbl,
aes(x = condition, y = Post_Median_RB_Mean),
color = "black") +
geom_abline(intercept = -10,
slope = 0,
linetype = "dashed") +
geom_abline(intercept = 10,
slope = 0,
linetype = "dashed") +
lims(y = c(-100, 100)) +
coord_flip() +
labs(
title = paste0("Relative Bias for ", param, " posterior median"),
subtitle = "Plot includes RB estimate for each parameter estimate (boxplot) and\n average RB esimate (black dot)",
caption = "Note. Dashed lines represent +/-10% relative bias"
) +
theme_bw() +
theme(panel.grid = element_blank())
p2 <- ggplot() +
stat_summary(
data = rb,
aes(x = condition, y = post_median_bias_est,
group = condition),
fun.data = cust.boxplot,
geom = "boxplot"
) +
geom_point(data = rb_tbl,
aes(x = condition, y = Post_Median_AB),
color = "black") +
geom_abline(intercept = 0,
slope = 0,
linetype = "dashed")+
coord_flip() +
labs(
title = paste0("Average Bias for ", param, " posterior median"),
subtitle = "Plot includes AB estimate for each parameter estimate (boxplot) and\n average AB esimate (black dot)",
caption = "Note. Dashed line represent 0 bias"
) +
theme_bw() +
theme(panel.grid = element_blank())
p1 + p2
Response Time Precision (\(\sigma_{lrt}\))
param = "RT Precision"
rb <- mydata %>%
filter(parameter_group == "sigma_lrt")
# tabular summary of relative bias
rb_tbl <- rb %>%
group_by(condition, N_cat, N_items, N) %>%
summarise(N_converge = n(),
true = mean(true_value),
avg_median_est = mean(post_q50),
avg_mean_est = mean(post_mean),
Post_Median_RB_Mean = mean(post_median_rb_est),
Post_Median_RB_SD = sd(post_median_rb_est),
Post_Mean_RB_Mean = mean(post_mean_rb_est),
Post_Mean_RB_SD = sd(post_mean_rb_est),
Post_Median_AB = mean(post_median_bias_est),
Post_Mean_AB = mean(post_mean_bias_est))`summarise()` has grouped output by 'condition', 'N_cat', 'N_items'. You can override using the `.groups` argument.kable(rb_tbl, format="html", digits=3) %>%
kable_styling(full_width = T) %>%
scroll_box(width="100%",height = "100%")| condition | N_cat | N_items | N | N_converge | true | avg_median_est | avg_mean_est | Post_Median_RB_Mean | Post_Median_RB_SD | Post_Mean_RB_Mean | Post_Mean_RB_SD | Post_Median_AB | Post_Mean_AB |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 1 | 2 | 5 | 500 | 485 | 4 | 4.05 | 4.07 | 1.293 | 8.14 | 1.861 | 8.46 | 0.052 | 0.074 |
| 2 | 2 | 5 | 2500 | 497 | 4 | 4.02 | 4.02 | 0.417 | 3.30 | 0.495 | 3.31 | 0.017 | 0.020 |
| 3 | 2 | 10 | 500 | 998 | 4 | 4.03 | 4.04 | 0.660 | 7.00 | 0.889 | 7.03 | 0.026 | 0.036 |
| 4 | 2 | 10 | 2500 | 1000 | 4 | 4.01 | 4.01 | 0.139 | 3.21 | 0.180 | 3.21 | 0.006 | 0.007 |
| 5 | 2 | 20 | 500 | 2000 | 4 | 4.01 | 4.01 | 0.175 | 6.75 | 0.343 | 6.76 | 0.007 | 0.014 |
| 6 | 2 | 20 | 2500 | 2000 | 4 | 4.00 | 4.00 | 0.081 | 3.07 | 0.111 | 3.07 | 0.003 | 0.004 |
| 7 | 5 | 5 | 500 | 500 | 4 | 4.04 | 4.05 | 0.999 | 7.18 | 1.290 | 7.23 | 0.040 | 0.052 |
| 8 | 5 | 5 | 2500 | 500 | 4 | 4.01 | 4.01 | 0.153 | 3.45 | 0.206 | 3.45 | 0.006 | 0.008 |
| 9 | 5 | 10 | 500 | 1000 | 4 | 4.01 | 4.02 | 0.328 | 7.35 | 0.517 | 7.37 | 0.013 | 0.021 |
| 10 | 5 | 10 | 2500 | 1000 | 4 | 4.00 | 4.00 | 0.076 | 3.13 | 0.116 | 3.13 | 0.003 | 0.005 |
| 11 | 5 | 20 | 500 | 2000 | 4 | 4.01 | 4.02 | 0.312 | 6.60 | 0.468 | 6.61 | 0.012 | 0.019 |
| 12 | 5 | 20 | 2500 | 2000 | 4 | 4.00 | 4.01 | 0.132 | 2.93 | 0.165 | 2.93 | 0.005 | 0.007 |
| 13 | 3 | 5 | 500 | 499 | 4 | 4.04 | 4.05 | 0.962 | 7.19 | 1.309 | 7.28 | 0.038 | 0.052 |
| 14 | 3 | 5 | 2500 | 500 | 4 | 4.02 | 4.02 | 0.507 | 3.46 | 0.565 | 3.46 | 0.020 | 0.023 |
| 15 | 3 | 10 | 500 | 1000 | 4 | 4.01 | 4.02 | 0.268 | 6.74 | 0.463 | 6.76 | 0.011 | 0.019 |
| 16 | 3 | 10 | 2500 | 1000 | 4 | 4.01 | 4.01 | 0.211 | 3.08 | 0.246 | 3.08 | 0.008 | 0.010 |
| 17 | 3 | 20 | 500 | 2000 | 4 | 4.00 | 4.01 | 0.081 | 6.82 | 0.242 | 6.84 | 0.003 | 0.010 |
| 18 | 3 | 20 | 2500 | 2000 | 4 | 4.00 | 4.01 | 0.119 | 2.93 | 0.152 | 2.93 | 0.005 | 0.006 |
| 19 | 7 | 5 | 500 | 500 | 4 | 4.00 | 4.01 | -0.042 | 7.56 | 0.225 | 7.59 | -0.002 | 0.009 |
| 20 | 7 | 5 | 2500 | 250 | 4 | 4.00 | 4.00 | 0.036 | 3.24 | 0.090 | 3.24 | 0.001 | 0.004 |
| 21 | 7 | 10 | 500 | 500 | 4 | 4.01 | 4.02 | 0.247 | 6.94 | 0.435 | 6.95 | 0.010 | 0.017 |
| 22 | 7 | 10 | 2500 | 500 | 4 | 4.00 | 4.00 | 0.092 | 3.13 | 0.136 | 3.12 | 0.004 | 0.005 |
| 23 | 7 | 20 | 500 | 1000 | 4 | 4.00 | 4.00 | -0.031 | 6.52 | 0.128 | 6.53 | -0.001 | 0.005 |
| 24 | 7 | 20 | 2500 | 760 | 4 | 4.00 | 4.00 | 0.037 | 3.13 | 0.065 | 3.13 | 0.001 | 0.003 |
# visualize RB estimates
p1 <- ggplot() +
stat_summary(
data = rb,
aes(x = condition, y = post_median_rb_est,
group = condition),
fun.data = cust.boxplot,
geom = "boxplot"
) +
geom_point(data = rb_tbl,
aes(x = condition, y = Post_Median_RB_Mean),
color = "black") +
geom_abline(intercept = -10,
slope = 0,
linetype = "dashed") +
geom_abline(intercept = 10,
slope = 0,
linetype = "dashed") +
lims(y = c(-100, 100)) +
coord_flip() +
labs(
title = paste0("Relative Bias for ", param, " posterior median"),
subtitle = "Plot includes RB estimate for each parameter estimate (boxplot) and\n average RB esimate (black dot)",
caption = "Note. Dashed lines represent +/-10% relative bias"
) +
theme_bw() +
theme(panel.grid = element_blank())
p2 <- ggplot() +
stat_summary(
data = rb,
aes(x = condition, y = post_median_bias_est,
group = condition),
fun.data = cust.boxplot,
geom = "boxplot"
) +
geom_point(data = rb_tbl,
aes(x = condition, y = Post_Median_AB),
color = "black") +
geom_abline(intercept = 0,
slope = 0,
linetype = "dashed")+
coord_flip() +
labs(
title = paste0("Average Bias for ", param, " posterior median"),
subtitle = "Plot includes AB estimate for each parameter estimate (boxplot) and\n average AB esimate (black dot)",
caption = "Note. Dashed line represent 0 bias"
) +
theme_bw() +
theme(panel.grid = element_blank())
p1 + p2
Response Time Factor Precision (\(\sigma_s\))
param = "Speed LV Precision"
rb <- mydata %>%
filter(parameter_group == "sigma_s")
# tabular summary of relative bias
rb_tbl <- rb %>%
group_by(condition, N_cat, N_items, N) %>%
summarise(N_converge = n(),
true = mean(true_value),
avg_median_est = mean(post_q50),
avg_mean_est = mean(post_mean),
Post_Median_RB_Mean = mean(post_median_rb_est),
Post_Median_RB_SD = sd(post_median_rb_est),
Post_Mean_RB_Mean = mean(post_mean_rb_est),
Post_Mean_RB_SD = sd(post_mean_rb_est),
Post_Median_AB = mean(post_median_bias_est),
Post_Mean_AB = mean(post_mean_bias_est))`summarise()` has grouped output by 'condition', 'N_cat', 'N_items'. You can override using the `.groups` argument.kable(rb_tbl, format="html", digits=3) %>%
kable_styling(full_width = T) %>%
scroll_box(width="100%",height = "100%")| condition | N_cat | N_items | N | N_converge | true | avg_median_est | avg_mean_est | Post_Median_RB_Mean | Post_Median_RB_SD | Post_Mean_RB_Mean | Post_Mean_RB_SD | Post_Median_AB | Post_Mean_AB |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 1 | 2 | 5 | 500 | 99 | 10 | 11.2 | 11.4 | 11.63 | 13.96 | 13.88 | 14.87 | 1.164 | 1.388 |
| 2 | 2 | 5 | 2500 | 97 | 10 | 10.8 | 10.8 | 7.68 | 6.82 | 8.10 | 6.91 | 0.768 | 0.810 |
| 3 | 2 | 10 | 500 | 100 | 10 | 10.6 | 10.7 | 6.25 | 9.73 | 6.86 | 9.91 | 0.625 | 0.686 |
| 4 | 2 | 10 | 2500 | 100 | 10 | 10.7 | 10.7 | 6.77 | 4.41 | 6.92 | 4.42 | 0.677 | 0.693 |
| 5 | 2 | 20 | 500 | 100 | 10 | 10.4 | 10.5 | 4.35 | 9.11 | 4.67 | 9.15 | 0.435 | 0.467 |
| 6 | 2 | 20 | 2500 | 100 | 10 | 10.6 | 10.6 | 5.76 | 3.65 | 5.83 | 3.63 | 0.576 | 0.583 |
| 7 | 5 | 5 | 500 | 100 | 10 | 11.0 | 11.1 | 10.07 | 12.04 | 11.18 | 12.37 | 1.007 | 1.118 |
| 8 | 5 | 5 | 2500 | 100 | 10 | 10.8 | 10.8 | 8.09 | 5.87 | 8.34 | 5.87 | 0.809 | 0.834 |
| 9 | 5 | 10 | 500 | 100 | 10 | 10.7 | 10.8 | 7.25 | 8.18 | 7.71 | 8.23 | 0.725 | 0.771 |
