ML-CFA: Parameter Bias - Latent Variable ICC
Last updated: 2020-06-01
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Knit directory: mcfa-para-est/
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rm(list=ls())
source(paste0(getwd(),"/code/load_packages.R"))
#source(paste0(getwd(),"/code/get_data.R"))sessionInfo()R version 3.6.3 (2020-02-29)
Platform: x86_64-w64-mingw32/x64 (64-bit)
Running under: Windows 10 x64 (build 18362)
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] xtable_1.8-4 kableExtra_1.1.0 cowplot_1.0.0
[4] MplusAutomation_0.7-3 data.table_1.12.8 patchwork_1.0.0
[7] forcats_0.5.0 stringr_1.4.0 dplyr_0.8.5
[10] purrr_0.3.4 readr_1.3.1 tidyr_1.1.0
[13] tibble_3.0.1 ggplot2_3.3.0 tidyverse_1.3.0
[16] workflowr_1.6.2
loaded via a namespace (and not attached):
[1] Rcpp_1.0.4.6 lubridate_1.7.8 lattice_0.20-38 assertthat_0.2.1
[5] rprojroot_1.3-2 digest_0.6.25 R6_2.4.1 cellranger_1.1.0
[9] plyr_1.8.6 backports_1.1.7 reprex_0.3.0 evaluate_0.14
[13] coda_0.19-3 httr_1.4.1 pillar_1.4.4 rlang_0.4.6
[17] readxl_1.3.1 rstudioapi_0.11 blob_1.2.1 texreg_1.36.23
[21] gsubfn_0.7 rmarkdown_2.1 proto_1.0.0 webshot_0.5.2
[25] pander_0.6.3 munsell_0.5.0 broom_0.5.6 compiler_3.6.3
[29] httpuv_1.5.2 modelr_0.1.8 xfun_0.14 pkgconfig_2.0.3
[33] htmltools_0.4.0 tidyselect_1.1.0 viridisLite_0.3.0 fansi_0.4.1
[37] crayon_1.3.4 dbplyr_1.4.4 withr_2.2.0 later_1.0.0
[41] grid_3.6.3 nlme_3.1-144 jsonlite_1.6.1 gtable_0.3.0
[45] lifecycle_0.2.0 DBI_1.1.0 git2r_0.27.1 magrittr_1.5
[49] scales_1.1.1 cli_2.0.2 stringi_1.4.6 fs_1.4.1
[53] promises_1.1.0 xml2_1.3.2 ellipsis_0.3.1 generics_0.0.2
[57] vctrs_0.3.0 boot_1.3-24 tools_3.6.3 glue_1.4.1
[61] hms_0.5.3 parallel_3.6.3 yaml_2.2.1 colorspace_1.4-1
[65] rvest_0.3.5 knitr_1.28 haven_2.3.0 # general options
theme_set(theme_bw())
options(digits=3)# set up vectors of variable names
pvec <- c(paste0('lambda1',1:6), paste0('lambda2',6:10), 'psiW12','psiB1', 'psiB2', 'psiB12', paste0('thetaB',1:10), 'icc_lv1_est', 'icc_lv2_est', paste0('icc_ov',1:10,'_est'))
# stored "true" values of parameters by each condition
ptvec <- c(rep('lambdaT',11), 'psiW12T', 'psiB1T', 'psiB2T', 'psiB12T', rep("thetaBT", 10), rep('icc_lv',2), rep('icc_ov',10))
result <- read_csv(paste0(w.d, "/data/results_bias_est.csv"))Parsed with column specification:
cols(
N1 = col_double(),
N2 = col_double(),
ICC_LV = col_double(),
ICC_OV = col_double(),
Variable = col_character(),
Estimator = col_character(),
TrueValue = col_double(),
RB = col_double(),
RMSE = col_double(),
Bias = col_double(),
SampVar = col_double(),
muRE = col_double(),
mwRE = col_double(),
uwRE = col_double(),
nRep = col_double(),
estMean = col_double(),
estSD = col_double()
)# Set conditions levels as categorical values
result <- result %>%
mutate(N1 = factor(N1, c("5", "10", "30")),
N2 = factor(N2, c("30", "50", "100", "200")),
ICC_OV = factor(ICC_OV, c("0.1","0.3", "0.5")),
ICC_LV = factor(ICC_LV, c("0.1", "0.5")),
wi = nRep/500)Summarizing Results
First, we will plot estimates (botxplots) to show how these estimates changed across conditions. To summarize the results we will average over the parameters that only differ y indices. Meaning we will describe the “average factor loading bias” by reporting the average bias for factor loadings. Additionally, different conditions resultedin different “sample sizes.” By this we mean the number of uses replications. The different number of cases per condition was accounted for by creating a “weight” variable for each row of the result object. This meant that conditions that had more usable replications counted more towards to averages reported (or count as much as if we averaged over the individual replications).
