ML-CFA: Parameter Bias - Factor (co)Variances
Last updated: 2020-06-10
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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 whisker_0.4 blob_1.2.1
[21] texreg_1.36.23 gsubfn_0.7 rmarkdown_2.1 proto_1.0.0
[25] webshot_0.5.2 pander_0.6.3 munsell_0.5.0 broom_0.5.6
[29] compiler_3.6.3 httpuv_1.5.2 modelr_0.1.8 xfun_0.14
[33] pkgconfig_2.0.3 htmltools_0.4.0 tidyselect_1.1.0 viridisLite_0.3.0
[37] fansi_0.4.1 crayon_1.3.4 dbplyr_1.4.4 withr_2.2.0
[41] later_1.0.0 grid_3.6.3 nlme_3.1-144 jsonlite_1.6.1
[45] gtable_0.3.0 lifecycle_0.2.0 DBI_1.1.0 git2r_0.27.1
[49] magrittr_1.5 scales_1.1.1 cli_2.0.2 stringi_1.4.6
[53] fs_1.4.1 promises_1.1.0 xml2_1.3.2 ellipsis_0.3.1
[57] generics_0.0.2 vctrs_0.3.0 boot_1.3-24 tools_3.6.3
[61] glue_1.4.1 hms_0.5.3 parallel_3.6.3 yaml_2.2.1
[65] colorspace_1.4-1 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).
Level-2 Factor Covariance
sdat <- filter(result, Variable %in% c("psiB12"))
sdat <- sdat %>%
mutate(TrueValue = factor(TrueValue))
TRUEVALUE <- as.numeric(levels(sdat$TrueValue))
p1 <- ggplot(sdat, aes(y=estMean, x=TrueValue, group=TrueValue))+
geom_boxplot()+
geom_hline(yintercept = TRUEVALUE, color="red")+
labs(y="Average Level-2 Factor Covariance")
p2 <- ggplot(sdat, aes(y=estSD, x=TrueValue, group=TrueValue))+
geom_boxplot()+
labs(y="SD of Level-2 Factor Covariance")
p3 <- ggplot(sdat, aes(y=RB, x=TrueValue, group=TrueValue))+
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, x=TrueValue, group=TrueValue))+
geom_boxplot()+
labs(y="Root Mean Square Error")
p5 <- ggplot(sdat, aes(y=Bias, x=TrueValue, group=TrueValue))+
geom_boxplot()+
labs(y="Sqaured Bias")
p6 <- ggplot(sdat, aes(y=SampVar, x=TrueValue, group=TrueValue))+
geom_boxplot()+
labs(y="Sampling Variance of Estimates")
p <- (p1 + p2 + p3)/(p4 + p5 + p6) +
plot_annotation(title="Summarizing bias indices of LEVEL-2 FACTOR COVARIANCE")
p
Single Condition Breakdown
Estimation Method
ggplot(sdat, aes(y=estMean, x=TrueValue, group=TrueValue))+
geom_boxplot()+
geom_hline(yintercept = TRUEVALUE, color="red")+
labs(y="Average Level-2 Factor Covariance",
title="LEVEL-2 FACTOR COVARIANCE by Estimation Method",
subtitle="Parameter Estimates")+
facet_wrap(.~Estimator)
ggplot(sdat, aes(y=estSD, x=TrueValue, group=TrueValue))+
geom_boxplot()+
labs(y="SD of Level-2 Factor Covariances",
title="LEVEL-2 FACTOR COVARIANCE by Estimation Method",
subtitle="Standard Deviation of Estimates")+
facet_wrap(.~Estimator)
ggplot(sdat, aes(y=RB, x=TrueValue, group=TrueValue))+
geom_boxplot()+
geom_hline(yintercept=-10, color="red", linetype="dashed")+
geom_hline(yintercept=10, color="red", linetype="dashed")+
labs(y="Relative Bias",
title="LEVEL-2 FACTOR COVARIANCE by Estimation Method",
subtitle="Relative Bias of Estimates")+
facet_wrap(.~Estimator)
ggplot(sdat, aes(y=RMSE, x=TrueValue, group=TrueValue))+
geom_boxplot()+
labs(y="Root Mean Square Error",
title="LEVEL-2 FACTOR COVARIANCE by Estimation Method",
subtitle="Root Mean Square Error of Estimates")+
facet_wrap(.~Estimator)
ggplot(sdat, aes(y=Bias, x=TrueValue, group=TrueValue))+
geom_boxplot()+
labs(y="Sqaured Bias",
title="LEVEL-2 FACTOR COVARIANCE by Estimation Method",
subtitle="Squared Bias of Estiamtes")+
facet_wrap(.~Estimator)