| 10 | 5 | 10 | 2500 | 100 | 10 | 10.7 | 10.7 | 6.86 | 4.12 | 6.95 | 4.15 | 0.686 | 0.695 |
| 11 | 5 | 20 | 500 | 100 | 10 | 10.6 | 10.6 | 6.22 | 7.36 | 6.46 | 7.38 | 0.622 | 0.646 |
| 12 | 5 | 20 | 2500 | 100 | 10 | 10.6 | 10.6 | 5.71 | 2.94 | 5.79 | 2.97 | 0.572 | 0.580 |
| 13 | 3 | 5 | 500 | 100 | 10 | 10.8 | 11.0 | 8.40 | 12.55 | 9.91 | 13.22 | 0.840 | 0.991 |
| 14 | 3 | 5 | 2500 | 100 | 10 | 10.9 | 10.9 | 8.63 | 6.00 | 9.15 | 6.11 | 0.863 | 0.915 |
| 15 | 3 | 10 | 500 | 100 | 10 | 10.7 | 10.7 | 6.76 | 9.38 | 7.31 | 9.51 | 0.676 | 0.731 |
| 16 | 3 | 10 | 2500 | 100 | 10 | 10.8 | 10.8 | 8.05 | 4.77 | 8.17 | 4.74 | 0.805 | 0.817 |
| 17 | 3 | 20 | 500 | 100 | 10 | 10.6 | 10.6 | 6.08 | 7.88 | 6.42 | 7.91 | 0.608 | 0.642 |
| 18 | 3 | 20 | 2500 | 100 | 10 | 10.6 | 10.6 | 6.18 | 3.48 | 6.24 | 3.46 | 0.618 | 0.624 |
| 19 | 7 | 5 | 500 | 100 | 10 | 10.9 | 11.0 | 8.80 | 10.85 | 9.89 | 11.26 | 0.880 | 0.989 |
| 20 | 7 | 5 | 2500 | 50 | 10 | 10.8 | 10.8 | 8.05 | 4.92 | 8.26 | 5.07 | 0.805 | 0.826 |
| 21 | 7 | 10 | 500 | 50 | 10 | 10.5 | 10.6 | 5.45 | 9.35 | 5.93 | 9.48 | 0.545 | 0.593 |
| 22 | 7 | 10 | 2500 | 50 | 10 | 10.6 | 10.6 | 6.34 | 3.62 | 6.44 | 3.68 | 0.634 | 0.644 |
| 23 | 7 | 20 | 500 | 50 | 10 | 10.8 | 10.8 | 7.58 | 7.40 | 7.88 | 7.46 | 0.758 | 0.788 |
| 24 | 7 | 20 | 2500 | 38 | 10 | 10.6 | 10.6 | 5.89 | 3.39 | 5.97 | 3.42 | 0.589 | 0.597 |
# visualize RB estimates
p1 <- ggplot() +
stat_summary(
data = rb,
aes(x = condition, y = post_median_rb_est,
group = condition),
fun.data = cust.boxplot,
geom = "boxplot"
) +
geom_point(data = rb_tbl,
aes(x = condition, y = Post_Median_RB_Mean),
color = "black") +
geom_abline(intercept = -10,
slope = 0,
linetype = "dashed") +
geom_abline(intercept = 10,
slope = 0,
linetype = "dashed") +
lims(y = c(-100, 100)) +
coord_flip() +
labs(
title = paste0("Relative Bias for ", param, " posterior median"),
subtitle = "Plot includes RB estimate for each parameter estimate (boxplot) and\n average RB esimate (black dot)",
caption = "Note. Dashed lines represent +/-10% relative bias"
) +
theme_bw() +
theme(panel.grid = element_blank())
p2 <- ggplot() +
stat_summary(
data = rb,
aes(x = condition, y = post_median_bias_est,
group = condition),
fun.data = cust.boxplot,
geom = "boxplot"
) +
geom_point(data = rb_tbl,
aes(x = condition, y = Post_Median_AB),
color = "black") +
geom_abline(intercept = 0,
slope = 0,
linetype = "dashed")+
coord_flip() +
labs(
title = paste0("Average Bias for ", param, " posterior median"),
subtitle = "Plot includes AB estimate for each parameter estimate (boxplot) and\n average AB esimate (black dot)",
caption = "Note. Dashed line represent 0 bias"
) +
theme_bw() +
theme(panel.grid = element_blank())
p1 + p2
Factor Covariance (\(\sigma_{st}\))
param = "Latent Covariance"
rb <- mydata %>%
filter(parameter_group == "sigma_st")
# tabular summary of relative bias
rb_tbl <- rb %>%
group_by(condition, N_cat, N_items, N) %>%
summarise(N_converge = n(),
true = mean(true_value),
avg_median_est = mean(post_q50),
avg_mean_est = mean(post_mean),
Post_Median_RB_Mean = mean(post_median_rb_est),
Post_Median_RB_SD = sd(post_median_rb_est),
Post_Mean_RB_Mean = mean(post_mean_rb_est),
Post_Mean_RB_SD = sd(post_mean_rb_est),
Post_Median_AB = mean(post_median_bias_est),
Post_Mean_AB = mean(post_mean_bias_est))`summarise()` has grouped output by 'condition', 'N_cat', 'N_items'. You can override using the `.groups` argument.kable(rb_tbl, format="html", digits=3) %>%
kable_styling(full_width = T) %>%
scroll_box(width="100%",height = "100%")| condition | N_cat | N_items | N | N_converge | true | avg_median_est | avg_mean_est | Post_Median_RB_Mean | Post_Median_RB_SD | Post_Mean_RB_Mean | Post_Mean_RB_SD | Post_Median_AB | Post_Mean_AB |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 1 | 2 | 5 | 500 | 95 | -0.073 | -0.066 | -0.065 | -9.696 | 53.0 | -10.159 | 52.7 | 0.007 | 0.007 |
| 2 | 2 | 5 | 2500 | 98 | -0.073 | -0.067 | -0.067 | -7.757 | 24.1 | -7.722 | 24.1 | 0.006 | 0.006 |
| 3 | 2 | 10 | 500 | 100 | -0.073 | -0.068 | -0.068 | -6.543 | 40.5 | -6.705 | 40.4 | 0.005 | 0.005 |
| 4 | 2 | 10 | 2500 | 100 | -0.073 | -0.071 | -0.071 | -2.674 | 15.7 | -2.682 | 15.6 | 0.002 | 0.002 |
| 5 | 2 | 20 | 500 | 100 | -0.073 | -0.070 | -0.070 | -4.398 | 29.1 | -4.436 | 29.0 | 0.003 | 0.003 |
| 6 | 2 | 20 | 2500 | 100 | -0.073 | -0.068 | -0.068 | -6.567 | 12.3 | -6.601 | 12.3 | 0.005 | 0.005 |
| 7 | 5 | 5 | 500 | 98 | 0.073 | 0.068 | 0.068 | -6.782 | 37.8 | -6.667 | 37.7 | -0.005 | -0.005 |
| 8 | 5 | 5 | 2500 | 100 | 0.073 | 0.071 | 0.071 | -1.898 | 21.0 | -1.939 | 21.0 | -0.001 | -0.001 |
| 9 | 5 | 10 | 500 | 100 | 0.073 | 0.068 | 0.068 | -6.132 | 36.7 | -6.097 | 36.6 | -0.004 | -0.004 |
| 10 | 5 | 10 | 2500 | 100 | 0.073 | 0.070 | 0.070 | -3.685 | 13.0 | -3.671 | 13.0 | -0.003 | -0.003 |
| 11 | 5 | 20 | 500 | 100 | 0.073 | 0.069 | 0.069 | -4.966 | 26.8 | -4.769 | 26.9 | -0.004 | -0.003 |
| 12 | 5 | 20 | 2500 | 100 | 0.073 | 0.071 | 0.071 | -1.868 | 12.0 | -1.864 | 12.0 | -0.001 | -0.001 |
| 13 | 3 | 5 | 500 | 100 | 0.073 | 0.064 | 0.064 | -12.052 | 45.4 | -11.991 | 45.5 | -0.009 | -0.009 |
| 14 | 3 | 5 | 2500 | 100 | 0.073 | 0.073 | 0.073 | 0.547 | 23.4 | 0.596 | 23.3 | 0.000 | 0.000 |
| 15 | 3 | 10 | 500 | 100 | 0.073 | 0.073 | 0.073 | 0.225 | 33.8 | 0.154 | 33.7 | 0.000 | 0.000 |
| 16 | 3 | 10 | 2500 | 100 | 0.073 | 0.073 | 0.073 | 0.384 | 16.2 | 0.374 | 16.2 | 0.000 | 0.000 |
| 17 | 3 | 20 | 500 | 100 | 0.073 | 0.079 | 0.079 | 9.010 | 27.5 | 8.971 | 27.5 | 0.007 | 0.007 |
| 18 | 3 | 20 | 2500 | 100 | 0.073 | 0.075 | 0.075 | 2.506 | 12.1 | 2.481 | 12.1 | 0.002 | 0.002 |
| 19 | 7 | 5 | 500 | 100 | 0.073 | 0.070 | 0.070 | -3.895 | 37.4 | -3.890 | 37.3 | -0.003 | -0.003 |
| 20 | 7 | 5 | 2500 | 50 | 0.073 | 0.075 | 0.075 | 3.010 | 18.5 | 2.993 | 18.5 | 0.002 | 0.002 |
| 21 | 7 | 10 | 500 | 50 | 0.073 | 0.075 | 0.076 | 3.827 | 29.8 | 3.862 | 29.8 | 0.003 | 0.003 |
| 22 | 7 | 10 | 2500 | 50 | 0.073 | 0.073 | 0.073 | 0.952 | 12.4 | 0.966 | 12.4 | 0.001 | 0.001 |
| 23 | 7 | 20 | 500 | 50 | 0.073 | 0.073 | 0.073 | -0.113 | 21.7 | 0.074 | 21.7 | 0.000 | 0.000 |
| 24 | 7 | 20 | 2500 | 38 | 0.073 | 0.073 | 0.073 | 1.068 | 11.7 | 1.071 | 11.8 | 0.001 | 0.001 |
# visualize RB estimates
p1 <- ggplot() +
stat_summary(
data = rb,
aes(x = condition, y = post_median_rb_est,
group = condition),
fun.data = cust.boxplot,
geom = "boxplot"
) +
geom_point(data = rb_tbl,
aes(x = condition, y = Post_Median_RB_Mean),
color = "black") +
geom_abline(intercept = -10,
slope = 0,
linetype = "dashed") +
geom_abline(intercept = 10,
slope = 0,
linetype = "dashed") +
lims(y = c(-100, 100)) +
coord_flip() +
labs(
title = paste0("Relative Bias for ", param, " posterior median"),
subtitle = "Plot includes RB estimate for each parameter estimate (boxplot) and\n average RB esimate (black dot)",
caption = "Note. Dashed lines represent +/-10% relative bias"
) +
theme_bw() +
theme(panel.grid = element_blank())
p2 <- ggplot() +
stat_summary(
data = rb,
aes(x = condition, y = post_median_bias_est,
group = condition),
fun.data = cust.boxplot,
geom = "boxplot"
) +
geom_point(data = rb_tbl,
aes(x = condition, y = Post_Median_AB),
color = "black") +
geom_abline(intercept = 0,
slope = 0,
linetype = "dashed")+
coord_flip() +
labs(
title = paste0("Average Bias for ", param, " posterior median"),
subtitle = "Plot includes AB estimate for each parameter estimate (boxplot) and\n average AB esimate (black dot)",
caption = "Note. Dashed line represent 0 bias"
) +
theme_bw() +
theme(panel.grid = element_blank())
p1 + p2Warning: Removed 11 rows containing non-finite values (stat_summary).
