Analysing multitrait-multimethod data with structural equation models for ordinal variables applying the WLSMV...

Area of Science:

• Psychometrics
• Statistical Modeling

Background:

• Assessing psychological construct validity often uses multitrait-multimethod (MTMM) analysis.
• MTMM models for categorical data are essential for item-level insights.
• The CTC(M-1) model serves as an MTMM example for ordinal variables.

Purpose of the Study:

• To investigate sample size requirements for the WLSMV estimator in MTMM analysis.
• To evaluate the performance of the WLSMV estimator across varying model complexity and sample sizes.
• To examine chi-squared approximation, parameter bias, standard error bias, and reliability.

Main Methods:

• A simulation study based on an empirical CTC(M-1) model application.
• Varied the number of items per trait-method unit (2-8).
• Tested sample sizes of 250, 500, 750, and 1000 observations.

Main Results:

• The WLSMV estimator showed good, slightly liberal chi-squared approximation.
• Stable and reliable parameter estimates were achieved with small sample sizes (≥250) for simpler models (2-4 items).
• More complex models (≥5 items) required larger sample sizes (≥500), with the most complex model needing ≥1000 observations.

Conclusions:

• The WLSMV estimator is suitable for MTMM analysis with moderate sample sizes and model complexity.
• Researchers should consider model complexity when determining adequate sample size for MTMM studies.
• Findings provide guidance for sample size planning in psychometric research using categorical data.