ggplot(sdat, aes(y=SampVar, x=TrueValue, group=TrueValue))+
geom_boxplot()+
labs(y="Sampling Variance",
title="LEVEL-2 FACTOR COVARIANCE by Estimation Method",
subtitle="Sampling Variance of Estimates")+
facet_wrap(.~Estimator)
c <- sdat %>%
group_by(Estimator, TrueValue) %>%
summarise(est = weighted.mean(estMean, wi),
RB = weighted.mean(RB, wi),
RMSE = weighted.mean(RMSE, wi),
Bias = weighted.mean(Bias, wi),
SampVar =weighted.mean(SampVar, wi))
kable(c, format='html', digits=3,
caption="Summary Indices of LEVEL-2 FACTOR COVARIANCE by Estimation Method") %>%
kable_styling(full_width = T)| Estimator | TrueValue | est | RB | RMSE | Bias | SampVar |
|---|---|---|---|---|---|---|
| MLR | 0.0333 | 0.032 | -4.29 | 0.006 | 0.000 | 0.006 |
| MLR | 0.3 | 0.295 | -1.66 | 0.041 | 0.000 | 0.041 |
| ULSMV | 0.0333 | 0.032 | -4.57 | 0.009 | 0.000 | 0.009 |
| ULSMV | 0.3 | 0.318 | 5.91 | 0.050 | 0.001 | 0.049 |
| WLSMV | 0.0333 | 0.026 | -21.04 | 0.004 | 0.000 | 0.004 |
| WLSMV | 0.3 | 0.271 | -9.62 | 0.035 | 0.001 | 0.034 |
Level-2 Sample Size
ggplot(sdat, aes(y=estMean, x=TrueValue, group=TrueValue))+
geom_boxplot()+
geom_hline(yintercept = TRUEVALUE, color="red")+
labs(y="Average Level-2 Factor Covariance",
title="LEVEL-2 FACTOR COVARIANCE by Level-2 Sample Size",
subtitle="Parameter Estimates")+
facet_wrap(.~N2)
ggplot(sdat, aes(y=estSD, x=TrueValue, group=TrueValue))+
geom_boxplot()+
labs(y="SD of Level-2 Factor Covariances",
title="LEVEL-2 FACTOR COVARIANCE by Level-2 Sample Size",
subtitle="Standard Deviation of Parameter Estimates")+
facet_wrap(.~N2)
ggplot(sdat, aes(y=RB, x=TrueValue, group=TrueValue))+
geom_boxplot()+
geom_hline(yintercept=-10, color="red", linetype="dashed")+
geom_hline(yintercept=10, color="red", linetype="dashed")+
labs(y="Relative Bias",
title="LEVEL-2 FACTOR COVARIANCE by Level-2 Sample Size",
subtitle="Relative Bias Parameter Estimates")+
facet_wrap(.~N2)
ggplot(sdat, aes(y=RMSE, x=TrueValue, group=TrueValue))+
geom_boxplot()+
labs(y="Root Mean Square Error",
title="LEVEL-2 FACTOR COVARIANCE by Level-2 Sample Size",
subtitle="Root Mean Square Error")+
facet_wrap(.~N2)
ggplot(sdat, aes(y=Bias, x=TrueValue, group=TrueValue))+
geom_boxplot()+
labs(y="Sqaured Bias",
title="LEVEL-2 FACTOR COVARIANCE by Level-2 Sample Size",
subtitle="Squared Bias of Parameter Estimates")+
facet_wrap(.~N2)
ggplot(sdat, aes(y=SampVar, x=TrueValue, group=TrueValue))+
geom_boxplot()+
labs(y="Sampling Variance of Estimates",
title="LEVEL-2 FACTOR COVARIANCE by Level-2 Sample Size",
subtitle="Sampling Variance of Parameter Estimates")+
facet_wrap(.~N2)
c <- sdat %>%
group_by(N2, TrueValue) %>%
summarise(est = weighted.mean(estMean, wi),
RB = weighted.mean(RB, wi),
RMSE = weighted.mean(RMSE, wi),
Bias = weighted.mean(Bias, wi),
SampVar =weighted.mean(SampVar, wi))
kable(c, format='html', digits=3,
caption="Summary Indices of LEVEL-2 FACTOR COVARIANCE by Level-2 Sample Size") %>%
kable_styling(full_width = T)| N2 | TrueValue | est | RB | RMSE | Bias | SampVar |
|---|---|---|---|---|---|---|
| 30 | 0.0333 | 0.027 | -18.93 | 0.018 | 0.000 | 0.017 |
| 30 | 0.3 | 0.292 | -2.64 | 0.096 | 0.002 | 0.094 |
| 50 | 0.0333 | 0.027 | -18.70 | 0.008 | 0.000 | 0.008 |
| 50 | 0.3 | 0.297 | -1.09 | 0.050 | 0.001 | 0.049 |