PID Relationship (\(\rho\))
param = "PID Relationship"
rb <- mydata %>%
filter(parameter_group == "rho")
# tabular summary of relative bias
rb_tbl <- rb %>%
group_by(condition, N_cat, N_items, N) %>%
summarise(N_converge = n(),
true = mean(true_value),
avg_median_est = mean(post_q50),
avg_mean_est = mean(post_mean),
Post_Median_RB_Mean = mean(post_median_rb_est),
Post_Median_RB_SD = sd(post_median_rb_est),
Post_Mean_RB_Mean = mean(post_mean_rb_est),
Post_Mean_RB_SD = sd(post_mean_rb_est),
Post_Median_AB = mean(post_median_bias_est),
Post_Mean_AB = mean(post_mean_bias_est))`summarise()` has grouped output by 'condition', 'N_cat', 'N_items'. You can override using the `.groups` argument.kable(rb_tbl, format="html", digits=3) %>%
kable_styling(full_width = T) %>%
scroll_box(width="100%",height = "100%")| condition | N_cat | N_items | N | N_converge | true | avg_median_est | avg_mean_est | Post_Median_RB_Mean | Post_Median_RB_SD | Post_Mean_RB_Mean | Post_Mean_RB_SD | Post_Median_AB | Post_Mean_AB |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 1 | 2 | 5 | 500 | 82 | 0.1 | 0.133 | 0.145 | 33.04 | 56.1 | 45.25 | 56.9 | 0.033 | 0.045 |
| 2 | 2 | 5 | 2500 | 80 | 0.1 | 0.137 | 0.139 | 37.40 | 41.2 | 38.83 | 41.2 | 0.037 | 0.039 |
| 3 | 2 | 10 | 500 | 85 | 0.1 | 0.099 | 0.102 | -1.20 | 39.6 | 2.24 | 38.6 | -0.001 | 0.002 |
| 4 | 2 | 10 | 2500 | 97 | 0.1 | 0.144 | 0.144 | 43.85 | 24.9 | 44.37 | 24.9 | 0.044 | 0.044 |
| 5 | 2 | 20 | 500 | 97 | 0.1 | 0.093 | 0.094 | -7.13 | 25.0 | -5.89 | 24.9 | -0.007 | -0.006 |
| 6 | 2 | 20 | 2500 | 100 | 0.1 | 0.136 | 0.137 | 36.33 | 16.2 | 36.65 | 16.2 | 0.036 | 0.037 |
| 7 | 5 | 5 | 500 | 91 | 0.1 | 0.136 | 0.141 | 35.60 | 61.5 | 41.07 | 59.6 | 0.036 | 0.041 |
| 8 | 5 | 5 | 2500 | 97 | 0.1 | 0.166 | 0.166 | 65.98 | 42.3 | 66.22 | 42.2 | 0.066 | 0.066 |
| 9 | 5 | 10 | 500 | 94 | 0.1 | 0.121 | 0.123 | 21.37 | 40.0 | 23.12 | 39.5 | 0.021 | 0.023 |
| 10 | 5 | 10 | 2500 | 100 | 0.1 | 0.146 | 0.147 | 46.40 | 22.2 | 46.55 | 22.1 | 0.046 | 0.047 |
| 11 | 5 | 20 | 500 | 98 | 0.1 | 0.110 | 0.111 | 10.46 | 31.6 | 11.04 | 31.4 | 0.010 | 0.011 |
| 12 | 5 | 20 | 2500 | 100 | 0.1 | 0.141 | 0.141 | 40.98 | 13.8 | 41.01 | 13.9 | 0.041 | 0.041 |
| 13 | 3 | 5 | 500 | 97 | 0.1 | 0.136 | 0.143 | 36.34 | 67.0 | 42.98 | 65.2 | 0.036 | 0.043 |
| 14 | 3 | 5 | 2500 | 98 | 0.1 | 0.164 | 0.165 | 63.92 | 39.3 | 64.79 | 39.4 | 0.064 | 0.065 |
| 15 | 3 | 10 | 500 | 99 | 0.1 | 0.126 | 0.129 | 26.41 | 44.2 | 28.59 | 43.6 | 0.026 | 0.029 |
| 16 | 3 | 10 | 2500 | 100 | 0.1 | 0.151 | 0.151 | 51.16 | 26.7 | 51.46 | 26.7 | 0.051 | 0.051 |
| 17 | 3 | 20 | 500 | 99 | 0.1 | 0.108 | 0.109 | 8.04 | 30.4 | 8.81 | 30.1 | 0.008 | 0.009 |
| 18 | 3 | 20 | 2500 | 100 | 0.1 | 0.137 | 0.137 | 36.93 | 16.7 | 37.03 | 16.8 | 0.037 | 0.037 |
| 19 | 7 | 5 | 500 | 87 | 0.1 | 0.121 | 0.126 | 20.96 | 56.2 | 25.68 | 55.1 | 0.021 | 0.026 |
| 20 | 7 | 5 | 2500 | 45 | 0.1 | 0.153 | 0.154 | 53.33 | 31.3 | 53.77 | 31.0 | 0.053 | 0.054 |
| 21 | 7 | 10 | 500 | 49 | 0.1 | 0.119 | 0.121 | 19.35 | 39.9 | 20.80 | 39.1 | 0.019 | 0.021 |
| 22 | 7 | 10 | 2500 | 49 | 0.1 | 0.141 | 0.142 | 41.47 | 18.9 | 41.63 | 18.9 | 0.041 | 0.042 |
| 23 | 7 | 20 | 500 | 50 | 0.1 | 0.110 | 0.111 | 9.96 | 28.2 | 10.53 | 28.0 | 0.010 | 0.011 |
| 24 | 7 | 20 | 2500 | 38 | 0.1 | 0.131 | 0.131 | 30.84 | 15.0 | 31.03 | 15.3 | 0.031 | 0.031 |
# visualize RB estimates
p1 <- ggplot() +
stat_summary(
data = rb,
aes(x = condition, y = post_median_rb_est,
group = condition),
fun.data = cust.boxplot,
geom = "boxplot"
) +
geom_point(data = rb_tbl,
aes(x = condition, y = Post_Median_RB_Mean),
color = "black") +
geom_abline(intercept = -10,
slope = 0,
linetype = "dashed") +
geom_abline(intercept = 10,
slope = 0,
linetype = "dashed") +
lims(y = c(-100, 100)) +
coord_flip() +
labs(
title = paste0("Relative Bias for ", param, " posterior median"),
subtitle = "Plot includes RB estimate for each parameter estimate (boxplot) and\n average RB esimate (black dot)",
caption = "Note. Dashed lines represent +/-10% relative bias"
) +
theme_bw() +
theme(panel.grid = element_blank())
p2 <- ggplot() +
stat_summary(
data = rb,
aes(x = condition, y = post_median_bias_est,
group = condition),
fun.data = cust.boxplot,
geom = "boxplot"
) +
geom_point(data = rb_tbl,
aes(x = condition, y = Post_Median_AB),
color = "black") +
geom_abline(intercept = 0,
slope = 0,
linetype = "dashed")+
coord_flip() +
labs(
title = paste0("Average Bias for ", param, " posterior median"),
subtitle = "Plot includes AB estimate for each parameter estimate (boxplot) and\n average AB esimate (black dot)",
caption = "Note. Dashed line represent 0 bias"
) +
theme_bw() +
theme(panel.grid = element_blank())
p1 + p2Warning: Removed 103 rows containing non-finite values (stat_summary).
Factor Reliability (\(\omega\))
param = "RELIABILITY"
rb <- mydata %>%
filter(parameter_group == "omega")
# tabular summary of relative bias
rb_tbl <- rb %>%
group_by(condition, N_cat, N_items, N) %>%
summarise(N_converge = n(),
true = mean(true_value),
avg_median_est = mean(post_q50),
avg_mean_est = mean(post_mean),
Post_Median_RB_Mean = mean(post_median_rb_est),
Post_Median_RB_SD = sd(post_median_rb_est),
Post_Mean_RB_Mean = mean(post_mean_rb_est),
Post_Mean_RB_SD = sd(post_mean_rb_est),
Post_Median_AB = mean(post_median_bias_est),
Post_Mean_AB = mean(post_mean_bias_est))`summarise()` has grouped output by 'condition', 'N_cat', 'N_items'. You can override using the `.groups` argument.kable(rb_tbl, format="html", digits=3) %>%
kable_styling(full_width = T) %>%
scroll_box(width="100%",height = "100%")| condition | N_cat | N_items | N | N_converge | true | avg_median_est | avg_mean_est | Post_Median_RB_Mean | Post_Median_RB_SD | Post_Mean_RB_Mean | Post_Mean_RB_SD | Post_Median_AB | Post_Mean_AB |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 1 | 2 | 5 | 500 | 63 | 0.802 | 0.770 | 0.756 | -3.943 | 8.237 | -5.68 | 8.731 | -0.032 | -0.046 |
| 2 | 2 | 5 | 2500 | 78 | 0.802 | 0.767 | 0.765 | -4.310 | 3.899 | -4.65 | 3.972 | -0.035 | -0.037 |
| 3 | 2 | 10 | 500 | 88 | 0.890 | 0.876 | 0.873 | -1.532 | 2.557 | -1.88 | 2.667 | -0.014 | -0.017 |
| 4 | 2 | 10 | 2500 | 97 | 0.890 | 0.860 | 0.860 | -3.341 | 1.473 | -3.41 | 1.482 | -0.030 | -0.030 |
| 5 | 2 | 20 | 500 | 96 | 0.942 | 0.933 | 0.932 | -0.926 | 0.826 | -1.00 | 0.845 | -0.009 | -0.009 |
| 6 | 2 | 20 | 2500 | 100 | 0.942 | 0.924 | 0.924 | -1.923 | 0.412 | -1.94 | 0.413 | -0.018 | -0.018 |
| 7 | 5 | 5 | 500 | 87 | 0.802 | 0.766 | 0.763 | -4.439 | 4.466 | -4.85 | 4.594 | -0.036 | -0.039 |
| 8 | 5 | 5 | 2500 | 99 | 0.802 | 0.749 | 0.749 | -6.566 | 2.077 | -6.66 | 2.088 | -0.053 | -0.053 |
| 9 | 5 | 10 | 500 | 95 | 0.890 | 0.862 | 0.861 | -3.167 | 1.832 | -3.27 | 1.850 | -0.028 | -0.029 |
| 10 | 5 | 10 | 2500 | 97 | 0.890 | 0.856 | 0.856 | -3.848 | 0.753 | -3.86 | 0.749 | -0.034 | -0.034 |
| 11 | 5 | 20 | 500 | 98 | 0.942 | 0.926 | 0.926 | -1.691 | 0.791 | -1.72 | 0.800 | -0.016 | -0.016 |
| 12 | 5 | 20 | 2500 | 99 | 0.942 | 0.922 | 0.922 | -2.080 | 0.301 | -2.09 | 0.303 | -0.020 | -0.020 |
| 13 | 3 | 5 | 500 | 89 | 0.802 | 0.772 | 0.767 | -3.686 | 5.148 | -4.33 | 5.392 | -0.030 | -0.035 |
| 14 | 3 | 5 | 2500 | 100 | 0.802 | 0.747 | 0.746 | -6.822 | 2.694 | -6.96 | 2.706 | -0.055 | -0.056 |
| 15 | 3 | 10 | 500 | 100 | 0.890 | 0.862 | 0.861 | -3.160 | 2.175 | -3.31 | 2.216 | -0.028 | -0.029 |
| 16 | 3 | 10 | 2500 | 100 | 0.890 | 0.853 | 0.852 | -4.211 | 0.967 | -4.25 | 0.964 | -0.037 | -0.038 |
| 17 | 3 | 20 | 500 | 100 | 0.942 | 0.926 | 0.926 | -1.670 | 0.840 | -1.71 | 0.838 | -0.016 | -0.016 |
| 18 | 3 | 20 | 2500 | 99 | 0.942 | 0.920 | 0.920 | -2.352 | 0.434 | -2.36 | 0.435 | -0.022 | -0.022 |
| 19 | 7 | 5 | 500 | 81 | 0.802 | 0.776 | 0.774 | -3.182 | 4.796 | -3.51 | 4.938 | -0.026 | -0.028 |
| 20 | 7 | 5 | 2500 | 43 | 0.802 | 0.753 | 0.752 | -6.139 | 1.879 | -6.21 | 1.893 | -0.049 | -0.050 |
| 21 | 7 | 10 | 500 | 46 | 0.890 | 0.867 | 0.866 | -2.582 | 1.527 | -2.68 | 1.538 | -0.023 | -0.024 |
| 22 | 7 | 10 | 2500 | 49 | 0.890 | 0.858 | 0.858 | -3.579 | 0.765 | -3.60 | 0.761 | -0.032 | -0.032 |
| 23 | 7 | 20 | 500 | 49 | 0.942 | 0.928 | 0.928 | -1.504 | 0.623 | -1.52 | 0.625 | -0.014 | -0.014 |
| 24 | 7 | 20 | 2500 | 38 | 0.942 | 0.923 | 0.923 | -1.972 | 0.319 | -1.98 | 0.320 | -0.019 | -0.019 |
# visualize RB estimates
p1 <- ggplot() +
stat_summary(
data = rb,
aes(x = condition, y = post_median_rb_est,
group = condition),
fun.data = cust.boxplot,
geom = "boxplot"
) +
geom_point(data = rb_tbl,
aes(x = condition, y = Post_Median_RB_Mean),
color = "black") +
geom_abline(intercept = -10,
slope = 0,
linetype = "dashed") +
geom_abline(intercept = 10,
slope = 0,
linetype = "dashed") +
lims(y = c(-100, 100)) +
coord_flip() +
labs(
title = paste0("Relative Bias for ", param, " posterior median"),
subtitle = "Plot includes RB estimate for each parameter estimate (boxplot) and\n average RB esimate (black dot)",
caption = "Note. Dashed lines represent +/-10% relative bias"
) +
theme_bw() +
theme(panel.grid = element_blank())
p2 <- ggplot() +
stat_summary(
data = rb,
aes(x = condition, y = post_median_bias_est,
group = condition),
fun.data = cust.boxplot,
geom = "boxplot"
) +
geom_point(data = rb_tbl,
aes(x = condition, y = Post_Median_AB),
color = "black") +
geom_abline(intercept = 0,
slope = 0,
linetype = "dashed")+
coord_flip() +
labs(
title = paste0("Average Bias for ", param, " posterior median"),
subtitle = "Plot includes AB estimate for each parameter estimate (boxplot) and\n average AB esimate (black dot)",
caption = "Note. Dashed line represent 0 bias"
) +
theme_bw() +
theme(panel.grid = element_blank())
p1 + p2
Effect of Simulated Conditions