Latent Variable ICC
sdat <- filter(result, Variable %like% 'icc_lv')
sdat <- sdat %>%
group_by(N1, N2, ICC_OV, ICC_LV, Estimator) %>%
summarise(estMean = weighted.mean(estMean, wi),
estSD = weighted.mean(estSD, wi),
RB = weighted.mean(RB, wi),
RMSE = weighted.mean(RMSE, wi),
Bias = weighted.mean(Bias, wi),
SampVar = weighted.mean(SampVar, wi))
# first, plot estimates
p1 <- ggplot(sdat, aes(y=estMean))+
geom_boxplot()+
labs(y="Average Latent Variable ICC")
p2 <- ggplot(sdat, aes(y=estSD))+
geom_boxplot()+
labs(y="SD of Latent Variable ICC")
p3 <- ggplot(sdat, aes(y=RB))+
geom_boxplot()+
geom_hline(yintercept=-10, color="red", linetype="dashed")+
geom_hline(yintercept=10, color="red", linetype="dashed")+
labs(y="Relative Bias")
p4 <- ggplot(sdat, aes(y=RMSE))+
geom_boxplot()+
labs(y="Root Mean Square Error")
p5 <- ggplot(sdat, aes(y=Bias))+
geom_boxplot()+
labs(y="Sqaured Bias")
p6 <- ggplot(sdat, aes(y=SampVar))+
geom_boxplot()+
labs(y="Sampling Variance of Estimates")
p <- (p1 + p2 + p3)/(p4 + p5 + p6) +
plot_annotation(title="Summarizing bias indices of LATENT VARIABLE ICC")
p
Single Condition Breakdown
Estimation Method
ggplot(sdat, aes(y=estMean))+
geom_boxplot()+
labs(y="Average Latent Variable ICC",
title="LATENT VARIABLE ICC by Estimation Method",
subtitle="Parameter Estimates")+
facet_wrap(.~Estimator)
ggplot(sdat, aes(y=estSD))+
geom_boxplot()+
labs(y="SD of Latent Variable ICC",
title="LATENT VARIABLE ICC by Estimation Method",
subtitle="Standard Deviation of Estimates")+
facet_wrap(.~Estimator)
ggplot(sdat, aes(y=RB))+
geom_boxplot()+
geom_hline(yintercept=-10, color="red", linetype="dashed")+
geom_hline(yintercept=10, color="red", linetype="dashed")+
labs(y="Relative Bias",
title="LATENT VARIABLE ICC by Estimation Method",
subtitle="Relative Bias of Estimates")+
facet_wrap(.~Estimator)
ggplot(sdat, aes(y=RMSE))+
geom_boxplot()+
labs(y="Root Mean Square Error",
title="LATENT VARIABLE ICC by Estimation Method",
subtitle="Root Mean Square Error of Estimates")+
facet_wrap(.~Estimator)
ggplot(sdat, aes(y=Bias))+
geom_boxplot()+
labs(y="Sqaured Bias",
title="LATENT VARIABLE ICC by Estimation Method",
subtitle="Squared Bias of Estiamtes")+
facet_wrap(.~Estimator)
ggplot(sdat, aes(y=SampVar))+
geom_boxplot()+
labs(y="Sampling Variance",
title="LATENT VARIABLE ICC by Estimation Method",
subtitle="Sampling Variance of Estimates")+
facet_wrap(.~Estimator)
c <- sdat %>%
group_by(Estimator) %>%
summarise(est = mean(estMean),
RB = mean(RB),
RMSE = mean(RMSE),
Bias = mean(Bias),
SampVar =mean(SampVar))
kable(c, format='html', digits=3,
caption="Summary Indices of LATENT VARIABLE ICC by Estimation Method") %>%
kable_styling(full_width = T)| Estimator | est | RB | RMSE | Bias | SampVar |
|---|---|---|---|---|---|
| MLR | 0.303 | 8.218 | 0.006 | 0.001 | 0.006 |
| ULSMV | 0.308 | 9.481 | 0.007 | 0.001 | 0.006 |
| WLSMV | 0.287 | -0.585 | 0.007 | 0.001 | 0.006 |
Level-2 Sample Size
ggplot(sdat, aes(y=estMean))+
geom_boxplot()+
labs(y="Average Latent Variable ICC",
title="LATENT VARIABLE ICC by Level-2 Sample Size",
subtitle="Parameter Estimates")+
facet_wrap(.~N2)
ggplot(sdat, aes(y=estSD))+
geom_boxplot()+
labs(y="SD of Latent Variable ICC",
title="LATENT VARIABLE ICC by Level-2 Sample Size",
subtitle="Standard Deviation of Parameter Estimates")+
facet_wrap(.~N2)
ggplot(sdat, aes(y=RB))+
geom_boxplot()+
geom_hline(yintercept=-10, color="red", linetype="dashed")+
geom_hline(yintercept=10, color="red", linetype="dashed")+
labs(y="Relative Bias",
title="LATENT VARIABLE ICC by Level-2 Sample Size",