| 100 | 0.0333 | 0.031 | -6.27 | 0.004 | 0.000 | 0.004 |
| 100 | 0.3 | 0.295 | -1.83 | 0.024 | 0.000 | 0.024 |
| 200 | 0.0333 | 0.033 | -1.59 | 0.002 | 0.000 | 0.002 |
| 200 | 0.3 | 0.297 | -1.13 | 0.012 | 0.000 | 0.012 |
Level-1 Sample Size
ggplot(sdat, aes(y=estMean, x=TrueValue, group=TrueValue))+
geom_boxplot()+
geom_hline(yintercept = TRUEVALUE, color="red")+
labs(y="Average Level-2 Factor Covariance",
title="LEVEL-2 FACTOR COVARIANCE by Level-1",
subtitle="Parameter Estimates")+
facet_wrap(.~N1)
ggplot(sdat, aes(y=estSD, x=TrueValue, group=TrueValue))+
geom_boxplot()+
labs(y="SD of Level-2 Factor Covariances",
title="LEVEL-2 FACTOR COVARIANCE by Level-1 Sample Size",
subtitle="Standard Deviation of Parameter Estimates")+
facet_wrap(.~N1)
ggplot(sdat, aes(y=RB, x=TrueValue, group=TrueValue))+
geom_boxplot()+
geom_hline(yintercept=-10, color="red", linetype="dashed")+
geom_hline(yintercept=10, color="red", linetype="dashed")+
labs(y="Relative Bias",
title="LEVEL-2 FACTOR COVARIANCE by Level-1 Sample Size",
subtitle="Relative Bias of Parameter Estimates")+
facet_wrap(.~N1)
ggplot(sdat, aes(y=RMSE, x=TrueValue, group=TrueValue))+
geom_boxplot()+
labs(y="Root Mean Square Error",
title="LEVEL-2 FACTOR COVARIANCE by Level-1 Sample Size",
subtitle="Root Mean Square Error")+
facet_wrap(.~N1)
ggplot(sdat, aes(y=Bias, x=TrueValue, group=TrueValue))+
geom_boxplot()+
labs(y="Sqaured Bias",
title="LEVEL-2 FACTOR COVARIANCE by Level-1 Sample Size",
subtitle="Squared Bias of Parameter Estimates")+
facet_wrap(.~N1)
ggplot(sdat, aes(y=SampVar, x=TrueValue, group=TrueValue))+
geom_boxplot()+
labs(y="Sampling Variance of Estimates",
title="LEVEL-2 FACTOR COVARIANCE by Level-1 Sample Size",
subtitle="Sampling Variance of Parameter Estimates")+
facet_wrap(.~N1)
c <- sdat %>%
group_by(N1, TrueValue) %>%
summarise(est = weighted.mean(estMean, wi),
RB = weighted.mean(RB, wi),
RMSE = weighted.mean(RMSE, wi),
Bias = weighted.mean(Bias, wi),
SampVar =weighted.mean(SampVar, wi))
kable(c, format='html', digits=3,
caption="Summary Indices of LEVEL-2 FACTOR COVARIANCE by Level-1 Sample Size") %>%
kable_styling(full_width = T)| N1 | TrueValue | est | RB | RMSE | Bias | SampVar |
|---|---|---|---|---|---|---|
| 5 | 0.0333 | 0.029 | -13.14 | 0.012 | 0.000 | 0.012 |
| 5 | 0.3 | 0.298 | -0.65 | 0.056 | 0.001 | 0.055 |
| 10 | 0.0333 | 0.030 | -8.55 | 0.006 | 0.000 | 0.006 |
| 10 | 0.3 | 0.294 | -1.86 | 0.040 | 0.001 | 0.039 |
| 30 | 0.0333 | 0.031 | -8.31 | 0.004 | 0.000 | 0.004 |
| 30 | 0.3 | 0.293 | -2.20 | 0.033 | 0.000 | 0.033 |
ICC Observed Variables
ggplot(sdat, aes(y=estMean, x=TrueValue, group=TrueValue))+
geom_boxplot()+
geom_hline(yintercept = TRUEVALUE, color="red")+
labs(y="Average Level-2 Factor Covariance",
title="LEVEL-2 FACTOR COVARIANCE by ICC of Observed Variables",
subtitle="Parameter Estimates")+
facet_wrap(.~ICC_OV)
ggplot(sdat, aes(y=estSD, x=TrueValue, group=TrueValue))+
geom_boxplot()+
labs(y="SD of Level-2 Factor Covariances",
title="LEVEL-2 FACTOR COVARIANCE by ICC of Observed Variables",
subtitle="Standard Deviation of Parameter Estimates")+
facet_wrap(.~ICC_OV)
ggplot(sdat, aes(y=RB, x=TrueValue, group=TrueValue))+
geom_boxplot()+
geom_hline(yintercept=-10, color="red", linetype="dashed")+
geom_hline(yintercept=10, color="red", linetype="dashed")+