Factor Loadings (\(\lambda\))
rb <- mydata %>%
filter(parameter_group == "lambda") %>%
group_by(condition, iter, N, N_cat, N_items) %>%
summarise(
rb_est = mean(post_median_bias_est)
)`summarise()` has grouped output by 'condition', 'iter', 'N', 'N_cat'. You can override using the `.groups` argument.## ANOVA on Relative Bias values
anova_assumptions_check(
dat = rb, outcome = 'rb_est',
factors = c('N_cat', 'N_items', 'N'),
model = as.formula('rb_est ~ N_cat*N_items*N'))
=============================
Tests and Plots of Normality:
Shapiro-Wilks Test of Normality of Residuals:
Shapiro-Wilk normality test
data: res
W = 0.9, p-value <0.0000000000000002
K-S Test for Normality of Residuals:Warning in ks.test(aov.out$residuals, "pnorm", alternative = "two.sided"): ties
should not be present for the Kolmogorov-Smirnov test
One-sample Kolmogorov-Smirnov test
data: aov.out$residuals
D = 0.4, p-value <0.0000000000000002
alternative hypothesis: two-sided`stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
`stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
`stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
=============================
Tests of Homogeneity of Variance
Levenes Test: N_cat
Levene's Test for Homogeneity of Variance (center = "mean")
Df F value Pr(>F)
group 3 65.7 <0.0000000000000002 ***
2131
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Levenes Test: N_items
Levene's Test for Homogeneity of Variance (center = "mean")
Df F value Pr(>F)
group 2 203 <0.0000000000000002 ***
2132
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Levenes Test: N
Levene's Test for Homogeneity of Variance (center = "mean")
Df F value Pr(>F)
group 1 296 <0.0000000000000002 ***
2133
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1fit <- summary(aov(rb_est ~ N_cat*N_items*N, data=rb))
fit Df Sum Sq Mean Sq F value Pr(>F)
N_cat 3 0.22 0.0737 12.19 0.00000006560313220 ***
N_items 2 0.44 0.2216 36.65 0.00000000000000023 ***
N 1 0.01 0.0090 1.49 0.22191
N_cat:N_items 6 0.56 0.0937 15.50 < 0.0000000000000002 ***
N_cat:N 3 0.12 0.0391 6.47 0.00024 ***
N_items:N 2 0.20 0.1018 16.85 0.00000005519239311 ***
N_cat:N_items:N 6 0.18 0.0294 4.86 0.00006074631845613 ***
Residuals 2111 12.76 0.0060
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1eta_est <- (fit[[1]]$`Sum Sq`/sum(fit[[1]]$`Sum Sq`))[1:7]
cbind(omega2(fit),p_omega2(fit), eta_est) omega^2 partial-omega^2 eta_est
N_cat 0.0140 0.0155 0.015255
N_items 0.0297 0.0323 0.030573
N 0.0002 0.0002 0.000623
N_cat:N_items 0.0363 0.0392 0.038795
N_cat:N 0.0068 0.0076 0.008091
N_items:N 0.0132 0.0146 0.014052
N_cat:N_items:N 0.0097 0.0107 0.012168saved_omega[1,] <- omega2(fit)
saved_eta[1,] <- eta_estItem Thresholds (\(\tau\))
rb <- mydata %>%
filter(parameter_group == "tau") %>%
group_by(condition, iter, N, N_cat, N_items) %>%
summarise(
rb_est = mean(post_median_bias_est)
)`summarise()` has grouped output by 'condition', 'iter', 'N', 'N_cat'. You can override using the `.groups` argument.## ANOVA on Relative Bias values
anova_assumptions_check(
dat = rb, outcome = 'rb_est',
factors = c('N_cat', 'N_items', 'N'),
model = as.formula('rb_est ~ N_cat*N_items*N'))
=============================
Tests and Plots of Normality:
Shapiro-Wilks Test of Normality of Residuals:
Shapiro-Wilk normality test
data: res
W = 1, p-value <0.0000000000000002
K-S Test for Normality of Residuals:Warning in ks.test(aov.out$residuals, "pnorm", alternative = "two.sided"): ties
should not be present for the Kolmogorov-Smirnov test
One-sample Kolmogorov-Smirnov test
data: aov.out$residuals
D = 0.4, p-value <0.0000000000000002
alternative hypothesis: two-sided`stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
`stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
`stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
=============================
Tests of Homogeneity of Variance
Levenes Test: N_cat
Levene's Test for Homogeneity of Variance (center = "mean")
Df F value Pr(>F)
group 3 7.41 0.000062 ***
2134
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Levenes Test: N_items
Levene's Test for Homogeneity of Variance (center = "mean")
Df F value Pr(>F)
group 2 18.1 0.000000016 ***
2135
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Levenes Test: N
Levene's Test for Homogeneity of Variance (center = "mean")
Df F value Pr(>F)
group 1 32.3 0.000000015 ***
2136
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1fit <- summary(aov(rb_est ~ N_cat*N_items*N, data=rb))
fit Df Sum Sq Mean Sq F value Pr(>F)
N_cat 3 5.59 1.862 939.17 < 0.0000000000000002 ***
N_items 2 0.00 0.000 0.11 0.896
N 1 0.06 0.058 29.38 0.000000066 ***
N_cat:N_items 6 0.03 0.005 2.65 0.015 *
N_cat:N 3 0.05 0.017 8.52 0.000012707 ***
N_items:N 2 0.00 0.001 0.37 0.692
N_cat:N_items:N 6 0.01 0.002 0.89 0.501
Residuals 2114 4.19 0.002
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1eta_est <- (fit[[1]]$`Sum Sq`/sum(fit[[1]]$`Sum Sq`))[1:7]
cbind(omega2(fit),p_omega2(fit), eta_est) omega^2 partial-omega^2 eta_est
N_cat 0.5618 0.5683 0.5625320
N_items -0.0004 -0.0008 0.0000437
N 0.0057 0.0131 0.0058656
N_cat:N_items 0.0020 0.0046 0.0031735
N_cat:N 0.0045 0.0104 0.0051015
N_items:N -0.0003 -0.0006 0.0001468
N_cat:N_items:N -0.0001 -0.0003 0.0010667saved_omega[2,] <- omega2(fit)
saved_eta[2,] <- eta_estLatent Response Variance (\(\theta\))
rb <- mydata %>%
filter(parameter_group == "theta") %>%
group_by(condition, iter, N, N_cat, N_items) %>%
summarise(
rb_est = mean(post_median_bias_est)
)`summarise()` has grouped output by 'condition', 'iter', 'N', 'N_cat'. You can override using the `.groups` argument.## ANOVA on Relative Bias values
anova_assumptions_check(
dat = rb, outcome = 'rb_est',
factors = c('N_cat', 'N_items', 'N'),
model = as.formula('rb_est ~ N_cat*N_items*N'))
=============================
Tests and Plots of Normality:
Shapiro-Wilks Test of Normality of Residuals:
Shapiro-Wilk normality test
data: res
W = 0.8, p-value <0.0000000000000002
K-S Test for Normality of Residuals:Warning in ks.test(aov.out$residuals, "pnorm", alternative = "two.sided"): ties
should not be present for the Kolmogorov-Smirnov test
One-sample Kolmogorov-Smirnov test
data: aov.out$residuals
D = 0.4, p-value <0.0000000000000002
alternative hypothesis: two-sided`stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
`stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
`stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
=============================
Tests of Homogeneity of Variance
Levenes Test: N_cat
Levene's Test for Homogeneity of Variance (center = "mean")
Df F value Pr(>F)
group 3 55 <0.0000000000000002 ***
2129
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Levenes Test: N_items
Levene's Test for Homogeneity of Variance (center = "mean")
Df F value Pr(>F)
group 2 112 <0.0000000000000002 ***
2130
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Levenes Test: N
Levene's Test for Homogeneity of Variance (center = "mean")
Df F value Pr(>F)
group 1 250 <0.0000000000000002 ***
2131
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1fit <- summary(aov(rb_est ~ N_cat*N_items*N, data=rb))
eta_est <- (fit[[1]]$`Sum Sq`/sum(fit[[1]]$`Sum Sq`))[1:7]
cbind(omega2(fit),p_omega2(fit), eta_est) omega^2 partial-omega^2 eta_est
N_cat 0.0049 0.0051 0.00620
N_items 0.0018 0.0019 0.00272
N 0.0342 0.0348 0.03462
N_cat:N_items 0.0079 0.0082 0.01055
N_cat:N 0.0013 0.0014 0.00264
N_items:N 0.0013 0.0014 0.00218
N_cat:N_items:N 0.0012 0.0013 0.00387saved_omega[3,] <- omega2(fit)
saved_eta[3,] <- eta_estResponse Time Intercepts (\(\beta_{lrt}\))
rb <- mydata %>%
filter(parameter_group == "beta_lrt") %>%
group_by(condition, iter, N, N_cat, N_items) %>%
summarise(
rb_est = mean(post_median_bias_est)
)`summarise()` has grouped output by 'condition', 'iter', 'N', 'N_cat'. You can override using the `.groups` argument.## ANOVA on Relative Bias values
anova_assumptions_check(
dat = rb, outcome = 'rb_est',
factors = c('N_cat', 'N_items', 'N'),
model = as.formula('rb_est ~ N_cat*N_items*N'))
=============================
Tests and Plots of Normality:
Shapiro-Wilks Test of Normality of Residuals:
Shapiro-Wilk normality test
data: res
W = 1, p-value = 0.0000000000000003
K-S Test for Normality of Residuals:Warning in ks.test(aov.out$residuals, "pnorm", alternative = "two.sided"): ties
should not be present for the Kolmogorov-Smirnov test
One-sample Kolmogorov-Smirnov test
data: aov.out$residuals
D = 0.5, p-value <0.0000000000000002
alternative hypothesis: two-sided`stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
`stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
`stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
=============================
Tests of Homogeneity of Variance
Levenes Test: N_cat
Levene's Test for Homogeneity of Variance (center = "mean")
Df F value Pr(>F)
group 3 0.67 0.57
2134
Levenes Test: N_items
Levene's Test for Homogeneity of Variance (center = "mean")
Df F value Pr(>F)
group 2 83.7 <0.0000000000000002 ***
2135
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Levenes Test: N
Levene's Test for Homogeneity of Variance (center = "mean")
Df F value Pr(>F)
group 1 188 <0.0000000000000002 ***
2136
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1fit <- summary(aov(rb_est ~ N_cat*N_items*N, data=rb))
fit Df Sum Sq Mean Sq F value Pr(>F)
N_cat 3 0.019 0.0063 8.16 0.000021 ***
N_items 2 0.097 0.0483 62.85 < 0.0000000000000002 ***
N 1 0.121 0.1213 157.92 < 0.0000000000000002 ***
N_cat:N_items 6 0.005 0.0008 1.05 0.392
N_cat:N 3 0.004 0.0012 1.57 0.194
N_items:N 2 0.002 0.0011 1.42 0.242
N_cat:N_items:N 6 0.009 0.0015 1.90 0.077 .
