Sample Size Determination
Last updated: 2020-11-04
Checks: 6 1
Knit directory: pools-projects/
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POOLS Model
The POOLS model is generally a four factor model with 10-14 items per factor.
Power Analysis Simulation Study
Here, we vary the sample size between 100 and 1000 (steps of 50) to determine the approximate minimal sample size needed to reject that the data fails to fit the model.
Populaiton Model
pop_model <- "
# POOLS Items (~40)
EF =~ .6*p11 + .6*p12 + .6*p13 + .6*p14 + .6*p15 + .6*p16 + .6*p17 + .6*p18 + .6*p19 + .6*p110
ST =~ .6*p21 + .6*p22 + .6*p23 + .6*p24 + .6*p25 + .6*p26 + .6*p27 + .6*p28 + .6*p29 + .6*p210
IN =~ .6*p31 + .6*p32 + .6*p33 + .6*p34 + .6*p35 + .6*p36 + .6*p37 + .6*p38 + .6*p39 + .6*p310
EN =~ .6*p41 + .6*p42 + .6*p43 + .6*p44 + .6*p45 + .6*p46 + .6*p47 + .6*p48 + .6*p49 + .6*p410
# Self-Efficacy Items (12)
# omegas: .85, .82, .8
se1 =~ .75*eff1 + .75*eff2 + .75*eff3 +.75*eff4
se2 =~ .75*eff5 + .75*eff6 + .7*eff7 +.7*eff8
se3 =~ .7*eff9 + .7*eff10 + .7*eff11 +.7*eff12
# Teacher-Team Inno Scale (omega = .89)
tt =~ .8*ttis1 + .8*ttis2 + .8*ttis3 + .8*ttis4
# NEO FFM
# Alphas: .77, .81, .82, .86, .86
A =~ .7*ffmA1 + .7*ffmA2 + .7*ffmA3 + .7*ffmA4 + .7*ffmA5 + .7*ffmA6 + .7*ffmA7 + .7*ffmA8 + .7*ffmA9 + .7*ffmA10
C =~ .7*ffmC1 + .7*ffmC2 + .7*ffmC3 + .7*ffmC4 + .7*ffmC5 + .7*ffmC6 + .7*ffmC7 + .7*ffmC8 + .7*ffmC9 + .7*ffmC10
O =~ .7*ffmO1 + .7*ffmO2 + .7*ffmO3 + .7*ffmO4 + .7*ffmO5 + .7*ffmO6 + .7*ffmO7 + .7*ffmO8 + .7*ffmO9 + .7*ffmO10
E =~ .7*ffmE1 + .7*ffmE2 + .7*ffmE3 + .7*ffmE4 + .7*ffmE5 + .7*ffmE6 + .7*ffmE7 + .7*ffmE8 + .7*ffmE9 + .7*ffmE10
N =~ .7*ffmN1 + .7*ffmN2 + .7*ffmN3 + .7*ffmN4 + .7*ffmN5 + .7*ffmN6 + .7*ffmN7 + .7*ffmN8 + .7*ffmN9 + .7*ffmN10
# Latent Variable Covariance Matrix
# POOLS
EF ~~ 1*EF + .3*ST + .2*In + .2*EN
ST ~~ 1*ST + .1*IN + .3*EN
IN ~~ 1*IN + .3*EN
EN ~~ 1*EN
# SE
se1 ~~ 1*se1 + .5*se2 + .4*se3
se2 ~~ 1*se2 + .3*se3
se3 ~~ 1*se3
# FFM (taken from deyoung table 6)
A ~~ 1*A + (0.38)*C + (0.11)*O + (0.15)*E + (-0.24)*N
C ~~ 1*C + (0.11)*O + (0.18)*E + (-0.24)*N
O ~~ 1*O + (0.26)*E + (-0.13)*N
E ~~ 1*E + (-0.33)*N
N ~~ 1*N
# Research questions
# 1. FFM accounting for variance of POOLS
# (need to come up with better values)
EF ~ .1*A + .3*C + .4*O + .1*E + (-0.2)*N
ST ~ .1*A + .3*C + .4*O + .1*E + (-0.2)*N
EN ~ .1*A + .3*C + .4*O + .1*E + (-0.2)*N
IN ~ .1*A + .3*C + .4*O + .1*E + (-0.2)*N
# 2. relationship between SE & Pools
EF ~ .3*se1 + .2*se2 + .4*se3