labs(y="Relative Bias",
title="LEVEL-2 FACTOR COVARIANCE by ICC of Observed Variables",
subtitle="Relative Bias of Parameter Estimates")+
facet_wrap(.~ICC_OV)
ggplot(sdat, aes(y=RMSE, x=TrueValue, group=TrueValue))+
geom_boxplot()+
labs(y="Root Mean Square Error",
title="LEVEL-2 FACTOR COVARIANCE by ICC of Observed Variables",
subtitle="Root Mean Square Error of Parameter Estimates")+
facet_wrap(.~ICC_OV)
ggplot(sdat, aes(y=Bias, x=TrueValue, group=TrueValue))+
geom_boxplot()+
labs(y="Sqaured Bias",
title="LEVEL-2 FACTOR COVARIANCE by ICC of Observed Variables",
subtitle="Squared Bias of Parameter Estimates")+
facet_wrap(.~ICC_OV)
ggplot(sdat, aes(y=SampVar, x=TrueValue, group=TrueValue))+
geom_boxplot()+
labs(y="Sampling Variance of Estimates",
title="LEVEL-2 FACTOR COVARIANCE by ICC of Observed Variables",
subtitle="Sampling Variance of Parameter Estimates")+
facet_wrap(.~ICC_OV)
c <- sdat %>%
group_by(ICC_OV, TrueValue) %>%
summarise(est = weighted.mean(estMean, wi),
RB = weighted.mean(RB, wi),
RMSE = weighted.mean(RMSE, wi),
Bias = weighted.mean(Bias, wi),
SampVar =weighted.mean(SampVar, wi))
kable(c, format='html', digits=3, caption="Summary Indices of LEVEL-2 FACTOR COVARIANCE by ICC of Observed Variables") %>%
kable_styling(full_width = T)| ICC_OV | TrueValue | est | RB | RMSE | Bias | SampVar |
|---|---|---|---|---|---|---|
| 0.1 | 0.0333 | 0.032 | -4.14 | 0.002 | 0.000 | 0.002 |
| 0.1 | 0.3 | 0.295 | -1.75 | 0.021 | 0.000 | 0.021 |
| 0.3 | 0.0333 | 0.032 | -2.74 | 0.005 | 0.000 | 0.005 |
| 0.3 | 0.3 | 0.293 | -2.19 | 0.037 | 0.001 | 0.036 |
| 0.5 | 0.0333 | 0.025 | -25.62 | 0.015 | 0.000 | 0.015 |
| 0.5 | 0.3 | 0.297 | -1.01 | 0.061 | 0.001 | 0.059 |
ICC Latent Variables
ggplot(sdat, aes(y=estMean, x=TrueValue, group=TrueValue))+
geom_boxplot()+
geom_hline(yintercept = TRUEVALUE, color="red")+
labs(y="Average Level-2 Factor Covariance",
title="LEVEL-2 FACTOR COVARIANCE by ICC of Latent Variables",
subtitle="Parameter Estimates")+
facet_wrap(.~ICC_LV)
ggplot(sdat, aes(y=estSD, x=TrueValue, group=TrueValue))+
geom_boxplot()+
labs(y="SD of Level-2 Factor Covariances",
title="LEVEL-2 FACTOR COVARIANCE by ICC of Latent Variables",
subtitle="Standard Deviation of Parameter Estimates")+
facet_wrap(.~ICC_LV)
ggplot(sdat, aes(y=RB, x=TrueValue, group=TrueValue))+
geom_boxplot()+
geom_hline(yintercept=-10, color="red", linetype="dashed")+
geom_hline(yintercept=10, color="red", linetype="dashed")+
labs(y="Relative Bias",
title="LEVEL-2 FACTOR COVARIANCE by ICC of Latent Variables",
subtitle="Relative Bias of Parameter Estimates")+
facet_wrap(.~ICC_LV)
ggplot(sdat, aes(y=RMSE, x=TrueValue, group=TrueValue))+
geom_boxplot()+
labs(y="Root Mean Square Error",
title="LEVEL-2 FACTOR COVARIANCE by ICC of Latent Variables",
subtitle="Root Mean Square Error of Parameter Estimates")+
facet_wrap(.~ICC_LV)
ggplot(sdat, aes(y=Bias, x=TrueValue, group=TrueValue))+
geom_boxplot()+
labs(y="Sqaured Bias",
title="LEVEL-2 FACTOR COVARIANCE by ICC of Latent Variables",
subtitle="Squared Bias of Parameter Estimates")+
facet_wrap(.~ICC_LV)
ggplot(sdat, aes(y=SampVar, x=TrueValue, group=TrueValue))+
geom_boxplot()+
labs(y="Sampling Variance of Estimates",
title="LEVEL-2 FACTOR COVARIANCE by ICC of Latent Variables",