Residuals 2114 1.624 0.0008
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1eta_est <- (fit[[1]]$`Sum Sq`/sum(fit[[1]]$`Sum Sq`))[1:7]
cbind(omega2(fit),p_omega2(fit), eta_est) omega^2 partial-omega^2 eta_est
N_cat 0.0088 0.0099 0.01000
N_items 0.0505 0.0547 0.05136
N 0.0641 0.0684 0.06453
N_cat:N_items 0.0001 0.0001 0.00257
N_cat:N 0.0007 0.0008 0.00193
N_items:N 0.0003 0.0004 0.00116
N_cat:N_items:N 0.0022 0.0025 0.00466saved_omega[4,] <- omega2(fit)
saved_eta[4,] <- eta_estResponse Time Precision (\(\sigma_{lrt}\))
rb <- mydata %>%
filter(parameter_group == "sigma_lrt") %>%
group_by(condition, iter, N, N_cat, N_items) %>%
summarise(
rb_est = mean(post_median_bias_est)
)`summarise()` has grouped output by 'condition', 'iter', 'N', 'N_cat'. You can override using the `.groups` argument.## ANOVA on Relative Bias values
anova_assumptions_check(
dat = rb, outcome = 'rb_est',
factors = c('N_cat', 'N_items', 'N'),
model = as.formula('rb_est ~ N_cat*N_items*N'))
=============================
Tests and Plots of Normality:
Shapiro-Wilks Test of Normality of Residuals:
Shapiro-Wilk normality test
data: res
W = 1, p-value <0.0000000000000002
K-S Test for Normality of Residuals:Warning in ks.test(aov.out$residuals, "pnorm", alternative = "two.sided"): ties
should not be present for the Kolmogorov-Smirnov test
One-sample Kolmogorov-Smirnov test
data: aov.out$residuals
D = 0.4, p-value <0.0000000000000002
alternative hypothesis: two-sided`stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
`stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
`stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
=============================
Tests of Homogeneity of Variance
Levenes Test: N_cat
Levene's Test for Homogeneity of Variance (center = "mean")
Df F value Pr(>F)
group 3 5.06 0.0017 **
2134
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Levenes Test: N_items
Levene's Test for Homogeneity of Variance (center = "mean")
Df F value Pr(>F)
group 2 129 <0.0000000000000002 ***
2135
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Levenes Test: N
Levene's Test for Homogeneity of Variance (center = "mean")
Df F value Pr(>F)
group 1 361 <0.0000000000000002 ***
2136
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1fit <- summary(aov(rb_est ~ N_cat*N_items*N, data=rb))
fit Df Sum Sq Mean Sq F value Pr(>F)
N_cat 3 0.06 0.0206 3.37 0.01781 *
N_items 2 0.14 0.0676 11.07 0.000016 ***
N 1 0.07 0.0739 12.10 0.00051 ***
N_cat:N_items 6 0.06 0.0100 1.64 0.13233
N_cat:N 3 0.03 0.0100 1.63 0.17972
N_items:N 2 0.04 0.0216 3.53 0.02952 *
N_cat:N_items:N 6 0.02 0.0027 0.43 0.85622
Residuals 2114 12.91 0.0061
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1eta_est <- (fit[[1]]$`Sum Sq`/sum(fit[[1]]$`Sum Sq`))[1:7]
cbind(omega2(fit),p_omega2(fit), eta_est) omega^2 partial-omega^2 eta_est
N_cat 0.0033 0.0033 0.00463
N_items 0.0092 0.0093 0.01015
N 0.0051 0.0052 0.00554
N_cat:N_items 0.0018 0.0018 0.00451
N_cat:N 0.0009 0.0009 0.00224
N_items:N 0.0023 0.0024 0.00323
N_cat:N_items:N -0.0016 -0.0016 0.00119saved_omega[5,] <- omega2(fit)
saved_eta[5,] <- eta_estResponse Time Factor Precision (\(\sigma_s\))
rb <- mydata %>%
filter(parameter_group == "sigma_s") %>%
group_by(condition, iter, N, N_cat, N_items) %>%
summarise(
rb_est = mean(post_median_bias_est)
)`summarise()` has grouped output by 'condition', 'iter', 'N', 'N_cat'. You can override using the `.groups` argument.## ANOVA on Relative Bias values
anova_assumptions_check(
dat = rb, outcome = 'rb_est',
factors = c('N_cat', 'N_items', 'N'),
model = as.formula('rb_est ~ N_cat*N_items*N'))
=============================
Tests and Plots of Normality:
Shapiro-Wilks Test of Normality of Residuals:
Shapiro-Wilk normality test
data: res
W = 1, p-value <0.0000000000000002
K-S Test for Normality of Residuals:Warning in ks.test(aov.out$residuals, "pnorm", alternative = "two.sided"): ties
should not be present for the Kolmogorov-Smirnov test
One-sample Kolmogorov-Smirnov test
data: aov.out$residuals
D = 0.1, p-value <0.0000000000000002
alternative hypothesis: two-sided`stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
`stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
`stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
=============================
Tests of Homogeneity of Variance
Levenes Test: N_cat
Levene's Test for Homogeneity of Variance (center = "mean")
Df F value Pr(>F)
group 3 3.13 0.025 *
2130
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Levenes Test: N_items
Levene's Test for Homogeneity of Variance (center = "mean")
Df F value Pr(>F)
group 2 57.2 <0.0000000000000002 ***
2131
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Levenes Test: N
Levene's Test for Homogeneity of Variance (center = "mean")
Df F value Pr(>F)
group 1 406 <0.0000000000000002 ***
2132
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1fit <- summary(aov(rb_est ~ N_cat*N_items*N, data=rb))
fit Df Sum Sq Mean Sq F value Pr(>F)
N_cat 3 0 0.12 0.19 0.905
N_items 2 37 18.46 28.85 0.00000000000044 ***
N 1 1 0.76 1.19 0.275
N_cat:N_items 6 5 0.89 1.39 0.213
N_cat:N 3 2 0.63 0.98 0.400
N_items:N 2 5 2.44 3.82 0.022 *
N_cat:N_items:N 6 5 0.88 1.37 0.222
Residuals 2110 1350 0.64
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1eta_est <- (fit[[1]]$`Sum Sq`/sum(fit[[1]]$`Sum Sq`))[1:7]
cbind(omega2(fit),p_omega2(fit), eta_est) omega^2 partial-omega^2 eta_est
N_cat -0.0011 -0.0011 0.000257
N_items 0.0253 0.0254 0.026267
N 0.0001 0.0001 0.000544
N_cat:N_items 0.0011 0.0011 0.003807
N_cat:N 0.0000 0.0000 0.001342
N_items:N 0.0026 0.0026 0.003477
N_cat:N_items:N 0.0010 0.0010 0.003749saved_omega[6,] <- omega2(fit)
saved_eta[6,] <- eta_estFactor Covariance (\(\sigma_{st}\))
rb <- mydata %>%
filter(parameter_group == "sigma_st") %>%
group_by(condition, iter, N, N_cat, N_items) %>%
summarise(
rb_est = mean(post_median_bias_est)
)`summarise()` has grouped output by 'condition', 'iter', 'N', 'N_cat'. You can override using the `.groups` argument.## ANOVA on Relative Bias values
anova_assumptions_check(
dat = rb, outcome = 'rb_est',
factors = c('N_cat', 'N_items', 'N'),
model = as.formula('rb_est ~ N_cat*N_items*N'))
=============================
Tests and Plots of Normality:
Shapiro-Wilks Test of Normality of Residuals:
Shapiro-Wilk normality test
data: res
W = 1, p-value <0.0000000000000002
K-S Test for Normality of Residuals:Warning in ks.test(aov.out$residuals, "pnorm", alternative = "two.sided"): ties
should not be present for the Kolmogorov-Smirnov test
One-sample Kolmogorov-Smirnov test
data: aov.out$residuals
D = 0.5, p-value <0.0000000000000002
alternative hypothesis: two-sided`stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
`stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
`stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
=============================
Tests of Homogeneity of Variance
Levenes Test: N_cat
Levene's Test for Homogeneity of Variance (center = "mean")
Df F value Pr(>F)
group 3 3.23 0.022 *
2125
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Levenes Test: N_items
Levene's Test for Homogeneity of Variance (center = "mean")
Df F value Pr(>F)
group 2 62.3 <0.0000000000000002 ***
2126
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Levenes Test: N
Levene's Test for Homogeneity of Variance (center = "mean")
Df F value Pr(>F)
group 1 371 <0.0000000000000002 ***
2127
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1fit <- summary(aov(rb_est ~ N_cat*N_items*N, data=rb))
fit Df Sum Sq Mean Sq F value Pr(>F)
N_cat 3 0.017 0.00581 13.25 0.000000014 ***
N_items 2 0.002 0.00088 2.00 0.136
N 1 0.001 0.00075 1.72 0.190
N_cat:N_items 6 0.007 0.00113 2.59 0.017 *
N_cat:N 3 0.001 0.00031 0.71 0.546
N_items:N 2 0.002 0.00114 2.61 0.074 .
