Correlation among Parameter Estimates: Factor Loadings
Last updated: 2020-05-27
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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"))
# subset to data with admissible replications
sim_results <- filter(sim_results, Converge==1 & Admissible==1)General Descrition
On this page, we are investigating the correlation among parameter estimates between estimation methods. We do this by
- Subsetting the data to the parameter of interest
- Reshaping the data to wide
- Compute the correlation
- Compute the proportion of admissible cases by comparison (i.e., proportion of replications that were used to compute correlation). This gives us an indication of how convergence varied across estimation methods
- Reshape to long data for plotting
- Plot correlation estimates in boxplots with points overlayed
Factor Loadings
Data Manipulation
# keep variables
keepVar <- c("Condition", "Replication", "ss_l1", "ss_l2", "icc_ov", "icc_lv", "Estimator", paste0("lambda", c(11:16, 26:29, 210)))
sim_res1 <- sim_results[, keepVar]
sim_res1 <- sim_res1%>%
pivot_longer(cols = starts_with("lambda"),
names_to = "lambda",
values_to = "est") %>%
pivot_wider(id_cols=c("Condition","Replication", "ss_l1", "ss_l2", "icc_ov", "icc_lv", "lambda"),
names_from = "Estimator",
values_from = "est")
cor.est <- sim_res1 %>%
group_by(ss_l1, ss_l2, icc_ov, icc_lv, lambda) %>%
summarise(
r_mlr_ulsmv = cor(MLR, ULSMV,use = "pairwise.complete"),
cprop_mlr_ulsmv = (1-(sum(is.na(MLR + ULSMV))/500)) ,
r_mlr_wlsmv = cor(MLR, WLSMV,use = "pairwise.complete"),
cprop_mlr_wlsmv = (1-(sum(is.na(MLR + WLSMV))/500)),
r_ulsmv_wlsmv = cor(ULSMV, WLSMV,use = "pairwise.complete"),
cprop_ulsmv_wlsmv = (1-(sum(is.na(ULSMV + WLSMV))/500))
)
a1 <- cor.est %>%
pivot_longer(cols= starts_with("r_"),
names_to= "Cor",
values_to = "Est") %>%
mutate(Cor = substring(Cor, 3))
a2 <- cor.est %>%
pivot_longer(cols= starts_with("cprop_"),
names_to= "Cor",
values_to = "Cprop")%>%
mutate(Cor = substring(Cor, 7))
cor.est <- left_join(a1[,c(1:5,9:10)], a2[,c(1:5,9:10)]) %>%
group_by(ss_l1, ss_l2, icc_ov, icc_lv, Cor)%>%
summarise(Est = mean(Est),
Cprop = mean(Cprop))Joining, by = c("ss_l1", "ss_l2", "icc_ov", "icc_lv", "lambda", "Cor")cor.est$Cor <- factor(cor.est$Cor,
levels=c("mlr_ulsmv", "mlr_wlsmv", "ulsmv_wlsmv"),
labels=c("cor(MLR, ULSMV)",
"cor(MLR, WLSMV)",
"cor(ULSMV, WLSMV)"),
ordered=T)
cor.est$C90 <- as.factor(ifelse(cor.est$Cprop >= 0.9, ">= 90%", "< 90%"))
cor.est$C95 <- as.factor(ifelse(cor.est$Cprop >= 0.95, ">= 95%", "< 95%"))Single Conditions
All Conditions
cols=c("< 90%"="#56B4E9", ">= 90%"="#CC79A7")
p <- ggplot(cor.est, aes(x=Cor, y=Est)) +
geom_boxplot(outlier.shape = NA) +
geom_jitter(data=filter(cor.est, C90=="< 90%"),
width=0.3, aes(x=Cor, y=Est, color="< 90%")) +
geom_jitter(data=filter(cor.est, C90==">= 90%"),