subtitle="Sampling Variance of Parameter Estimates")+
facet_wrap(.~ICC_LV)
c <- sdat %>%
group_by(ICC_LV, TrueValue) %>%
summarise(est = weighted.mean(estMean, wi),
RB = weighted.mean(RB, wi),
RMSE = weighted.mean(RMSE, wi),
Bias = weighted.mean(Bias, wi),
SampVar =weighted.mean(SampVar, wi))
kable(c, format='html', digits=3,
caption="Summary Indices of LEVEL-2 FACTOR COVARIANCE by ICC of Latent Variables") %>%
kable_styling(full_width = T)| ICC_LV | TrueValue | est | RB | RMSE | Bias | SampVar |
|---|---|---|---|---|---|---|
| 0.1 | 0.0333 | 0.030 | -9.65 | 0.007 | 0.000 | 0.006 |
| 0.5 | 0.3 | 0.295 | -1.62 | 0.042 | 0.001 | 0.042 |
Loadings by Estimation Method and Sample Sizes
Estimation Method & Level-2 Sample Size
ggplot(sdat, aes(y=estMean, x=TrueValue, group=TrueValue))+
geom_boxplot()+
geom_hline(yintercept = TRUEVALUE, color="red")+
labs(y="Average Level-2 Factor Covariance")+
facet_grid(N2~Estimator)
ggplot(sdat, aes(y=RB, x=TrueValue, group=TrueValue))+
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=TrueValue, group=TrueValue))+
geom_boxplot()+
labs(y="Root Mean Square Error")+
facet_grid(N2~Estimator)
c <- sdat %>%
group_by(Estimator, N2, TrueValue) %>%
summarise(est = weighted.mean(estMean, wi),
RB = weighted.mean(RB, wi),
RMSE = weighted.mean(RMSE, wi),
Bias = weighted.mean(Bias, wi),
SampVar =weighted.mean(SampVar, wi))
c1 <- cbind(c[ c$Estimator == 'MLR', c( 'N2','TrueValue', 'est', 'RB', 'RMSE')],
c[ c$Estimator == 'ULSMV', c('est', 'RB', 'RMSE')],
c[ c$Estimator == 'WLSMV', c('est', 'RB', 'RMSE')])
colnames(c1) <- c('N2','True Value', 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 | True Value | est | RB | RMSE | est | RB | RMSE | est | RB | RMSE |
|---|---|---|---|---|---|---|---|---|---|---|
| 30 | 0.0333 | 0.030 | -9.580 | 0.015 | 0.031 | -6.413 | 0.027 | 0.018 | -46.43 | 0.010 |
| 30 | 0.3 | 0.292 | -2.788 | 0.089 | 0.344 | 14.675 | 0.123 | 0.236 | -21.49 | 0.076 |
| 50 | 0.0333 | 0.030 | -8.497 | 0.009 | 0.028 | -14.999 | 0.010 | 0.022 | -34.92 | 0.007 |
| 50 | 0.3 | 0.297 | -1.008 | 0.047 | 0.326 | 8.504 | 0.058 | 0.265 | -11.65 | 0.044 |
| 100 | 0.0333 | 0.033 | -2.047 | 0.004 | 0.033 | -1.441 | 0.004 | 0.028 | -15.72 | 0.003 |
| 100 | 0.3 | 0.294 | -1.859 | 0.024 | 0.307 | 2.461 | 0.026 | 0.281 | -6.37 | 0.023 |
| 200 | 0.0333 | 0.033 | 0.069 | 0.002 | 0.034 | 0.654 | 0.002 | 0.031 | -5.53 | 0.002 |
| 200 | 0.3 | 0.297 | -1.118 | 0.012 | 0.302 | 0.620 | 0.013 | 0.291 | -2.94 | 0.012 |
Estimation Method & Level-1 Sample Size
ggplot(sdat, aes(y=estMean, x=TrueValue, group=TrueValue))+
geom_boxplot()+
geom_hline(yintercept = TRUEVALUE, color="red")+
labs(y="Average Level-2 Factor Covariance")+
facet_grid(N1~Estimator)
ggplot(sdat, aes(y=RB, x=TrueValue, group=TrueValue))+
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, x=TrueValue, group=TrueValue))+
geom_boxplot()+
labs(y="Root Mean Square Error")+
facet_grid(N1~Estimator)
c <- sdat %>%
group_by(Estimator, N1, TrueValue) %>%
summarise(est = weighted.mean(estMean, wi),
RB = weighted.mean(RB, wi),
RMSE = weighted.mean(RMSE, wi),
Bias = weighted.mean(Bias, wi),
SampVar =weighted.mean(SampVar, wi))
c1 <- cbind(c[ c$Estimator == 'MLR', c( 'N1','TrueValue', 'est', 'RB', 'RMSE')],
c[ c$Estimator == 'ULSMV', c('est', 'RB', 'RMSE')],