subtitle="Relative Bias Parameter Estimates")+
facet_wrap(.~N2)
ggplot(sdat, aes(y=RMSE))+
geom_boxplot()+
labs(y="Root Mean Square Error",
title="LATENT VARIABLE ICC by Level-2 Sample Size",
subtitle="Root Mean Square Error")+
facet_wrap(.~N2)
ggplot(sdat, aes(y=Bias))+
geom_boxplot()+
labs(y="Sqaured Bias",
title="LATENT VARIABLE ICC by Level-2 Sample Size",
subtitle="Squared Bias of Parameter Estimates")+
facet_wrap(.~N2)
ggplot(sdat, aes(y=SampVar))+
geom_boxplot()+
labs(y="Sampling Variance of Estimates",
title="LATENT VARIABLE ICC by Level-2 Sample Size",
subtitle="Sampling Variance of Parameter Estimates")+
facet_wrap(.~N2)
c <- sdat %>%
group_by(N2) %>%
summarise(est = mean(estMean),
RB = mean(RB),
RMSE = mean(RMSE),
Bias = mean(Bias),
SampVar =mean(SampVar))
kable(c, format='html', digits=3,
caption="Summary Indices of LATENT VARIABLE ICC by Level-2 Sample Size") %>%
kable_styling(full_width = T)| N2 | est | RB | RMSE | Bias | SampVar |
|---|---|---|---|---|---|
| 30 | 0.300 | 12.084 | 0.013 | 0.002 | 0.011 |
| 50 | 0.299 | 7.252 | 0.008 | 0.001 | 0.007 |
| 100 | 0.300 | 3.188 | 0.004 | 0.000 | 0.004 |
| 200 | 0.299 | 0.295 | 0.002 | 0.000 | 0.002 |
Level-1 Sample Size
ggplot(sdat, aes(y=estMean))+
geom_boxplot()+
labs(y="Average Latent Variable ICC",
title="LATENT VARIABLE ICC by Level-1",
subtitle="Parameter Estimates")+
facet_wrap(.~N1)
ggplot(sdat, aes(y=estSD))+
geom_boxplot()+
labs(y="SD of Latent Variable ICC",
title="LATENT VARIABLE ICC by Level-1 Sample Size",
subtitle="Standard Deviation of Parameter Estimates")+
facet_wrap(.~N1)
ggplot(sdat, aes(y=RB))+
geom_boxplot()+
geom_hline(yintercept=-10, color="red", linetype="dashed")+
geom_hline(yintercept=10, color="red", linetype="dashed")+
labs(y="Relative Bias",
title="LATENT VARIABLE ICC by Level-1 Sample Size",
subtitle="Relative Bias of Parameter Estimates")+
facet_wrap(.~N1)
ggplot(sdat, aes(y=RMSE))+
geom_boxplot()+
labs(y="Root Mean Square Error",
title="LATENT VARIABLE ICC by Level-1 Sample Size",
subtitle="Root Mean Square Error")+
facet_wrap(.~N1)
ggplot(sdat, aes(y=Bias))+
geom_boxplot()+
labs(y="Sqaured Bias",
title="LATENT VARIABLE ICC by Level-1 Sample Size",
subtitle="Squared Bias of Parameter Estimates")+
facet_wrap(.~N1)
ggplot(sdat, aes(y=SampVar))+
geom_boxplot()+
labs(y="Sampling Variance of Estimates",
title="LATENT VARIABLE ICC by Level-1 Sample Size",
subtitle="Sampling Variance of Parameter Estimates")+
facet_wrap(.~N1)
c <- sdat %>%
group_by(N1) %>%
summarise(est = mean(estMean),
RB = mean(RB),
RMSE = mean(RMSE),
Bias = mean(Bias),
SampVar =mean(SampVar))
kable(c, format='html', digits=3,
caption="Summary Indices of LATENT VARIABLE ICC by Level-1 Sample Size") %>%
kable_styling(full_width = T)| N1 | est | RB | RMSE | Bias | SampVar |
|---|---|---|---|---|---|
| 5 | 0.302 | 9.76 | 0.009 | 0.001 | 0.008 |
| 10 | 0.298 | 4.43 | 0.006 | 0.001 | 0.005 |
| 30 | 0.298 | 2.92 | 0.004 | 0.000 | 0.004 |
ICC Observed Variables
ggplot(sdat, aes(y=estMean))+
geom_boxplot()+
labs(y="Average Latent Variable ICC",
title="LATENT VARIABLE ICC by ICC of Observed Variables",
subtitle="Parameter Estimates")+
facet_wrap(.~ICC_OV)
ggplot(sdat, aes(y=estSD))+
geom_boxplot()+
labs(y="SD of Latent Variable ICC",
title="LATENT VARIABLE ICC by ICC of Observed Variables",
subtitle="Standard Deviation of Parameter Estimates")+
facet_wrap(.~ICC_OV)
ggplot(sdat, aes(y=RB))+
geom_boxplot()+
geom_hline(yintercept=-10, color="red", linetype="dashed")+
geom_hline(yintercept=10, color="red", linetype="dashed")+
labs(y="Relative Bias",