width=0.3, aes(x=Cor, y=Est, color=">= 90%")) +
lims(y=c(0,1))+
labs(y="Correlation",
x=NULL,
title="Correlation amoung Estimates: Factor Loadings")+
scale_color_manual(name="% Admissible", values=cols)+
theme_bw()+
theme(panel.grid = element_blank())
p
By Level-1 Sample Size
p <- ggplot(cor.est, aes(x=Cor, y=Est)) +
geom_boxplot(outlier.shape = NA) +
geom_jitter(data=filter(cor.est, C90=="< 90%"),
width=0.3, aes(x=Cor, y=Est, color="< 90%")) +
geom_jitter(data=filter(cor.est, C90==">= 90%"),
width=0.3, aes(x=Cor, y=Est, color=">= 90%")) +
lims(y=c(0,1))+
labs(y="Correlation",
x=NULL,
title="Correlation amoung Estimates: Factor Loadings",
subtitle = "Conditional on Level-1 Sample Size")+
scale_color_manual(name="% Admissible", values=cols)+
facet_wrap(.~ss_l1)+
theme_bw()+
theme(panel.grid = element_blank(),
axis.text.x = element_text(angle=90))
p
By Level-2 Sample Size
p <- ggplot(cor.est, aes(x=Cor, y=Est)) +
geom_boxplot(outlier.shape = NA) +
geom_jitter(data=filter(cor.est, C90=="< 90%"),
width=0.3, aes(x=Cor, y=Est, color="< 90%")) +
geom_jitter(data=filter(cor.est, C90==">= 90%"),
width=0.3, aes(x=Cor, y=Est, color=">= 90%")) +
lims(y=c(0,1))+
labs(y="Correlation",
x=NULL,
title="Correlation amoung Estimates: Factor Loadings",
subtitle = "Conditional on Level-2 Sample Size")+
scale_color_manual(name="% Admissible", values=cols)+
facet_wrap(.~ss_l2, nrow=1)+
theme_bw()+
theme(panel.grid = element_blank(),
axis.text.x = element_text(angle=90))
p
By Observed Variable ICC
p <- ggplot(cor.est, aes(x=Cor, y=Est)) +
geom_boxplot(outlier.shape = NA) +
geom_jitter(data=filter(cor.est, C90=="< 90%"),
width=0.3, aes(x=Cor, y=Est, color="< 90%")) +
geom_jitter(data=filter(cor.est, C90==">= 90%"),
width=0.3, aes(x=Cor, y=Est, color=">= 90%")) +
lims(y=c(0,1))+
labs(y="Correlation",
x=NULL,
title="Correlation amoung Estimates: Factor Loadings",
subtitle = "Conditional on Observed Variable ICC")+
scale_color_manual(name="% Admissible", values=cols)+
facet_wrap(.~icc_ov)+
theme_bw()+
theme(panel.grid = element_blank(),
axis.text.x = element_text(angle=90))
p
By Latent Variable ICC
p <- ggplot(cor.est, aes(x=Cor, y=Est)) +
geom_boxplot(outlier.shape = NA) +
geom_jitter(data=filter(cor.est, C90=="< 90%"),
width=0.3, aes(x=Cor, y=Est, color="< 90%")) +
geom_jitter(data=filter(cor.est, C90==">= 90%"),
width=0.3, aes(x=Cor, y=Est, color=">= 90%")) +
lims(y=c(0,1))+
labs(y="Correlation",
x=NULL,
title="Correlation amoung Estimates: Factor Loadings",
subtitle = "Conditional on Latent Variable ICC")+
scale_color_manual(name="% Admissible", values=cols)+
facet_wrap(.~icc_lv)+
theme_bw()+
theme(panel.grid = element_blank(),
axis.text.x = element_text(angle=90))
p
Publication Figure
cols=c("< 90%"="#56B4E9", ">= 90%"="#CC79A7")
shps=c("< 90%"=16, ">= 90%"=17)
p <- ggplot(cor.est, aes(x=Cor, y=Est)) +