ST ~ .3*se1 + .2*se2 + .4*se3
IN ~ .3*se1 + .2*se2 + .4*se3
EN ~ .3*se1 + .2*se2 + .4*se3
# 3. Team inno predicting POOLS
EF ~ .2*tt
ST ~ .2*tt
IN ~ .2*tt
EN ~ .2*tt
# 4. demographics
EF ~ 0.1*sex
ST ~ 0.1*sex
IN ~ 0.1*sex
EN ~ 0.1*sex
# categorical variables
sex | 0.4*t1
"
dat <- simulateData(pop_model, model.type = "sem")Warning in lav_partable_flat(FLAT, blocks = "group", meanstructure =
meanstructure, : lavaan WARNING: thresholds are defined for exogenous variables:
sex#Impose missing
datmiss <- imposeMissing(
dat,
nforms = 7,
itemGroups = list(c(1:107),
c(),
c(41:56),
c( 77:86, 87:96, 97:106),
c( 57:66, 87:96, 97:106),
c( 57:66, 67:76, 97:106),
c( 57:66, 67:76, 77:86 ),
c( 67:76, 77:86, 87:96 )
))
naniar::vis_miss(datmiss)
Estimation Model
est_model <- '
# 1. Latent variable definition
# POOLS
EF =~ 1*p11 + p12 + p13 + p14 + p15# + p16 + p17 + p18 + p19 + p110
ST =~ 1*p21 + p22 + p23 + p24 + p25# + p26 + p27 + p28 + p29 + p210
IN =~ 1*p31 + p32 + p33 + p34 + p35# + p36 + p37 + p38 + p39 + p310
EN =~ 1*p41 + p42 + p43 + p44 + p45# + p46 + p47 + p48 + p49 + p410
# Self-Efficacy Items
se1 =~ NA*eff1 + eff2 + eff3 + eff4
se2 =~ NA*eff5 + eff6 + eff7 + eff8
se3 =~ NA*eff9 + eff10 + eff11 + eff12
# Teacher-Team Inno Scale
tt =~ NA*ttis1 + ttis2 + ttis3 + ttis4
# NEO FFM
A =~ NA*ffmA1 + ffmA2 + ffmA3 + ffmA4 + ffmA5 + ffmA6 + ffmA7 + ffmA8 + ffmA9 + ffmA10
C =~ NA*ffmC1 + ffmC2 + ffmC3 + ffmC4 + ffmC5 + ffmC6 + ffmC7 + ffmC8 + ffmC9 + ffmC10
O =~ NA*ffmO1 + ffmO2 + ffmO3 + ffmO4 + ffmO5 + ffmO6 + ffmO7 + ffmO8 + ffmO9 + ffmO10
E =~ NA*ffmE1 + ffmE2 + ffmE3 + ffmE4 + ffmE5 + ffmE6 + ffmE7 + ffmE8 + ffmE9 + ffmE10
N =~ NA*ffmN1 + ffmN2 + ffmN3 + ffmN4 + ffmN5 + ffmN6 + ffmN7 + ffmN8 + ffmN9 + ffmN10
# 2. Latent variable covariances
# POOLS
EF ~~ EF + ST + IN + EN
ST ~~ ST + IN + EN
IN ~~ IN + EN
# SE
se1 ~~ 1*se1 + se2 + se3
se2 ~~ 1*se2 + se3
se3 ~~ 1*se3
# Team Inno.
tt ~~ 1*tt
# FFM
A ~~ 1*A + C + O + E + N
C ~~ 1*C + O + E + N
O ~~ 1*O + E + N
E ~~ 1*E + N
N ~~ 1*N
# Research questions
# 1. FFM accounting for variance of POOLS
EF ~ A + C + O + E + N
ST ~ A + C + O + E + N
IN ~ A + C + O + E + N
EN ~ A + C + O + E + N
# 2. relationship between SE & Pools
EF ~ se1 + se2 + se3
ST ~ se1 + se2 + se3
IN ~ se1 + se2 + se3
EN ~ se1 + se2 + se3
# 3. Team inno predicting POOLS
EF ~ tt
ST ~ tt
IN ~ tt
EN ~ tt
'
# use missing = "ML" for FIML
fit <- cfa(est_model, datmiss, estimator = "ML", missing = "ML")
summary(fit, standardized=T, fit.measures=T)