c[ c$Estimator == 'WLSMV', c('est', 'RB', 'RMSE')])
colnames(c1) <- c('N1','True Value', rep(c('est', 'RB', 'RMSE'), 3))
kable(c1, format='html', digits=3, row.names = F) %>%
kable_styling(full_width = T) %>%
add_header_above(c(' '=2, 'MLR'=3, 'ULSMV'=3, 'WLSMV'=3))| N1 | True Value | est | RB | RMSE | est | RB | RMSE | est | RB | RMSE |
|---|---|---|---|---|---|---|---|---|---|---|
| 5 | 0.0333 | 0.031 | -5.95 | 0.011 | 0.031 | -7.99 | 0.018 | 0.024 | -28.50 | 0.007 |
| 5 | 0.3 | 0.296 | -1.20 | 0.053 | 0.329 | 9.77 | 0.070 | 0.267 | -10.91 | 0.044 |
| 10 | 0.0333 | 0.032 | -3.46 | 0.006 | 0.032 | -2.93 | 0.007 | 0.027 | -20.09 | 0.004 |
| 10 | 0.3 | 0.295 | -1.62 | 0.039 | 0.317 | 5.70 | 0.048 | 0.269 | -10.25 | 0.033 |
| 30 | 0.0333 | 0.032 | -3.77 | 0.004 | 0.032 | -3.84 | 0.004 | 0.027 | -17.51 | 0.003 |
| 30 | 0.3 | 0.294 | -2.09 | 0.033 | 0.309 | 3.10 | 0.037 | 0.276 | -8.03 | 0.031 |
Estimation Method, Level-2 Sample Size & Level-1 Sample Size
ggplot(sdat, aes(y=estMean, x=TrueValue, group=TrueValue))+
geom_boxplot()+
geom_hline(yintercept = TRUEVALUE, color="red")+
labs(y="Average Level-12 Factor Covariance")+
facet_grid(N2+N1~Estimator)
ggplot(sdat, aes(y=RB, x=TrueValue, group=TrueValue))+
geom_boxplot()+
geom_hline(yintercept=-10, color="red", linetype="dashed")+
geom_hline(yintercept=10, color="red", linetype="dashed")+
labs(y="Relative Bias")+
facet_grid(N2+N1~Estimator)
ggplot(sdat, aes(y=RMSE, x=TrueValue, group=TrueValue))+
geom_boxplot()+
labs(y="Root Mean Square Error")+
facet_grid(N2+N1~Estimator)
c <- sdat %>%
group_by(Estimator, N2, N1, TrueValue) %>%
summarise(est = weighted.mean(estMean, wi),
RB = weighted.mean(RB, wi),
RMSE = weighted.mean(RMSE, wi),
Bias = weighted.mean(Bias, wi),
SampVar =weighted.mean(SampVar, wi))
c1 <- cbind(c[ c$Estimator == 'MLR', c( 'N2','N1', 'TrueValue', 'est', 'RB', 'RMSE')],
c[ c$Estimator == 'ULSMV', c('est', 'RB', 'RMSE')],
c[ c$Estimator == 'WLSMV', c('est', 'RB', 'RMSE')])
colnames(c1) <- c('N2','N1', 'True Value', rep(c('est', 'RB', 'RMSE'), 3))
kable(c1, format='html', digits=3, row.names = F) %>%
kable_styling(full_width = T) %>%
add_header_above(c(' '=3, 'MLR'=3, 'ULSMV'=3, 'WLSMV'=3))| N2 | N1 | True Value | est | RB | RMSE | est | RB | RMSE | est | RB | RMSE |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 30 | 5 | 0.0333 | 0.026 | -20.880 | 0.029 | 0.032 | -3.344 | 0.090 | 0.007 | -78.95 | 0.024 |
| 30 | 5 | 0.3 | 0.304 | 1.447 | 0.128 | 0.385 | 28.440 | 0.190 | 0.232 | -22.65 | 0.096 |
| 30 | 10 | 0.0333 | 0.032 | -2.680 | 0.014 | 0.033 | -2.048 | 0.022 | 0.019 | -44.10 | 0.009 |
| 30 | 10 | 0.3 | 0.288 | -3.979 | 0.084 | 0.338 | 12.656 | 0.118 | 0.226 | -24.61 | 0.069 |
| 30 | 30 | 0.0333 | 0.031 | -7.696 | 0.008 | 0.030 | -10.356 | 0.009 | 0.020 | -39.12 | 0.006 |
| 30 | 30 | 0.3 | 0.286 | -4.822 | 0.066 | 0.321 | 6.997 | 0.082 | 0.246 | -17.89 | 0.067 |
| 50 | 5 | 0.0333 | 0.029 | -11.997 | 0.015 | 0.019 | -42.178 | 0.022 | 0.010 | -69.17 | 0.014 |
| 50 | 5 | 0.3 | 0.294 | -2.001 | 0.061 | 0.333 | 10.853 | 0.080 | 0.252 | -16.14 | 0.057 |
| 50 | 10 | 0.0333 | 0.032 | -3.079 | 0.007 | 0.032 | -3.936 | 0.008 | 0.025 | -26.35 | 0.006 |
| 50 | 10 | 0.3 | 0.295 | -1.657 | 0.047 | 0.326 | 8.675 | 0.059 | 0.261 | -12.96 | 0.042 |