title="LATENT VARIABLE ICC by ICC of Observed Variables",
subtitle="Relative Bias of Parameter Estimates")+
facet_wrap(.~ICC_OV)
ggplot(sdat, aes(y=RMSE))+
geom_boxplot()+
labs(y="Root Mean Square Error",
title="LATENT VARIABLE ICC by ICC of Observed Variables",
subtitle="Root Mean Square Error of Parameter Estimates")+
facet_wrap(.~ICC_OV)
ggplot(sdat, aes(y=Bias))+
geom_boxplot()+
labs(y="Sqaured Bias",
title="LATENT VARIABLE ICC by ICC of Observed Variables",
subtitle="Squared Bias of Parameter Estimates")+
facet_wrap(.~ICC_OV)
ggplot(sdat, aes(y=SampVar))+
geom_boxplot()+
labs(y="Sampling Variance of Estimates",
title="LATENT VARIABLE ICC by ICC of Observed Variables",
subtitle="Sampling Variance of Parameter Estimates")+
facet_wrap(.~ICC_OV)
c <- sdat %>%
group_by(ICC_OV) %>%
summarise(est = mean(estMean),
RB = mean(RB),
RMSE = mean(RMSE),
Bias = mean(Bias),
SampVar =mean(SampVar))
kable(c, format='html', digits=3, caption="Summary Indices of LATENT VARIABLE ICC by ICC of Observed Variables") %>%
kable_styling(full_width = T)| ICC_OV | est | RB | RMSE | Bias | SampVar |
|---|---|---|---|---|---|
| 0.1 | 0.289 | -4.29 | 0.004 | 0.000 | 0.003 |
| 0.3 | 0.297 | 3.33 | 0.006 | 0.000 | 0.005 |
| 0.5 | 0.311 | 18.08 | 0.010 | 0.002 | 0.008 |
ICC Latent Variables
ggplot(sdat, aes(y=estMean))+
geom_boxplot()+
labs(y="Average Latent Variable ICC",
title="LATENT VARIABLE ICC by ICC of Latent Variables",
subtitle="Parameter Estimates")+
facet_wrap(.~ICC_LV)
ggplot(sdat, aes(y=estSD))+
geom_boxplot()+
labs(y="SD of Latent Variable ICC",
title="LATENT VARIABLE ICC by ICC of Latent Variables",
subtitle="Standard Deviation of Parameter Estimates")+
facet_wrap(.~ICC_LV)
ggplot(sdat, aes(y=RB))+
geom_boxplot()+
geom_hline(yintercept=-10, color="red", linetype="dashed")+
geom_hline(yintercept=10, color="red", linetype="dashed")+
labs(y="Relative Bias",
title="LATENT VARIABLE ICC by ICC of Latent Variables",
subtitle="Relative Bias of Parameter Estimates")+
facet_wrap(.~ICC_LV)
ggplot(sdat, aes(y=RMSE))+
geom_boxplot()+
labs(y="Root Mean Square Error",
title="LATENT VARIABLE ICC by ICC of Latent Variables",
subtitle="Root Mean Square Error of Parameter Estimates")+
facet_wrap(.~ICC_LV)
ggplot(sdat, aes(y=Bias))+
geom_boxplot()+
labs(y="Sqaured Bias",
title="LATENT VARIABLE ICC by ICC of Latent Variables",
subtitle="Squared Bias of Parameter Estimates")+
facet_wrap(.~ICC_LV)
ggplot(sdat, aes(y=SampVar))+
geom_boxplot()+
labs(y="Sampling Variance of Estimates",
title="LATENT VARIABLE ICC by ICC of Latent Variables",
subtitle="Sampling Variance of Parameter Estimates")+
facet_wrap(.~ICC_LV)
c <- sdat %>%
group_by(ICC_LV) %>%
summarise(est = mean(estMean),
RB = mean(RB),
RMSE = mean(RMSE),
Bias = mean(Bias),
SampVar =mean(SampVar))
kable(c, format='html', digits=3,
caption="Summary Indices of LATENT VARIABLE ICC by ICC of Latent Variables") %>%
kable_styling(full_width = T)| ICC_LV | est | RB | RMSE | Bias | SampVar |
|---|---|---|---|---|---|
| 0.1 | 0.115 | 14.68 | 0.006 | 0.001 | 0.005 |
| 0.5 | 0.484 | -3.27 | 0.007 | 0.001 | 0.007 |
By Estimation Method and Sample Sizes
Estimation Method & Level-2 Sample Size
ggplot(sdat, aes(y=estMean))+
geom_boxplot()+
labs(y="Average Latent Variable ICC")+
facet_grid(N2~Estimator)
ggplot(sdat, aes(y=RB))+
geom_boxplot()+
geom_hline(yintercept=-10, color="red", linetype="dashed")+
geom_hline(yintercept=10, color="red", linetype="dashed")+
labs(y="Relative Bias")+
facet_grid(N2~Estimator)
ggplot(sdat, aes(y=RMSE))+
geom_boxplot()+
labs(y="Root Mean Square Error")+
facet_grid(N2~Estimator)
c <- sdat %>%