# ================================== #
# funciton:
# data_function_categorization()
#
# Purpose:
# categorize the continuous response
# into the 5 discrete categories we
# will observe in the analysis.
# We plan to treat the data as continuous.
# But, we will also use a robust estimation
# method DWLS and
# PML (pairwise maximum likelihood)
data_function_categorization <- function(data){
tauCreate <- function(x){
e <- rnorm(4,0, 0.01)
BREAKS <- c(-Inf, -1.4+e[1], -0.4+e[2], 0.2+e[3], 1+e[4], Inf)
x <- cut(x,
breaks=BREAKS,
labels = c(-2, -1, 0, 1, 2))
as.numeric(x)-3 # center at 0
}
data[,1:106] <- apply(data[,1:106], 2, tauCreate)
data
}
missdata_mech <- miss(
nforms = 7,
itemGroups = list(c(1:107),
c(),
c(41:56),
c( 77:86, 87:96, 97:106),
c( 57:66, 87:96, 97:106),
c( 57:66, 67:76, 97:106),
c( 57:66, 67:76, 77:86 ),
c( 67:76, 77:86, 87:96 ))
)
sim_res <- sim(
nRep = 5, n = 500,
lavaanfun = "sem",
model = list(model=est_model, estimator = "ML", missing = "ML"),
generate = pop_model,
miss = missdata_mech,
datafun = data_function_categorization
)
sessionInfo()R version 4.0.2 (2020-06-22)
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 mvtnorm_1.1-1 naniar_0.6.0
[5] simsem_0.5-15 lavaanPlot_0.5.1 semTools_0.5-3 lavaan_0.6-7
[9] data.table_1.13.0 patchwork_1.0.1 forcats_0.5.0 stringr_1.4.0
[13] dplyr_1.0.1 purrr_0.3.4 readr_1.3.1 tidyr_1.1.1
[17] tibble_3.0.3 ggplot2_3.3.2 tidyverse_1.3.0 workflowr_1.6.2
loaded via a namespace (and not attached):
[1] fs_1.5.0 lubridate_1.7.9 webshot_0.5.2 RColorBrewer_1.1-2
[5] httr_1.4.2 rprojroot_1.3-2 tools_4.0.2 backports_1.1.7
[9] R6_2.4.1 DBI_1.1.0 colorspace_1.4-1 withr_2.2.0
[13] tidyselect_1.1.0 mnormt_2.0.1 emmeans_1.4.8 compiler_4.0.2
[17] git2r_0.27.1 cli_2.0.2 rvest_0.3.6 xml2_1.3.2
[21] sandwich_2.5-1 labeling_0.3 scales_1.1.1 digest_0.6.25
[25] pbivnorm_0.6.0 rmarkdown_2.3 pkgconfig_2.0.3 htmltools_0.5.0
[29] dbplyr_1.4.4 htmlwidgets_1.5.1 rlang_0.4.7 readxl_1.3.1
[33] rstudioapi_0.11 farver_2.0.3 visNetwork_2.0.9 generics_0.0.2
[37] zoo_1.8-8 jsonlite_1.7.0 magrittr_1.5 Matrix_1.2-18
[41] Rcpp_1.0.5 munsell_0.5.0 fansi_0.4.1 visdat_0.5.3
[45] lifecycle_0.2.0 stringi_1.4.6 multcomp_1.4-13 yaml_2.2.1
[49] MASS_7.3-51.6 grid_4.0.2 blob_1.2.1 promises_1.1.1
[53] crayon_1.3.4 lattice_0.20-41 haven_2.3.1 splines_4.0.2
[57] hms_0.5.3 tmvnsim_1.0-2 knitr_1.29 pillar_1.4.6
[61] estimability_1.3 codetools_0.2-16 stats4_4.0.2 reprex_0.3.0
[65] glue_1.4.1 evaluate_0.14 modelr_0.1.8 vctrs_0.3.2
[69] httpuv_1.5.4 cellranger_1.1.0 gtable_0.3.0 assertthat_0.2.1
[73] xfun_0.16 broom_0.7.0 coda_0.19-3 later_1.1.0.1
[77] viridisLite_0.3.0 survival_3.2-3 DiagrammeR_1.0.6.1 TH.data_1.0-10
[81] ellipsis_0.3.1