| 50 | 30 | 0.0333 | 0.030 | -10.696 | 0.005 | 0.030 | -10.496 | 0.006 | 0.024 | -28.17 | 0.005 |
| 50 | 30 | 0.3 | 0.301 | 0.410 | 0.037 | 0.320 | 6.686 | 0.042 | 0.279 | -7.16 | 0.036 |
| 100 | 5 | 0.0333 | 0.033 | -0.521 | 0.006 | 0.033 | 0.247 | 0.007 | 0.027 | -20.34 | 0.006 |
| 100 | 5 | 0.3 | 0.292 | -2.534 | 0.031 | 0.315 | 5.054 | 0.034 | 0.278 | -7.37 | 0.030 |
| 100 | 10 | 0.0333 | 0.032 | -3.859 | 0.003 | 0.032 | -4.584 | 0.003 | 0.027 | -18.14 | 0.003 |
| 100 | 10 | 0.3 | 0.297 | -0.842 | 0.022 | 0.308 | 2.563 | 0.025 | 0.283 | -5.79 | 0.022 |
| 100 | 30 | 0.0333 | 0.033 | -1.537 | 0.002 | 0.033 | 0.296 | 0.002 | 0.030 | -10.43 | 0.002 |
| 100 | 30 | 0.3 | 0.293 | -2.262 | 0.019 | 0.301 | 0.353 | 0.021 | 0.282 | -6.11 | 0.019 |
| 200 | 5 | 0.0333 | 0.034 | 1.155 | 0.003 | 0.033 | 0.407 | 0.003 | 0.030 | -8.80 | 0.003 |
| 200 | 5 | 0.3 | 0.296 | -1.167 | 0.015 | 0.304 | 1.343 | 0.017 | 0.291 | -2.85 | 0.015 |
| 200 | 10 | 0.0333 | 0.032 | -3.825 | 0.002 | 0.033 | -1.211 | 0.002 | 0.031 | -7.87 | 0.002 |
| 200 | 10 | 0.3 | 0.299 | -0.431 | 0.011 | 0.304 | 1.408 | 0.012 | 0.292 | -2.51 | 0.011 |
| 200 | 30 | 0.0333 | 0.034 | 2.874 | 0.001 | 0.034 | 2.688 | 0.001 | 0.033 | -0.44 | 0.001 |
| 200 | 30 | 0.3 | 0.295 | -1.759 | 0.009 | 0.298 | -0.819 | 0.011 | 0.290 | -3.42 | 0.009 |
Relative Efficiency by Sample Sizes
c <- sdat %>%
group_by(Estimator, N2, N1) %>%
summarise(mu = weighted.mean(muRE, wi),
mw = weighted.mean(mwRE, wi),
uw = weighted.mean(uwRE, wi))
c1 <- c[ c$Estimator == 'MLR', c( 'N2','N1', 'mu', 'mw', 'uw')]
colnames(c1) <- c('N2','N1', c('MLR/ULSMV', 'MLR/WLSMV', 'ULSMV/WLSMV'))
kable(c1, format='html', digits=3, row.names = F) %>%
kable_styling(full_width = T)| N2 | N1 | MLR/ULSMV | MLR/WLSMV | ULSMV/WLSMV |
|---|---|---|---|---|
| 30 | 5 | 1.579 | 2.01 | 1.48 |
| 30 | 10 | 1.054 | 1.48 | 1.41 |
| 30 | 30 | 1.021 | 1.31 | 1.27 |
| 50 | 5 | 1.247 | 1.60 | 1.28 |
| 50 | 10 | 1.040 | 1.31 | 1.24 |
| 50 | 30 | 0.985 | 1.12 | 1.14 |
| 100 | 5 | 1.100 | 1.22 | 1.11 |
| 100 | 10 | 1.004 | 1.13 | 1.12 |
| 100 | 30 | 0.974 | 1.05 | 1.07 |
| 200 | 5 | 0.997 | 1.06 | 1.06 |
| 200 | 10 | 0.980 | 1.03 | 1.05 |
| 200 | 30 | 0.975 | 1.01 | 1.04 |
Relative Efficiency by All Conditions
c <- sdat %>%
group_by(Estimator, N2, N1, ICC_OV, ICC_LV) %>%
summarise(mu = weighted.mean(muRE, wi),
mw = weighted.mean(mwRE, wi),
uw = weighted.mean(uwRE, wi))
c1 <- cbind(c[ c$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 | 3.780 | 3.404 | 0.900 |
| 30 | 5 | 0.1 | 0.5 | 3.233 | 4.291 | 1.327 |
| 30 | 5 | 0.3 | 0.1 | 1.112 | 1.711 | 1.538 |
| 30 | 5 | 0.3 | 0.5 | 0.924 | 1.208 | 1.307 |
| 30 | 5 | 0.5 | 0.1 | 0.630 | 1.679 | 2.667 |
| 30 | 5 | 0.5 | 0.5 | 0.848 | 1.287 | 1.517 |
| 30 | 10 | 0.1 | 0.1 | 1.400 | 1.626 | 1.161 |
| 30 | 10 | 0.1 | 0.5 | 1.579 | 2.500 | 1.584 |
| 30 | 10 | 0.3 | 0.1 | 1.009 | 1.443 | 1.430 |
| 30 | 10 | 0.3 | 0.5 | 0.945 | 1.207 | 1.277 |
| 30 | 10 | 0.5 | 0.1 | 0.794 | 1.478 | 1.861 |
| 30 | 10 | 0.5 | 0.5 | 0.833 | 1.159 | 1.391 |
| 30 | 30 | 0.1 | 0.1 | 1.054 | 1.204 | 1.142 |
| 30 | 30 | 0.1 | 0.5 | 1.300 | 2.063 | 1.586 |
| 30 | 30 | 0.3 | 0.1 | 0.993 | 1.300 | 1.310 |
| 30 | 30 | 0.3 | 0.5 | 0.960 | 1.103 | 1.149 |
| 30 | 30 | 0.5 | 0.1 | 0.839 | 1.108 | 1.321 |
| 30 | 30 | 0.5 | 0.5 | 0.892 | 1.031 | 1.155 |