group_by(Estimator, N2) %>%
summarise(est = mean(estMean),
RB = mean(RB),
RMSE = mean(RMSE),
Bias = mean(Bias),
SampVar =mean(SampVar))
c1 <- cbind(c[ c$Estimator == 'MLR', c( 'N2', 'est', 'RB', 'RMSE')],
c[ c$Estimator == 'ULSMV', c('est', 'RB', 'RMSE')],
c[ c$Estimator == 'WLSMV', c('est', 'RB', 'RMSE')])
colnames(c1) <- c('N2', rep(c('est', 'RB', 'RMSE'), 3))
kable(c1, format='html', digits=3, row.names = F) %>%
kable_styling(full_width = T) %>%
add_header_above(c(' '=1, 'MLR'=3, 'ULSMV'=3, 'WLSMV'=3))| N2 | est | RB | RMSE | est | RB | RMSE | est | RB | RMSE |
|---|---|---|---|---|---|---|---|---|---|
| 30 | 0.307 | 16.47 | 0.012 | 0.319 | 20.55 | 0.013 | 0.273 | -0.777 | 0.013 |
| 50 | 0.304 | 10.57 | 0.007 | 0.308 | 10.95 | 0.008 | 0.284 | 0.230 | 0.008 |
| 100 | 0.302 | 4.82 | 0.004 | 0.304 | 5.06 | 0.004 | 0.293 | -0.318 | 0.004 |
| 200 | 0.300 | 1.01 | 0.002 | 0.301 | 1.35 | 0.002 | 0.296 | -1.473 | 0.002 |
Estimation Method & Level-1 Sample Size
ggplot(sdat, aes(y=estMean))+
geom_boxplot()+
labs(y="Average Latent Variable ICC")+
facet_grid(N1~Estimator)
ggplot(sdat, aes(y=RB))+
geom_boxplot()+
geom_hline(yintercept=-10, color="red", linetype="dashed")+
geom_hline(yintercept=10, color="red", linetype="dashed")+
labs(y="Relative Bias")+
facet_grid(N1~Estimator)
ggplot(sdat, aes(y=RMSE))+
geom_boxplot()+
labs(y="Root Mean Square Error")+
facet_grid(N1~Estimator)
c <- sdat %>%
group_by(Estimator, N1) %>%
summarise(est = mean(estMean),
RB = mean(RB),
RMSE = mean(RMSE),
Bias = mean(Bias),
SampVar =mean(SampVar))
c1 <- cbind(c[ c$Estimator == 'MLR', c( 'N1', 'est', 'RB', 'RMSE')],
c[ c$Estimator == 'ULSMV', c('est', 'RB', 'RMSE')],
c[ c$Estimator == 'WLSMV', c('est', 'RB', 'RMSE')])
colnames(c1) <- c('N1', rep(c('est', 'RB', 'RMSE'), 3))
kable(c1, format='html', digits=3, row.names = F) %>%
kable_styling(full_width = T) %>%
add_header_above(c(' '=1, 'MLR'=3, 'ULSMV'=3, 'WLSMV'=3))| N1 | est | RB | RMSE | est | RB | RMSE | est | RB | RMSE |
|---|---|---|---|---|---|---|---|---|---|
| 5 | 0.307 | 13.40 | 0.009 | 0.313 | 14.66 | 0.010 | 0.285 | 1.24 | 0.009 |
| 10 | 0.302 | 7.00 | 0.006 | 0.307 | 8.18 | 0.006 | 0.285 | -1.88 | 0.006 |
| 30 | 0.300 | 4.25 | 0.004 | 0.304 | 5.60 | 0.004 | 0.290 | -1.11 | 0.005 |
Estimation Method, Level-2 Sample Size & Level-1 Sample Size
ggplot(sdat, aes(y=estMean,x=N1, group=N1))+
geom_boxplot()+
labs(y="Average Latent Variable ICC")+
facet_grid(N2~Estimator)
ggplot(sdat, aes(y=RB,x=N1, group=N1))+
geom_boxplot()+
geom_hline(yintercept=-10, color="red", linetype="dashed")+
geom_hline(yintercept=10, color="red", linetype="dashed")+
labs(y="Relative Bias")+
facet_grid(N2~Estimator)
ggplot(sdat, aes(y=RMSE,x=N1, group=N1))+
geom_boxplot()+
labs(y="Root Mean Square Error")+
facet_grid(N2~Estimator)
c <- sdat %>%
group_by(Estimator, N2, N1) %>%
summarise(est = mean(estMean),
RB = mean(RB),
RMSE = mean(RMSE),
Bias = mean(Bias),
SampVar =mean(SampVar))
c1 <- cbind(c[ c$Estimator == 'MLR', c( 'N2','N1', 'est', 'RB', 'RMSE')],
c[ c$Estimator == 'ULSMV', c('est', 'RB', 'RMSE')],
c[ c$Estimator == 'WLSMV', c('est', 'RB', 'RMSE')])
colnames(c1) <- c('N2','N1', rep(c('est', 'RB', 'RMSE'), 3))
kable(c1, format='html', digits=3, row.names = F) %>%
kable_styling(full_width = T) %>%
add_header_above(c(' '=2, 'MLR'=3, 'ULSMV'=3, 'WLSMV'=3))| N2 | N1 | est | RB | RMSE | est | RB | RMSE | est | RB | RMSE |
|---|---|---|---|---|---|---|---|---|---|---|
| 30 | 5 | 0.316 | 25.561 | 0.017 | 0.333 | 32.294 | 0.019 | 0.270 | 1.960 | 0.018 |
| 30 | 10 | 0.304 | 14.287 | 0.012 | 0.313 | 17.037 | 0.012 | 0.268 | -3.237 | 0.013 |
