20241224 - comparison table of measurement models

Author: isaactpetersen

15-Factor-Analysis-PCA.Rmd

@@ -588,6 +588,16 @@ A mean or sum score is a [measurement model](#measurementModel-sem) that assumes
 Another solution is to form a linear composite by adding and weighting the variables by the factor loadings, which retains the differences in correlations (i.e., a weighted sum), but this still ignores the estimated error, so it still may not be generalizable and meaningful.\index{factor analysis!decisions}\index{factor analysis}\index{principal component analysis}\index{linear composite}\index{measurement error}
 At the same time, weighted sums may be less generalizable than unit-weighted composites where each variable is given equal weight because some variability in factor loadings likely reflects sampling error.\index{factor analysis!decisions}\index{factor analysis}\index{principal component analysis}\index{linear composite}\index{structural equation modeling!factor loading}
 
+A comparison of various measurement models is in Table \@ref(tab:measurementModelsComparison).\index{factor analysis}\index{principal component analysis}\index{structural equation modeling!measurement model}\index{linear composite}\index{measurement error}
+
+Table: (\#tab:measurementModelsComparison) Comparison of Various Measurement Models. "PCA" = principal component analysis; "CFA" = confirmatory factor analysis; "EFA" = exploratory factor analysis; "SEM" = structural equation modeling; "IRT" = item response theory.
+
+| Measurement Model                             | Items' Factor Loadings        | Items' Residuals/Error                                |
+|-----------------------------------------------|-------------------------------|-------------------------------------------------------|
+| Mean/Sum Score                                | All are the same (fixed to 1) | Assumes items are measured without error (fixed to 0) |
+| PCA or Weighted Mean/Sum Score                | Allowed to differ             | Assumes items are measured without error (fixed to 0) |
+| Latent Variable Modeling (CFA, EFA, SEM, IRT) | Allowed to differ             | Estimates error for each item                         |
+
 ### Missing Data Handling {#missingDataHandling-factorAnalysis}
 
 The [PCA](#pca) default in SPSS is listwise deletion of missing data: if a participant is missing data on any variable, the subject gets excluded from the analysis, so you might end up with too few participants.\index{factor analysis!decisions}\index{principal component analysis}