N_cat:N_items:N 6 0.004 0.00067 1.52 0.166
Residuals 2105 0.922 0.00044
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1eta_est <- (fit[[1]]$`Sum Sq`/sum(fit[[1]]$`Sum Sq`))[1:7]
cbind(omega2(fit),p_omega2(fit), eta_est) omega^2 partial-omega^2 eta_est
N_cat 0.0168 0.0170 0.018218
N_items 0.0009 0.0009 0.001831
N 0.0003 0.0003 0.000788
N_cat:N_items 0.0044 0.0045 0.007112
N_cat:N -0.0004 -0.0004 0.000976
N_items:N 0.0015 0.0015 0.002393
N_cat:N_items:N 0.0014 0.0015 0.004192saved_omega[7,] <- omega2(fit)
saved_eta[7,] <- eta_estPID Relationship (\(\rho\))
rb <- mydata %>%
filter(parameter_group == "rho") %>%
group_by(condition, iter, N, N_cat, N_items) %>%
summarise(
rb_est = mean(post_median_bias_est)
)`summarise()` has grouped output by 'condition', 'iter', 'N', 'N_cat'. You can override using the `.groups` argument.## ANOVA on Relative Bias values
anova_assumptions_check(
dat = rb, outcome = 'rb_est',
factors = c('N_cat', 'N_items', 'N'),
model = as.formula('rb_est ~ N_cat*N_items*N'))
=============================
Tests and Plots of Normality:
Shapiro-Wilks Test of Normality of Residuals:
Shapiro-Wilk normality test
data: res
W = 1, p-value <0.0000000000000002
K-S Test for Normality of Residuals:Warning in ks.test(aov.out$residuals, "pnorm", alternative = "two.sided"): ties
should not be present for the Kolmogorov-Smirnov test
One-sample Kolmogorov-Smirnov test
data: aov.out$residuals
D = 0.5, p-value <0.0000000000000002
alternative hypothesis: two-sided`stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
`stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
`stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
=============================
Tests of Homogeneity of Variance
Levenes Test: N_cat
Levene's Test for Homogeneity of Variance (center = "mean")
Df F value Pr(>F)
group 3 0.85 0.46
2028
Levenes Test: N_items
Levene's Test for Homogeneity of Variance (center = "mean")
Df F value Pr(>F)
group 2 113 <0.0000000000000002 ***
2029
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Levenes Test: N
Levene's Test for Homogeneity of Variance (center = "mean")
Df F value Pr(>F)
group 1 157 <0.0000000000000002 ***
2030
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1fit <- summary(aov(rb_est ~ N_cat*N_items*N, data=rb))
fit Df Sum Sq Mean Sq F value Pr(>F)
N_cat 3 0.073 0.024 16.70 0.0000000001 ***
N_items 2 0.172 0.086 59.44 < 0.0000000000000002 ***
N 1 0.420 0.420 289.99 < 0.0000000000000002 ***
N_cat:N_items 6 0.010 0.002 1.20 0.303
N_cat:N 3 0.003 0.001 0.64 0.592
N_items:N 2 0.007 0.003 2.32 0.098 .
N_cat:N_items:N 6 0.042 0.007 4.82 0.0000679088 ***
Residuals 2008 2.909 0.001
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1eta_est <- (fit[[1]]$`Sum Sq`/sum(fit[[1]]$`Sum Sq`))[1:7]
cbind(omega2(fit),p_omega2(fit), eta_est) omega^2 partial-omega^2 eta_est
N_cat 0.0188 0.0227 0.01997
N_items 0.0466 0.0544 0.04737
N 0.1151 0.1245 0.11555
N_cat:N_items 0.0005 0.0006 0.00287
N_cat:N -0.0004 -0.0005 0.00076
N_items:N 0.0011 0.0013 0.00185
N_cat:N_items:N 0.0091 0.0112 0.01153saved_omega[8,] <- omega2(fit)
saved_eta[8,] <- eta_estFactor Reliability (\(\omega\))
rb <- mydata %>%
filter(parameter_group == "omega") %>%
group_by(condition, iter, N, N_cat, N_items) %>%
summarise(
rb_est = mean(post_median_bias_est)
)`summarise()` has grouped output by 'condition', 'iter', 'N', 'N_cat'. You can override using the `.groups` argument.## ANOVA on Relative Bias values
anova_assumptions_check(
dat = rb, outcome = 'rb_est',
factors = c('N_cat', 'N_items', 'N'),
model = as.formula('rb_est ~ N_cat*N_items*N'))
=============================
Tests and Plots of Normality:
Shapiro-Wilks Test of Normality of Residuals:
Shapiro-Wilk normality test
data: res
W = 0.8, p-value <0.0000000000000002
K-S Test for Normality of Residuals:Warning in ks.test(aov.out$residuals, "pnorm", alternative = "two.sided"): ties
should not be present for the Kolmogorov-Smirnov test
One-sample Kolmogorov-Smirnov test
data: aov.out$residuals
D = 0.5, p-value <0.0000000000000002
alternative hypothesis: two-sided`stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
`stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
`stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
=============================
Tests of Homogeneity of Variance
Levenes Test: N_cat
Levene's Test for Homogeneity of Variance (center = "mean")
Df F value Pr(>F)
group 3 3.36 0.018 *
1987
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Levenes Test: N_items
Levene's Test for Homogeneity of Variance (center = "mean")
Df F value Pr(>F)
group 2 363 <0.0000000000000002 ***
1988
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Levenes Test: N
Levene's Test for Homogeneity of Variance (center = "mean")
Df F value Pr(>F)
group 1 42 0.00000000011 ***
1989
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1fit <- summary(aov(rb_est ~ N_cat*N_items*N, data=rb))
fit Df Sum Sq Mean Sq F value Pr(>F)
N_cat 3 0.032 0.0105 21.23 0.00000000000016 ***
N_items 2 0.168 0.0842 169.56 < 0.0000000000000002 ***
N 1 0.062 0.0624 125.66 < 0.0000000000000002 ***
N_cat:N_items 6 0.004 0.0007 1.41 0.20634
N_cat:N 3 0.002 0.0007 1.38 0.24816
N_items:N 2 0.010 0.0052 10.43 0.00003113242259 ***
N_cat:N_items:N 6 0.013 0.0021 4.32 0.00024 ***
Residuals 1967 0.977 0.0005
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1eta_est <- (fit[[1]]$`Sum Sq`/sum(fit[[1]]$`Sum Sq`))[1:7]
cbind(omega2(fit),p_omega2(fit), eta_est) omega^2 partial-omega^2 eta_est
N_cat 0.0237 0.0296 0.02493
N_items 0.1319 0.1448 0.13274
N 0.0488 0.0589 0.04918
N_cat:N_items 0.0010 0.0012 0.00331
N_cat:N 0.0004 0.0006 0.00162
N_items:N 0.0074 0.0094 0.00817
N_cat:N_items:N 0.0078 0.0099 0.01015saved_omega[9,] <- omega2(fit)
saved_eta[9,] <- eta_estManuscript Figures and Tables (latex formated)
Tables
keep_cols <- c("condition", "iter", "N", "N_items", "N_cat", "parameter_group", "post_median_rb_est", "post_median_bias_est")
tbl_dat <- mydata %>%
select(all_of(keep_cols)) %>%
filter(
!is.na(parameter_group)
, parameter_group != "lambda (STD)"
)
# get average Rhat and SD for each condition and parameter group
sum_tab <- tbl_dat %>%
group_by(N_cat, N_items, N, parameter_group) %>%
summarise(
Post_Median_RB_Mean = mean(post_median_rb_est),
Post_Median_AB_Mean = mean(post_median_bias_est)
)`summarise()` has grouped output by 'N_cat', 'N_items', 'N'. You can override using the `.groups` argument.# table 1: 2 category data
T1 <- sum_tab %>%
filter(N_cat == 2) %>%
pivot_wider(
id_cols = c("parameter_group", "N")
, names_from = "N_items"
, values_from = all_of(c("Post_Median_RB_Mean", "Post_Median_AB_Mean"))
) %>%
arrange(.,parameter_group)
# reordering of rows to more logical for presentation
#T1 <- T1[c(3:4, 15:18, 1:2, 5:8, 13:14, 11:12, 9:10) ,]
print(
xtable(
T1[c(3:4, 15:18, 1:2, 5:8, 13:14, 11:12, 9:10) , ]
, caption = c("Posterior Bias: Dichotomous items")
,align = "lllrrrrrr"
),
include.rownames=F,
booktabs=T
)% latex table generated in R 4.0.5 by xtable 1.8-4 package
% Sun Feb 13 15:23:00 2022
\begin{table}[ht]
\centering
\begin{tabular}{llrrrrrr}
\toprule
parameter\_group & N & Post\_Median\_RB\_Mean\_5 & Post\_Median\_RB\_Mean\_10 & Post\_Median\_RB\_Mean\_20 & Post\_Median\_AB\_Mean\_5 & Post\_Median\_AB\_Mean\_10 & Post\_Median\_AB\_Mean\_20 \\
\midrule
lambda & 500 & -25.57 & -13.95 & -10.25 & -0.23 & -0.13 & -0.09 \\
lambda & 2500 & -16.49 & -13.87 & -13.83 & -0.15 & -0.12 & -0.12 \\
tau & 500 & -8.28 & -2.85 & 6.40 & -0.00 & 0.01 & -0.01 \\
tau & 2500 & -2.28 & -3.30 & -15.94 & -0.00 & -0.00 & -0.00 \\
theta & 500 & -9.86 & -5.68 & -4.72 & -0.18 & -0.10 & -0.09 \\
theta & 2500 & -11.40 & -10.66 & -10.84 & -0.21 & -0.19 & -0.20 \\
beta\_lrt & 500 & 0.09 & -1.07 & -1.31 & 0.00 & -0.02 & -0.02 \\
beta\_lrt & 2500 & 0.55 & 0.56 & 0.30 & 0.01 & 0.01 & 0.00 \\
sigma\_lrt & 500 & 1.29 & 0.66 & 0.17 & 0.05 & 0.03 & 0.01 \\
sigma\_lrt & 2500 & 0.42 & 0.14 & 0.08 & 0.02 & 0.01 & 0.00 \\
sigma\_s & 500 & 11.64 & 6.25 & 4.35 & 1.16 & 0.63 & 0.44 \\
sigma\_s & 2500 & 7.68 & 6.77 & 5.76 & 0.77 & 0.68 & 0.58 \\
sigma\_st & 500 & -9.70 & -6.54 & -4.40 & 0.01 & 0.00 & 0.00 \\
sigma\_st & 2500 & -7.76 & -2.67 & -6.57 & 0.01 & 0.00 & 0.00 \\
rho & 500 & 33.04 & -1.20 & -7.13 & 0.03 & -0.00 & -0.01 \\
rho & 2500 & 37.40 & 43.85 & 36.33 & 0.04 & 0.04 & 0.04 \\
omega & 500 & -3.94 & -1.53 & -0.93 & -0.03 & -0.01 & -0.01 \\
omega & 2500 & -4.31 & -3.34 & -1.92 & -0.03 & -0.03 & -0.02 \\
\bottomrule
\end{tabular}
\caption{Posterior Bias: Dichotomous items}