| 30 | 30 | 0.302 | 9.572 | 0.008 | 0.309 | 12.335 | 0.008 | 0.281 | -1.055 | 0.009 |
| 50 | 5 | 0.308 | 16.322 | 0.011 | 0.309 | 15.309 | 0.011 | 0.279 | 2.414 | 0.011 |
| 50 | 10 | 0.304 | 9.775 | 0.007 | 0.309 | 10.590 | 0.007 | 0.284 | -1.072 | 0.007 |
| 50 | 30 | 0.301 | 5.621 | 0.005 | 0.305 | 6.960 | 0.005 | 0.289 | -0.653 | 0.005 |
| 100 | 5 | 0.305 | 8.737 | 0.005 | 0.307 | 8.220 | 0.005 | 0.293 | 1.102 | 0.005 |
| 100 | 10 | 0.301 | 3.215 | 0.003 | 0.303 | 3.799 | 0.003 | 0.292 | -1.678 | 0.003 |
| 100 | 30 | 0.300 | 2.507 | 0.003 | 0.302 | 3.169 | 0.003 | 0.295 | -0.379 | 0.003 |
| 200 | 5 | 0.302 | 2.962 | 0.003 | 0.303 | 2.818 | 0.003 | 0.296 | -0.534 | 0.003 |
| 200 | 10 | 0.299 | 0.744 | 0.002 | 0.301 | 1.290 | 0.002 | 0.296 | -1.533 | 0.002 |
| 200 | 30 | 0.298 | -0.685 | 0.001 | 0.300 | -0.052 | 0.001 | 0.295 | -2.352 | 0.001 |
Relative Efficiency by Sample Sizes
sdat <- filter(result, Variable %like% 'icc_lv')
c <- sdat %>%
group_by(Estimator, N2, N1) %>%
summarise(mu = weighted.mean(muRE, wi),
mw = weighted.mean(mwRE, wi),
uw = weighted.mean(uwRE, wi))
c1 <- cbind(c[ c$Estimator == 'MLR', c( 'N2','N1', 'mu', 'mw', 'uw')])
colnames(c1) <- c('N2','N1',c('MLR/ULSMV', 'MLR/WLSMV', 'ULSMV/WLSMV'))
kable(c1, format='html', digits=3, row.names = F) %>%
kable_styling(full_width = T)| N2 | N1 | MLR/ULSMV | MLR/WLSMV | ULSMV/WLSMV |
|---|---|---|---|---|
| 30 | 5 | 1.982 | 1.865 | 1.054 |
| 30 | 10 | 1.199 | 1.211 | 1.026 |
| 30 | 30 | 1.077 | 1.122 | 1.036 |
| 50 | 5 | 1.337 | 1.449 | 1.080 |
| 50 | 10 | 1.088 | 1.126 | 1.030 |
| 50 | 30 | 1.020 | 1.022 | 1.003 |
| 100 | 5 | 1.119 | 1.134 | 1.016 |
| 100 | 10 | 1.030 | 1.058 | 1.025 |
| 100 | 30 | 1.003 | 0.998 | 0.996 |
| 200 | 5 | 1.033 | 1.052 | 1.017 |
| 200 | 10 | 1.004 | 1.015 | 1.011 |
| 200 | 30 | 0.999 | 0.992 | 0.993 |
Relative Efficiency by All Conditions
c <- sdat %>%
group_by(Estimator, N2, N1, ICC_OV, ICC_LV) %>%
summarise(mu = weighted.mean(muRE, wi),
mw = weighted.mean(mwRE, wi),
uw = weighted.mean(uwRE, wi))
c1 <- cbind(c[ c$Estimator == 'MLR', c( 'N2','N1','ICC_OV', 'ICC_LV', 'mu', 'mw', 'uw')])
colnames(c1) <- c('N2','N1', 'ICC_OV', 'ICC_LV',c('MLR/ULSMV', 'MLR/WLSMV', 'ULSMV/WLSMV'))
kable(c1, format='html', digits=3, row.names = F) %>%
kable_styling(full_width = T)| N2 | N1 | ICC_OV | ICC_LV | MLR/ULSMV | MLR/WLSMV | ULSMV/WLSMV |
|---|---|---|---|---|---|---|
| 30 | 5 | 0.1 | 0.1 | 5.621 | 4.385 | 0.784 |
| 30 | 5 | 0.1 | 0.5 | 3.549 | 3.452 | 0.973 |
| 30 | 5 | 0.3 | 0.1 | 1.142 | 1.661 | 1.454 |
| 30 | 5 | 0.3 | 0.5 | 1.017 | 0.846 | 0.833 |
| 30 | 5 | 0.5 | 0.1 | 0.846 | 1.735 | 2.054 |
| 30 | 5 | 0.5 | 0.5 | 1.005 | 0.844 | 0.839 |
| 30 | 10 | 0.1 | 0.1 | 1.488 | 1.377 | 0.926 |
| 30 | 10 | 0.1 | 0.5 | 1.925 | 1.944 | 1.008 |
| 30 | 10 | 0.3 | 0.1 | 1.005 | 1.407 | 1.401 |
| 30 | 10 | 0.3 | 0.5 | 1.037 | 0.897 | 0.865 |
| 30 | 10 | 0.5 | 0.1 | 0.903 | 1.403 | 1.554 |
| 30 | 10 | 0.5 | 0.5 | 1.068 | 0.853 | 0.798 |
| 30 | 30 | 0.1 | 0.1 | 1.058 | 1.007 | 0.951 |
| 30 | 30 | 0.1 | 0.5 | 1.324 | 1.651 | 1.247 |
| 30 | 30 | 0.3 | 0.1 | 1.012 | 1.213 | 1.199 |
| 30 | 30 | 0.3 | 0.5 | 1.022 | 0.897 | 0.878 |
| 30 | 30 | 0.5 | 0.1 | 0.873 | 1.116 | 1.280 |
| 30 | 30 | 0.5 | 0.5 | 1.057 | 0.899 | 0.851 |
| 50 | 5 | 0.1 | 0.1 | 2.361 | 2.323 | 0.984 |
| 50 | 5 | 0.1 | 0.5 | 2.235 | 2.803 | 1.253 |
| 50 | 5 | 0.3 | 0.1 | 1.017 | 1.375 | 1.352 |
| 50 | 5 | 0.3 | 0.5 | 1.003 | 0.914 | 0.912 |
| 50 | 5 | 0.5 | 0.1 | 0.939 | 1.404 | 1.495 |
| 50 | 5 | 0.5 | 0.5 | 1.007 | 0.864 | 0.858 |