geom_boxplot(outlier.shape = NA) +
geom_jitter(data=filter(cor.est, C90=="< 90%"),
width=0.3, size=2, alpha=0.7,
aes(x=Cor, y=Est,
color="< 90%", shape="< 90%")) +
geom_jitter(data=filter(cor.est, C90==">= 90%"),
width=0.3, size=2, alpha=0.7,
aes(x=Cor, y=Est,
color=">= 90%", shape=">= 90%")) +
lims(y=c(0,1))+
labs(y="Correlation",
x=NULL)+
scale_color_manual(name="% Admissible", values=cols)+
scale_shape_manual(name="% Admissible", values=shps)+
theme_bw()+
theme(panel.grid = element_blank(),
legend.position = c(0.5,0.25),
legend.text = element_text(size=12),
legend.title = element_text(size=12),
axis.title.y = element_text(size=12),
axis.text.y = element_text(size=10),
axis.text.x = element_text(angle=20, hjust=1,
vjust = 1, size=12))
p
ggsave("fig/estimate_correlation_factor_loading.pdf",p, units="in", height=3.5, width=5)sessionInfo()R version 4.0.0 (2020-04-24)
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 pander_0.6.3 cellranger_1.1.0
[9] yaml_2.2.1 pillar_1.4.4 backports_1.1.6 lattice_0.20-41
[13] glue_1.4.1 digest_0.6.25 promises_1.1.0 rvest_0.3.5
[17] colorspace_1.4-1 htmltools_0.4.0 httpuv_1.5.2 plyr_1.8.6
[21] pkgconfig_2.0.3 broom_0.5.6 haven_2.3.0 scales_1.1.1
[25] webshot_0.5.2 whisker_0.4 later_1.0.0 git2r_0.27.1
[29] farver_2.0.3 generics_0.0.2 ellipsis_0.3.1 withr_2.2.0
[33] cli_2.0.2 proto_1.0.0 magrittr_1.5 crayon_1.3.4
[37] readxl_1.3.1 evaluate_0.14 fs_1.4.1 fansi_0.4.1
[41] nlme_3.1-147 xml2_1.3.2 tools_4.0.0 hms_0.5.3
[45] lifecycle_0.2.0 munsell_0.5.0 reprex_0.3.0 compiler_4.0.0
[49] rlang_0.4.6 grid_4.0.0 rstudioapi_0.11 texreg_1.36.23
[53] labeling_0.3 rmarkdown_2.1 boot_1.3-24 gtable_0.3.0
[57] DBI_1.1.0 R6_2.4.1 lubridate_1.7.8 knitr_1.28
[61] rprojroot_1.3-2 stringi_1.4.6 parallel_4.0.0 Rcpp_1.0.4.6
[65] vctrs_0.3.0 dbplyr_1.4.3 tidyselect_1.1.0 xfun_0.14
[69] coda_0.19-3
sessionInfo()R version 4.0.0 (2020-04-24)
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 pander_0.6.3 cellranger_1.1.0
[9] yaml_2.2.1 pillar_1.4.4 backports_1.1.6 lattice_0.20-41
[13] glue_1.4.1 digest_0.6.25 promises_1.1.0 rvest_0.3.5
[17] colorspace_1.4-1 htmltools_0.4.0 httpuv_1.5.2 plyr_1.8.6
[21] pkgconfig_2.0.3 broom_0.5.6 haven_2.3.0 scales_1.1.1
[25] webshot_0.5.2 whisker_0.4 later_1.0.0 git2r_0.27.1
[29] farver_2.0.3 generics_0.0.2 ellipsis_0.3.1 withr_2.2.0
[33] cli_2.0.2 proto_1.0.0 magrittr_1.5 crayon_1.3.4
[37] readxl_1.3.1 evaluate_0.14 fs_1.4.1 fansi_0.4.1
[41] nlme_3.1-147 xml2_1.3.2 tools_4.0.0 hms_0.5.3
[45] lifecycle_0.2.0 munsell_0.5.0 reprex_0.3.0 compiler_4.0.0
[49] rlang_0.4.6 grid_4.0.0 rstudioapi_0.11 texreg_1.36.23
[53] labeling_0.3 rmarkdown_2.1 boot_1.3-24 gtable_0.3.0
[57] DBI_1.1.0 R6_2.4.1 lubridate_1.7.8 knitr_1.28
[61] rprojroot_1.3-2 stringi_1.4.6 parallel_4.0.0 Rcpp_1.0.4.6
[65] vctrs_0.3.0 dbplyr_1.4.3 tidyselect_1.1.0 xfun_0.14
[69] coda_0.19-3