| 50 | 5 | 0.1 | 0.1 | 2.235 | 2.043 | 0.914 |
| 50 | 5 | 0.1 | 0.5 | 2.063 | 3.627 | 1.758 |
| 50 | 5 | 0.3 | 0.1 | 0.998 | 1.274 | 1.276 |
| 50 | 5 | 0.3 | 0.5 | 0.965 | 1.120 | 1.160 |
| 50 | 5 | 0.5 | 0.1 | 0.888 | 1.353 | 1.523 |
| 50 | 5 | 0.5 | 0.5 | 0.870 | 1.087 | 1.250 |
| 50 | 10 | 0.1 | 0.1 | 1.170 | 1.168 | 0.999 |
| 50 | 10 | 0.1 | 0.5 | 1.350 | 2.216 | 1.642 |
| 50 | 10 | 0.3 | 0.1 | 1.002 | 1.195 | 1.193 |
| 50 | 10 | 0.3 | 0.5 | 0.951 | 1.075 | 1.130 |
| 50 | 10 | 0.5 | 0.1 | 0.914 | 1.190 | 1.303 |
| 50 | 10 | 0.5 | 0.5 | 0.874 | 1.093 | 1.250 |
| 50 | 30 | 0.1 | 0.1 | 1.002 | 1.077 | 1.075 |
| 50 | 30 | 0.1 | 0.5 | 1.081 | 1.370 | 1.268 |
| 50 | 30 | 0.3 | 0.1 | 0.987 | 1.130 | 1.145 |
| 50 | 30 | 0.3 | 0.5 | 0.975 | 1.048 | 1.075 |
| 50 | 30 | 0.5 | 0.1 | 0.936 | 1.047 | 1.118 |
| 50 | 30 | 0.5 | 0.5 | 0.907 | 1.022 | 1.126 |
| 100 | 5 | 0.1 | 0.1 | 1.257 | 1.196 | 0.952 |
| 100 | 5 | 0.1 | 0.5 | 1.596 | 1.949 | 1.221 |
| 100 | 5 | 0.3 | 0.1 | 0.970 | 1.088 | 1.122 |
| 100 | 5 | 0.3 | 0.5 | 0.966 | 1.022 | 1.058 |
| 100 | 5 | 0.5 | 0.1 | 0.959 | 1.155 | 1.205 |
| 100 | 5 | 0.5 | 0.5 | 0.937 | 1.045 | 1.115 |
| 100 | 10 | 0.1 | 0.1 | 1.023 | 1.039 | 1.016 |
| 100 | 10 | 0.1 | 0.5 | 1.107 | 1.471 | 1.329 |
| 100 | 10 | 0.3 | 0.1 | 0.996 | 1.074 | 1.078 |
| 100 | 10 | 0.3 | 0.5 | 0.972 | 1.031 | 1.060 |
| 100 | 10 | 0.5 | 0.1 | 0.993 | 1.115 | 1.123 |
| 100 | 10 | 0.5 | 0.5 | 0.933 | 1.032 | 1.106 |
| 100 | 30 | 0.1 | 0.1 | 0.999 | 1.048 | 1.049 |
| 100 | 30 | 0.1 | 0.5 | 1.006 | 1.111 | 1.105 |
| 100 | 30 | 0.3 | 0.1 | 0.998 | 1.057 | 1.058 |
| 100 | 30 | 0.3 | 0.5 | 0.963 | 1.002 | 1.041 |
| 100 | 30 | 0.5 | 0.1 | 0.935 | 1.048 | 1.122 |
| 100 | 30 | 0.5 | 0.5 | 0.933 | 1.010 | 1.082 |
| 200 | 5 | 0.1 | 0.1 | 1.026 | 1.024 | 0.998 |
| 200 | 5 | 0.1 | 0.5 | 1.100 | 1.214 | 1.104 |
| 200 | 5 | 0.3 | 0.1 | 0.994 | 1.036 | 1.042 |
| 200 | 5 | 0.3 | 0.5 | 0.975 | 1.000 | 1.026 |
| 200 | 5 | 0.5 | 0.1 | 0.976 | 1.060 | 1.086 |
| 200 | 5 | 0.5 | 0.5 | 0.912 | 1.006 | 1.103 |
| 200 | 10 | 0.1 | 0.1 | 0.989 | 0.999 | 1.010 |
| 200 | 10 | 0.1 | 0.5 | 0.993 | 1.083 | 1.090 |
| 200 | 10 | 0.3 | 0.1 | 0.990 | 1.016 | 1.026 |
| 200 | 10 | 0.3 | 0.5 | 0.984 | 1.005 | 1.021 |
| 200 | 10 | 0.5 | 0.1 | 0.979 | 1.037 | 1.059 |
| 200 | 10 | 0.5 | 0.5 | 0.944 | 1.020 | 1.081 |
| 200 | 30 | 0.1 | 0.1 | 0.991 | 1.005 | 1.013 |
| 200 | 30 | 0.1 | 0.5 | 0.998 | 1.013 | 1.015 |
| 200 | 30 | 0.3 | 0.1 | 0.998 | 1.019 | 1.021 |
| 200 | 30 | 0.3 | 0.5 | 0.972 | 0.998 | 1.028 |
| 200 | 30 | 0.5 | 0.1 | 0.995 | 1.040 | 1.046 |
| 200 | 30 | 0.5 | 0.5 | 0.897 | 1.004 | 1.119 |
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 whisker_0.4
[29] later_1.0.0 git2r_0.27.1 farver_2.0.3 generics_0.0.2
[33] ellipsis_0.3.1 withr_2.2.0 cli_2.0.2 proto_1.0.0
[37] magrittr_1.5 crayon_1.3.4 readxl_1.3.1 evaluate_0.14
[41] fs_1.4.1 fansi_0.4.1 nlme_3.1-144 xml2_1.3.2
[45] tools_3.6.3 hms_0.5.3 lifecycle_0.2.0 munsell_0.5.0
[49] reprex_0.3.0 compiler_3.6.3 rlang_0.4.6 grid_3.6.3
[53] rstudioapi_0.11 texreg_1.36.23 labeling_0.3 rmarkdown_2.1
[57] boot_1.3-24 gtable_0.3.0 DBI_1.1.0 R6_2.4.1
[61] lubridate_1.7.8 knitr_1.28 rprojroot_1.3-2 stringi_1.4.6
[65] parallel_3.6.3 Rcpp_1.0.4.6 vctrs_0.3.0 dbplyr_1.4.4
[69] tidyselect_1.1.0 xfun_0.14 coda_0.19-3