| 50 | 10 | 0.1 | 0.1 | 1.139 | 1.070 | 0.940 |
| 50 | 10 | 0.1 | 0.5 | 1.364 | 1.669 | 1.225 |
| 50 | 10 | 0.3 | 0.1 | 1.025 | 1.190 | 1.162 |
| 50 | 10 | 0.3 | 0.5 | 1.018 | 0.921 | 0.905 |
| 50 | 10 | 0.5 | 0.1 | 0.923 | 1.234 | 1.338 |
| 50 | 10 | 0.5 | 0.5 | 1.028 | 0.867 | 0.844 |
| 50 | 30 | 0.1 | 0.1 | 1.010 | 0.960 | 0.950 |
| 50 | 30 | 0.1 | 0.5 | 1.077 | 1.241 | 1.152 |
| 50 | 30 | 0.3 | 0.1 | 0.984 | 1.051 | 1.068 |
| 50 | 30 | 0.3 | 0.5 | 1.020 | 0.914 | 0.897 |
| 50 | 30 | 0.5 | 0.1 | 0.929 | 1.083 | 1.166 |
| 50 | 30 | 0.5 | 0.5 | 1.060 | 0.913 | 0.861 |
| 100 | 5 | 0.1 | 0.1 | 1.314 | 1.207 | 0.919 |
| 100 | 5 | 0.1 | 0.5 | 1.481 | 1.553 | 1.049 |
| 100 | 5 | 0.3 | 0.1 | 0.989 | 1.127 | 1.139 |
| 100 | 5 | 0.3 | 0.5 | 1.011 | 0.944 | 0.933 |
| 100 | 5 | 0.5 | 0.1 | 0.959 | 1.158 | 1.208 |
| 100 | 5 | 0.5 | 0.5 | 1.013 | 0.953 | 0.940 |
| 100 | 10 | 0.1 | 0.1 | 1.024 | 1.002 | 0.978 |
| 100 | 10 | 0.1 | 0.5 | 1.126 | 1.308 | 1.161 |
| 100 | 10 | 0.3 | 0.1 | 1.012 | 1.068 | 1.056 |
| 100 | 10 | 0.3 | 0.5 | 1.003 | 0.960 | 0.957 |
| 100 | 10 | 0.5 | 0.1 | 0.973 | 1.088 | 1.118 |
| 100 | 10 | 0.5 | 0.5 | 1.023 | 0.935 | 0.914 |
| 100 | 30 | 0.1 | 0.1 | 1.004 | 0.979 | 0.974 |
| 100 | 30 | 0.1 | 0.5 | 1.018 | 1.074 | 1.055 |
| 100 | 30 | 0.3 | 0.1 | 1.002 | 1.014 | 1.012 |
| 100 | 30 | 0.3 | 0.5 | 0.997 | 0.960 | 0.962 |
| 100 | 30 | 0.5 | 0.1 | 0.946 | 1.038 | 1.097 |
| 100 | 30 | 0.5 | 0.5 | 1.034 | 0.936 | 0.905 |
| 200 | 5 | 0.1 | 0.1 | 1.044 | 1.029 | 0.986 |
| 200 | 5 | 0.1 | 0.5 | 1.141 | 1.236 | 1.083 |
| 200 | 5 | 0.3 | 0.1 | 1.016 | 1.037 | 1.020 |
| 200 | 5 | 0.3 | 0.5 | 0.998 | 0.978 | 0.979 |
| 200 | 5 | 0.5 | 0.1 | 0.979 | 1.059 | 1.082 |
| 200 | 5 | 0.5 | 0.5 | 1.008 | 0.978 | 0.970 |
| 200 | 10 | 0.1 | 0.1 | 1.008 | 0.994 | 0.986 |
| 200 | 10 | 0.1 | 0.5 | 1.016 | 1.096 | 1.079 |
| 200 | 10 | 0.3 | 0.1 | 0.997 | 1.007 | 1.010 |
| 200 | 10 | 0.3 | 0.5 | 1.004 | 0.988 | 0.984 |
| 200 | 10 | 0.5 | 0.1 | 0.980 | 1.037 | 1.059 |
| 200 | 10 | 0.5 | 0.5 | 1.012 | 0.970 | 0.958 |
| 200 | 30 | 0.1 | 0.1 | 1.003 | 1.000 | 0.996 |
| 200 | 30 | 0.1 | 0.5 | 1.006 | 1.005 | 0.999 |
| 200 | 30 | 0.3 | 0.1 | 0.988 | 1.000 | 1.012 |
| 200 | 30 | 0.3 | 0.5 | 0.999 | 0.974 | 0.975 |
| 200 | 30 | 0.5 | 0.1 | 0.991 | 1.012 | 1.022 |
| 200 | 30 | 0.5 | 0.5 | 1.007 | 0.965 | 0.958 |
Manuscript Table
c <- sdat %>%
group_by(Estimator, N2, N1) %>%
summarise(est = weighted.mean(estMean, wi),
RB = weighted.mean(RB, wi),
RMSE = weighted.mean(RMSE, wi))
c1 <- cbind(c[ c$Estimator == 'MLR', c( 'N2','N1', 'est', 'RB', 'RMSE')],
c[ c$Estimator == 'ULSMV', c('est', 'RB', 'RMSE')],
c[ c$Estimator == 'WLSMV', c('est', 'RB', 'RMSE')])
colnames(c1) <- c('N2','N1', rep(c('est', 'RB', 'RMSE'), 3))
kable(c1, format='html', digits=3, row.names = F) %>%
kable_styling(full_width = T) %>%
add_header_above(c(' '=2, 'MLR'=3, 'ULSMV'=3, 'WLSMV'=3))| N2 | N1 | est | RB | RMSE | est | RB | RMSE | est | RB | RMSE |
|---|---|---|---|---|---|---|---|---|---|---|
| 30 | 5 | 0.348 | 16.522 | 0.017 | 0.406 | 26.150 | 0.022 | 0.344 | -4.953 | 0.025 |
| 30 | 10 | 0.336 | 8.725 | 0.012 | 0.351 | 14.435 | 0.013 | 0.309 | -5.982 | 0.015 |
| 30 | 30 | 0.328 | 4.342 | 0.008 | 0.323 | 7.871 | 0.008 | 0.287 | -4.978 | 0.009 |
| 50 | 5 | 0.344 | 11.310 | 0.011 | 0.365 | 15.943 | 0.012 | 0.342 | 0.381 | 0.014 |
| 50 | 10 | 0.330 | 5.927 | 0.007 | 0.330 | 7.873 | 0.007 | 0.301 | -3.748 | 0.008 |
| 50 | 30 | 0.319 | 3.155 | 0.005 | 0.318 | 4.464 | 0.005 | 0.294 | -2.975 | 0.005 |
| 100 | 5 | 0.328 | 6.820 | 0.005 | 0.329 | 7.804 | 0.006 | 0.314 | 0.356 | 0.005 |