\end{table}# table 2: 5 category data
T2 <- sum_tab %>%
filter(N_cat == 5) %>%
pivot_wider(
id_cols = c("parameter_group", "N")
, names_from = "N_items"
, values_from = all_of(c("Post_Median_RB_Mean", "Post_Median_AB_Mean"))
) %>%
arrange(.,parameter_group)
# reordering of rows to more logical for presentation
print(
xtable(
T2[c(3:4, 15:18, 1:2, 5:8, 13:14, 11:12, 9:10) , ]
, caption = c("Posterior Bias: Five category items")
,align = "lllrrrrrr"
),
include.rownames=F,
booktabs=T
)% latex table generated in R 4.0.5 by xtable 1.8-4 package
% Sun Feb 13 15:23:00 2022
\begin{table}[ht]
\centering
\begin{tabular}{llrrrrrr}
\toprule
parameter\_group & N & Post\_Median\_RB\_Mean\_5 & Post\_Median\_RB\_Mean\_10 & Post\_Median\_RB\_Mean\_20 & Post\_Median\_AB\_Mean\_5 & Post\_Median\_AB\_Mean\_10 & Post\_Median\_AB\_Mean\_20 \\
\midrule
lambda & 500 & -14.66 & -13.48 & -12.76 & -0.13 & -0.12 & -0.11 \\
lambda & 2500 & -14.93 & -14.61 & -14.40 & -0.13 & -0.13 & -0.13 \\
tau & 500 & -3.81 & -6.67 & -22.63 & 0.00 & -0.00 & 0.01 \\
tau & 2500 & -8.11 & -9.11 & -16.54 & -0.02 & -0.01 & -0.01 \\
theta & 500 & -9.39 & -9.83 & -9.50 & -0.17 & -0.18 & -0.17 \\
theta & 2500 & -11.81 & -11.84 & -11.76 & -0.21 & -0.21 & -0.21 \\
beta\_lrt & 500 & 0.53 & -0.30 & -0.82 & 0.01 & -0.00 & -0.01 \\
beta\_lrt & 2500 & 1.42 & 0.57 & 0.39 & 0.02 & 0.01 & 0.01 \\
sigma\_lrt & 500 & 1.00 & 0.33 & 0.31 & 0.04 & 0.01 & 0.01 \\
sigma\_lrt & 2500 & 0.15 & 0.08 & 0.13 & 0.01 & 0.00 & 0.01 \\
sigma\_s & 500 & 10.07 & 7.25 & 6.22 & 1.01 & 0.73 & 0.62 \\
sigma\_s & 2500 & 8.09 & 6.86 & 5.71 & 0.81 & 0.69 & 0.57 \\
sigma\_st & 500 & -6.78 & -6.13 & -4.97 & -0.00 & -0.00 & -0.00 \\
sigma\_st & 2500 & -1.90 & -3.69 & -1.87 & -0.00 & -0.00 & -0.00 \\
rho & 500 & 35.60 & 21.37 & 10.46 & 0.04 & 0.02 & 0.01 \\
rho & 2500 & 65.98 & 46.40 & 40.98 & 0.07 & 0.05 & 0.04 \\
omega & 500 & -4.44 & -3.17 & -1.69 & -0.04 & -0.03 & -0.02 \\
omega & 2500 & -6.57 & -3.85 & -2.08 & -0.05 & -0.03 & -0.02 \\
\bottomrule
\end{tabular}
\caption{Posterior Bias: Five category items}
\end{table}# table 3: 3 category data
T3 <- sum_tab %>%
filter(N_cat == 3) %>%
pivot_wider(
id_cols = c("parameter_group", "N")
, names_from = "N_items"
, values_from = all_of(c("Post_Median_RB_Mean", "Post_Median_AB_Mean"))
) %>%
arrange(.,parameter_group)
# reordering of rows to more logical for presentation
print(
xtable(
T3[c(3:4, 15:18, 1:2, 5:8, 13:14, 11:12, 9:10) , ]
, caption = c("Posterior Bias: three category items")
,align = "lllrrrrrr"
),
include.rownames=F,
booktabs=T
)% latex table generated in R 4.0.5 by xtable 1.8-4 package
% Sun Feb 13 15:23:00 2022
\begin{table}[ht]
\centering
\begin{tabular}{llrrrrrr}
\toprule
parameter\_group & N & Post\_Median\_RB\_Mean\_5 & Post\_Median\_RB\_Mean\_10 & Post\_Median\_RB\_Mean\_20 & Post\_Median\_AB\_Mean\_5 & Post\_Median\_AB\_Mean\_10 & Post\_Median\_AB\_Mean\_20 \\
\midrule
lambda & 500 & -14.18 & -13.31 & -12.47 & -0.13 & -0.12 & -0.11 \\
lambda & 2500 & -15.38 & -15.69 & -15.88 & -0.14 & -0.14 & -0.14 \\
tau & 500 & 58.04 & -50.96 & -67.29 & 0.12 & 0.11 & 0.11 \\
tau & 2500 & 54.39 & -48.43 & -52.75 & 0.12 & 0.11 & 0.11 \\
theta & 500 & -7.28 & -8.71 & -8.87 & -0.13 & -0.16 & -0.16 \\
theta & 2500 & -11.89 & -12.49 & -12.77 & -0.22 & -0.23 & -0.23 \\
beta\_lrt & 500 & 0.35 & 0.05 & -0.78 & 0.01 & 0.00 & -0.01 \\
beta\_lrt & 2500 & 1.43 & 0.75 & 0.06 & 0.02 & 0.01 & 0.00 \\
sigma\_lrt & 500 & 0.96 & 0.27 & 0.08 & 0.04 & 0.01 & 0.00 \\
sigma\_lrt & 2500 & 0.51 & 0.21 & 0.12 & 0.02 & 0.01 & 0.00 \\
sigma\_s & 500 & 8.40 & 6.76 & 6.08 & 0.84 & 0.68 & 0.61 \\
sigma\_s & 2500 & 8.63 & 8.05 & 6.18 & 0.86 & 0.81 & 0.62 \\
sigma\_st & 500 & -12.05 & 0.22 & 9.01 & -0.01 & 0.00 & 0.01 \\
sigma\_st & 2500 & 0.55 & 0.38 & 2.51 & 0.00 & 0.00 & 0.00 \\
rho & 500 & 36.35 & 26.41 & 8.04 & 0.04 & 0.03 & 0.01 \\
rho & 2500 & 63.92 & 51.16 & 36.93 & 0.06 & 0.05 & 0.04 \\
omega & 500 & -3.69 & -3.16 & -1.67 & -0.03 & -0.03 & -0.02 \\
omega & 2500 & -6.82 & -4.21 & -2.35 & -0.05 & -0.04 & -0.02 \\
\bottomrule
\end{tabular}
\caption{Posterior Bias: three category items}
\end{table}# table 4: 7 category data
T4 <- sum_tab %>%
filter(N_cat == 5) %>%
pivot_wider(
id_cols = c("parameter_group", "N")
, names_from = "N_items"
, values_from = all_of(c("Post_Median_RB_Mean", "Post_Median_AB_Mean"))
) %>%
arrange(.,parameter_group)
# reordering of rows to more logical for presentation
print(
xtable(
T4[c(3:4, 15:18, 1:2, 5:8, 13:14, 11:12, 9:10) , ]
, caption = c("Posterior Bias: seven category items")
,align = "lllrrrrrr"
),
include.rownames=F,
booktabs=T
)% latex table generated in R 4.0.5 by xtable 1.8-4 package
% Sun Feb 13 15:23:00 2022
\begin{table}[ht]
\centering
\begin{tabular}{llrrrrrr}
\toprule
parameter\_group & N & Post\_Median\_RB\_Mean\_5 & Post\_Median\_RB\_Mean\_10 & Post\_Median\_RB\_Mean\_20 & Post\_Median\_AB\_Mean\_5 & Post\_Median\_AB\_Mean\_10 & Post\_Median\_AB\_Mean\_20 \\
\midrule
lambda & 500 & -14.66 & -13.48 & -12.76 & -0.13 & -0.12 & -0.11 \\
lambda & 2500 & -14.93 & -14.61 & -14.40 & -0.13 & -0.13 & -0.13 \\
tau & 500 & -3.81 & -6.67 & -22.63 & 0.00 & -0.00 & 0.01 \\
tau & 2500 & -8.11 & -9.11 & -16.54 & -0.02 & -0.01 & -0.01 \\
theta & 500 & -9.39 & -9.83 & -9.50 & -0.17 & -0.18 & -0.17 \\
theta & 2500 & -11.81 & -11.84 & -11.76 & -0.21 & -0.21 & -0.21 \\
beta\_lrt & 500 & 0.53 & -0.30 & -0.82 & 0.01 & -0.00 & -0.01 \\
beta\_lrt & 2500 & 1.42 & 0.57 & 0.39 & 0.02 & 0.01 & 0.01 \\
sigma\_lrt & 500 & 1.00 & 0.33 & 0.31 & 0.04 & 0.01 & 0.01 \\
sigma\_lrt & 2500 & 0.15 & 0.08 & 0.13 & 0.01 & 0.00 & 0.01 \\
sigma\_s & 500 & 10.07 & 7.25 & 6.22 & 1.01 & 0.73 & 0.62 \\
sigma\_s & 2500 & 8.09 & 6.86 & 5.71 & 0.81 & 0.69 & 0.57 \\
sigma\_st & 500 & -6.78 & -6.13 & -4.97 & -0.00 & -0.00 & -0.00 \\
sigma\_st & 2500 & -1.90 & -3.69 & -1.87 & -0.00 & -0.00 & -0.00 \\
rho & 500 & 35.60 & 21.37 & 10.46 & 0.04 & 0.02 & 0.01 \\
rho & 2500 & 65.98 & 46.40 & 40.98 & 0.07 & 0.05 & 0.04 \\
omega & 500 & -4.44 & -3.17 & -1.69 & -0.04 & -0.03 & -0.02 \\
omega & 2500 & -6.57 & -3.85 & -2.08 & -0.05 & -0.03 & -0.02 \\
\bottomrule
\end{tabular}
\caption{Posterior Bias: seven category items}
\end{table}# effect size
print(
xtable(
t(saved_eta)
, caption = c("Effect of design factors on relative bias estimates: eta2")
,align = "lrrrrrrrrr", digits = 3
),
include.rownames=T,
booktabs=T
)% latex table generated in R 4.0.5 by xtable 1.8-4 package
% Sun Feb 13 15:23:00 2022
\begin{table}[ht]
\centering
\begin{tabular}{lrrrrrrrrr}
\toprule
& lambda & tau & theta & beta\_lrt & sigma\_lrt & sigma\_s & sigma\_ts & rho & omega \\
\midrule
N\_cat & 0.015 & 0.563 & 0.006 & 0.010 & 0.005 & 0.000 & 0.018 & 0.020 & 0.025 \\
N\_items & 0.031 & 0.000 & 0.003 & 0.051 & 0.010 & 0.026 & 0.002 & 0.047 & 0.133 \\
N & 0.001 & 0.006 & 0.035 & 0.065 & 0.006 & 0.001 & 0.001 & 0.116 & 0.049 \\
N\_cat:N\_items & 0.039 & 0.003 & 0.011 & 0.003 & 0.005 & 0.004 & 0.007 & 0.003 & 0.003 \\
N\_cat:N & 0.008 & 0.005 & 0.003 & 0.002 & 0.002 & 0.001 & 0.001 & 0.001 & 0.002 \\
N\_items:N & 0.014 & 0.000 & 0.002 & 0.001 & 0.003 & 0.003 & 0.002 & 0.002 & 0.008 \\
N\_cat:N\_items:N & 0.012 & 0.001 & 0.004 & 0.005 & 0.001 & 0.004 & 0.004 & 0.012 & 0.010 \\
\bottomrule
\end{tabular}
\caption{Effect of design factors on relative bias estimates: eta2}
\end{table}print(
xtable(
t(saved_omega)
, caption = c("Effect of design factors on relative bias estimates: omega2")
,align = "lrrrrrrrrr", digits = 3
),
include.rownames=T,
booktabs=T
)% latex table generated in R 4.0.5 by xtable 1.8-4 package
% Sun Feb 13 15:23:00 2022
\begin{table}[ht]
\centering
\begin{tabular}{lrrrrrrrrr}
\toprule
& lambda & tau & theta & beta\_lrt & sigma\_lrt & sigma\_s & sigma\_ts & rho & omega \\
\midrule
N\_cat & 0.014 & 0.562 & 0.005 & 0.009 & 0.003 & -0.001 & 0.017 & 0.019 & 0.024 \\
N\_items & 0.030 & -0.000 & 0.002 & 0.050 & 0.009 & 0.025 & 0.001 & 0.047 & 0.132 \\
N & 0.000 & 0.006 & 0.034 & 0.064 & 0.005 & 0.000 & 0.000 & 0.115 & 0.049 \\
N\_cat:N\_items & 0.036 & 0.002 & 0.008 & 0.000 & 0.002 & 0.001 & 0.004 & 0.000 & 0.001 \\
N\_cat:N & 0.007 & 0.004 & 0.001 & 0.001 & 0.001 & -0.000 & -0.000 & -0.000 & 0.000 \\
N\_items:N & 0.013 & -0.000 & 0.001 & 0.000 & 0.002 & 0.003 & 0.002 & 0.001 & 0.007 \\
N\_cat:N\_items:N & 0.010 & -0.000 & 0.001 & 0.002 & -0.002 & 0.001 & 0.001 & 0.009 & 0.008 \\
\bottomrule
\end{tabular}
\caption{Effect of design factors on relative bias estimates: omega2}
\end{table}Figures
Only make “nice” figures for omega to start.
rb <- mydata %>%
filter(parameter_group == "omega") %>%
group_by(condition, N_cat, N_items, N) %>%
mutate(Post_Median_ARB = mean(post_median_rb_est),
Post_Median_AB = mean(post_median_bias_est))
# Create summary stats for plotting
rb_tbl <- rb %>%
group_by(condition, condition_lbs, N_cat, N_items, N) %>%
summarise(Post_Median_ARB = mean(post_median_rb_est),
Post_Median_AB = mean(post_median_bias_est)) %>%
arrange(Post_Median_ARB)`summarise()` has grouped output by 'condition', 'condition_lbs', 'N_cat', 'N_items'. You can override using the `.groups` argument.rb_tbl$lbs = factor(
rb_tbl$condition_lbs,
levels=rb_tbl$condition_lbs,
ordered=T
)
rb$lbs <- factor(
rb$condition_lbs,
levels=rb_tbl$condition_lbs,
ordered=T
)
# visualize bias estimates
p1 <- ggplot() +
stat_summary(
data = rb,
aes(y = lbs, x = post_median_rb_est,
group = lbs),
fun.data = cust.boxplot,
geom = "boxplot"
) +
geom_point(data = rb_tbl,
aes(y = lbs, x = Post_Median_ARB),
color = "black") +
geom_vline(xintercept = -10,
linetype = "dashed") +
geom_vline(xintercept = 10,
linetype = "dashed") +
lims(x = c(-20, 20)) +
labs(y="Simulation Condition (arranged by ARB)",
x="Relative Bias")+
theme_bw() +
theme(panel.grid = element_blank())
p2 <- ggplot() +
stat_summary(
data = rb,
aes(y = lbs, x = post_median_bias_est,
group = lbs),
fun.data = cust.boxplot,
geom = "boxplot"
) +
geom_point(data = rb_tbl,
aes(y = lbs, x = Post_Median_AB),
color = "black") +
geom_vline(xintercept = 0,
linetype = "dashed")+
lims(x = c(-0.125, 0.125)) +
labs(x="Bias")+
theme_bw() +
theme(panel.grid = element_blank(),
axis.text.y = element_blank(),
axis.title.y = element_blank())
p <- p1 + p2 + plot_layout(guides="collect") + plot_annotation(tag_levels = "A")
pWarning: Removed 5 rows containing non-finite values (stat_summary).Warning: Removed 11 rows containing non-finite values (stat_summary).
ggsave(filename = "fig/study2_parameter_bias_omega_2357.pdf",plot=p,width = 7, height=4,units="in")Warning: Removed 5 rows containing non-finite values (stat_summary).
Warning: Removed 11 rows containing non-finite values (stat_summary).ggsave(filename = "fig/study2_parameter_bias_omega_2357.png",plot=p,width = 7, height=4,units="in")Warning: Removed 5 rows containing non-finite values (stat_summary).
Warning: Removed 11 rows containing non-finite values (stat_summary).ggsave(filename = "fig/study2_parameter_bias_omega_2357.eps",plot=p,width = 7, height=4,units="in")Warning: Removed 5 rows containing non-finite values (stat_summary).
Warning: Removed 11 rows containing non-finite values (stat_summary).# visualize bias estimates
rb <- mydata %>%
filter(parameter_group == "omega", N_cat%in%c(2,5)) %>%
group_by(condition, N_cat, N_items, N) %>%
mutate(Post_Median_ARB = mean(post_median_rb_est),
Post_Median_AB = mean(post_median_bias_est))
# Create summary stats for plotting
rb_tbl <- rb %>%
group_by(condition, condition_lbs, N_cat, N_items, N) %>%
summarise(Post_Median_ARB = mean(post_median_rb_est),
Post_Median_AB = mean(post_median_bias_est)) %>%
arrange(Post_Median_ARB)`summarise()` has grouped output by 'condition', 'condition_lbs', 'N_cat', 'N_items'. You can override using the `.groups` argument.rb_tbl$lbs = factor(
rb_tbl$condition_lbs,
levels=rb_tbl$condition_lbs,
ordered=T
)
rb$lbs <- factor(
rb$condition_lbs,
levels=rb_tbl$condition_lbs,
ordered=T
)
p1 <- ggplot() +
stat_summary(
data = rb,
aes(y = lbs, x = post_median_rb_est,
group = lbs),
fun.data = cust.boxplot,
geom = "boxplot"
) +
geom_point(data = rb_tbl,
aes(y = lbs, x = Post_Median_ARB),
color = "black") +
geom_vline(xintercept = -10,
linetype = "dashed") +
geom_vline(xintercept = 10,
linetype = "dashed") +
lims(x = c(-20, 20)) +
labs(y="Simulation Condition (arranged by ARB)",
x="Relative Bias")+
theme_bw() +
theme(panel.grid = element_blank())
p2 <- ggplot() +
stat_summary(
data = rb,
aes(y = lbs, x = post_median_bias_est,
group = lbs),
fun.data = cust.boxplot,
geom = "boxplot"
) +
geom_point(data = rb_tbl,
aes(y = lbs, x = Post_Median_AB),
color = "black") +
geom_vline(xintercept = 0,
linetype = "dashed")+
lims(x = c(-0.125, 0.125)) +
labs(x="Bias")+
theme_bw() +
theme(panel.grid = element_blank(),
axis.text.y = element_blank(),
axis.title.y = element_blank())
p <- p1 + p2 + plot_layout(guides="collect") + plot_annotation(tag_levels = "A")
pWarning: Removed 4 rows containing non-finite values (stat_summary).Warning: Removed 8 rows containing non-finite values (stat_summary).
ggsave(filename = "fig/study2_parameter_bias_omega_25.pdf",plot=p,width = 7, height=4,units="in")Warning: Removed 4 rows containing non-finite values (stat_summary).
Warning: Removed 8 rows containing non-finite values (stat_summary).ggsave(filename = "fig/study2_parameter_bias_omega_25.png",plot=p,width = 7, height=4,units="in")Warning: Removed 4 rows containing non-finite values (stat_summary).
Warning: Removed 8 rows containing non-finite values (stat_summary).ggsave(filename = "fig/study2_parameter_bias_omega_25.eps",plot=p,width = 7, height=4,units="in")Warning: Removed 4 rows containing non-finite values (stat_summary).
Warning: Removed 8 rows containing non-finite values (stat_summary).
sessionInfo()R version 4.0.5 (2021-03-31)
Platform: x86_64-w64-mingw32/x64 (64-bit)
Running under: Windows 10 x64 (build 22000)
Matrix products: default
locale:
[1] LC_COLLATE=English_United States.1252
[2] LC_CTYPE=English_United States.1252
[3] LC_MONETARY=English_United States.1252
[4] LC_NUMERIC=C
[5] LC_TIME=English_United States.1252
attached base packages:
[1] stats graphics grDevices utils datasets methods base
other attached packages:
[1] car_3.0-10 carData_3.0-4 mvtnorm_1.1-1
[4] LaplacesDemon_16.1.4 runjags_2.2.0-2 lme4_1.1-26
[7] Matrix_1.3-2 sirt_3.9-4 R2jags_0.6-1
[10] rjags_4-12 eRm_1.0-2 diffIRT_1.5
[13] statmod_1.4.35 xtable_1.8-4 kableExtra_1.3.4
[16] lavaan_0.6-7 polycor_0.7-10 bayesplot_1.8.0
[19] ggmcmc_1.5.1.1 coda_0.19-4 data.table_1.14.0
[22] patchwork_1.1.1 forcats_0.5.1 stringr_1.4.0
[25] dplyr_1.0.5 purrr_0.3.4 readr_1.4.0
[28] tidyr_1.1.3 tibble_3.1.0 ggplot2_3.3.5
[31] tidyverse_1.3.0 workflowr_1.6.2
loaded via a namespace (and not attached):
[1] minqa_1.2.4 TAM_3.5-19 colorspace_2.0-0 rio_0.5.26
[5] ellipsis_0.3.1 ggridges_0.5.3 rprojroot_2.0.2 fs_1.5.0
[9] rstudioapi_0.13 farver_2.1.0 fansi_0.4.2 lubridate_1.7.10
[13] xml2_1.3.2 splines_4.0.5 mnormt_2.0.2 knitr_1.31
[17] jsonlite_1.7.2 nloptr_1.2.2.2 broom_0.7.5 dbplyr_2.1.0
[21] compiler_4.0.5 httr_1.4.2 backports_1.2.1 assertthat_0.2.1
[25] cli_2.3.1 later_1.1.0.1 htmltools_0.5.1.1 tools_4.0.5
[29] gtable_0.3.0 glue_1.4.2 Rcpp_1.0.7 cellranger_1.1.0
[33] jquerylib_0.1.3 vctrs_0.3.6 svglite_2.0.0 nlme_3.1-152
[37] psych_2.0.12 xfun_0.21 ps_1.6.0 openxlsx_4.2.3
[41] rvest_1.0.0 lifecycle_1.0.0 MASS_7.3-53.1 scales_1.1.1
[45] ragg_1.1.1 hms_1.0.0 promises_1.2.0.1 parallel_4.0.5
[49] RColorBrewer_1.1-2 curl_4.3 yaml_2.2.1 sass_0.3.1
[53] reshape_0.8.8 stringi_1.5.3 highr_0.8 zip_2.1.1
[57] boot_1.3-27 rlang_0.4.10 pkgconfig_2.0.3 systemfonts_1.0.1
[61] evaluate_0.14 lattice_0.20-41 labeling_0.4.2 tidyselect_1.1.0
[65] GGally_2.1.1 plyr_1.8.6 magrittr_2.0.1 R6_2.5.0
[69] generics_0.1.0 DBI_1.1.1 foreign_0.8-81 pillar_1.5.1
[73] haven_2.3.1 withr_2.4.1 abind_1.4-5 modelr_0.1.8
[77] crayon_1.4.1 utf8_1.1.4 tmvnsim_1.0-2 rmarkdown_2.7
[81] grid_4.0.5 readxl_1.3.1 CDM_7.5-15 pbivnorm_0.6.0
[85] git2r_0.28.0 reprex_1.0.0 digest_0.6.27 webshot_0.5.2
[89] httpuv_1.5.5 textshaping_0.3.1 stats4_4.0.5 munsell_0.5.0
[93] viridisLite_0.3.0 bslib_0.2.4 R2WinBUGS_2.1-21