| 100 | 10 | 0.316 | 2.147 | 0.003 | 0.312 | 2.818 | 0.003 | 0.294 | -2.575 | 0.003 |
| 100 | 30 | 0.310 | 1.549 | 0.002 | 0.311 | 2.268 | 0.002 | 0.299 | -1.430 | 0.003 |
| 200 | 5 | 0.314 | 2.398 | 0.003 | 0.310 | 2.458 | 0.003 | 0.301 | -0.893 | 0.003 |
| 200 | 10 | 0.307 | 0.496 | 0.002 | 0.308 | 0.993 | 0.002 | 0.299 | -1.748 | 0.002 |
| 200 | 30 | 0.303 | -0.736 | 0.001 | 0.305 | -0.149 | 0.001 | 0.300 | -2.364 | 0.001 |
print(xtable(c1, digits = 3,align=c("l", "l", "l", rep("r",9)),
display=c("s", "d","d", rep("f",9)),
caption="Mean Latent Variable ICC, Relative Bias, and RMSE by Estimation Method",
label="tb:fct"),
booktabs = T, include.rownames = F,
caption.placement = "top")% latex table generated in R 3.6.3 by xtable 1.8-4 package
% Mon Jun 01 23:24:57 2020
\begin{table}[ht]
\centering
\caption{Mean Latent Variable ICC, Relative Bias, and RMSE by Estimation Method}
\label{tb:fct}
\begin{tabular}{llrrrrrrrrr}
\toprule
N2 & N1 & est & RB & RMSE & est & RB & RMSE & est & RB & RMSE \\
\midrule
30 & 5 & 0.348 & 16.522 & 0.017 & 0.406 & 26.150 & 0.022 & 0.344 & -4.953 & 0.025 \\
30 & 10 & 0.336 & 8.725 & 0.012 & 0.351 & 14.435 & 0.013 & 0.309 & -5.982 & 0.015 \\
30 & 30 & 0.328 & 4.342 & 0.008 & 0.323 & 7.871 & 0.008 & 0.287 & -4.978 & 0.009 \\
50 & 5 & 0.344 & 11.310 & 0.011 & 0.365 & 15.943 & 0.012 & 0.342 & 0.381 & 0.014 \\
50 & 10 & 0.330 & 5.927 & 0.007 & 0.330 & 7.873 & 0.007 & 0.301 & -3.748 & 0.008 \\
50 & 30 & 0.319 & 3.155 & 0.005 & 0.318 & 4.464 & 0.005 & 0.294 & -2.975 & 0.005 \\
100 & 5 & 0.328 & 6.820 & 0.005 & 0.329 & 7.804 & 0.006 & 0.314 & 0.356 & 0.005 \\
100 & 10 & 0.316 & 2.147 & 0.003 & 0.312 & 2.818 & 0.003 & 0.294 & -2.575 & 0.003 \\
100 & 30 & 0.310 & 1.549 & 0.002 & 0.311 & 2.268 & 0.002 & 0.299 & -1.430 & 0.003 \\
200 & 5 & 0.314 & 2.398 & 0.003 & 0.310 & 2.458 & 0.003 & 0.301 & -0.893 & 0.003 \\
200 & 10 & 0.307 & 0.496 & 0.002 & 0.308 & 0.993 & 0.002 & 0.299 & -1.748 & 0.002 \\
200 & 30 & 0.303 & -0.736 & 0.001 & 0.305 & -0.149 & 0.001 & 0.300 & -2.364 & 0.001 \\
\bottomrule
\end{tabular}
\end{table}
sessionInfo()R version 3.6.3 (2020-02-29)
Platform: x86_64-w64-mingw32/x64 (64-bit)
Running under: Windows 10 x64 (build 18362)
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] xtable_1.8-4 kableExtra_1.1.0 cowplot_1.0.0
[4] MplusAutomation_0.7-3 data.table_1.12.8 patchwork_1.0.0
[7] forcats_0.5.0 stringr_1.4.0 dplyr_0.8.5
[10] purrr_0.3.4 readr_1.3.1 tidyr_1.1.0
[13] tibble_3.0.1 ggplot2_3.3.0 tidyverse_1.3.0
[16] workflowr_1.6.2
loaded via a namespace (and not attached):
[1] httr_1.4.1 jsonlite_1.6.1 viridisLite_0.3.0 gsubfn_0.7
[5] modelr_0.1.8 assertthat_0.2.1 highr_0.8 pander_0.6.3
[9] blob_1.2.1 cellranger_1.1.0 yaml_2.2.1 pillar_1.4.4
[13] backports_1.1.7 lattice_0.20-38 glue_1.4.1 digest_0.6.25
[17] promises_1.1.0 rvest_0.3.5 colorspace_1.4-1 htmltools_0.4.0
[21] httpuv_1.5.2 plyr_1.8.6 pkgconfig_2.0.3 broom_0.5.6
[25] haven_2.3.0 scales_1.1.1 webshot_0.5.2 later_1.0.0
[29] git2r_0.27.1 farver_2.0.3 generics_0.0.2 ellipsis_0.3.1
[33] withr_2.2.0 cli_2.0.2 proto_1.0.0 magrittr_1.5
[37] crayon_1.3.4 readxl_1.3.1 evaluate_0.14 fs_1.4.1
[41] fansi_0.4.1 nlme_3.1-144 xml2_1.3.2 tools_3.6.3
[45] hms_0.5.3 lifecycle_0.2.0 munsell_0.5.0 reprex_0.3.0
[49] compiler_3.6.3 rlang_0.4.6 grid_3.6.3 rstudioapi_0.11
[53] texreg_1.36.23 labeling_0.3 rmarkdown_2.1 boot_1.3-24
[57] gtable_0.3.0 DBI_1.1.0 R6_2.4.1 lubridate_1.7.8
[61] knitr_1.28 rprojroot_1.3-2 stringi_1.4.6 parallel_3.6.3
[65] Rcpp_1.0.4.6 vctrs_0.3.0 dbplyr_1.4.4 tidyselect_1.1.0
[69] xfun_0.14 coda_0.19-3