Testing measurement invariance in longitudinal data with ordered-categorical measures.

Abstract

A goal of developmental research is to examine individual changes in constructs over time. The accuracy of the models answering such research questions hinges on the assumption of longitudinal measurement invariance: The repeatedly measured variables need to represent the same construct in the same metric over time. Measurement invariance can be studied through factor models examining the relations between the observed indicators and the latent constructs. In longitudinal research ordered-categorical indicators such as self- or observer-report Likert scales are commonly used, and these measures often do not approximate continuous normal distributions. The present didactic paper extends previous work on measurement invariance to the longitudinal case for ordered-categorical indicators. We address a number of problems that commonly arise in testing measurement invariance with longitudinal data including model identification and interpretation, sparse data, missing data, and estimation issues. We also develop a procedure and associated R program for gauging the practical significance of the violations of invariance. We illustrate these issues with an empirical example using a subscale from the Mexican American Cultural Values scale. Finally, we provide comparisons of the current capabilities of three major latent variable programs (lavaan, Mplus, OpenMx) and computer scripts for addressing longitudinal measurement invariance.

Are robots becoming unpopular? Changes in attitudes towards autonomous robotic systems in Europe

“…All discrepancies were small (i.e., < .05; cf. Liu et al, 2017) and, thus, did not indicate practically significant measurement non-invariance across the three waves. Measurement invariance across the 27 European countries was examined using a factor analysis alignment approach for ordered-categorical data (Asparouhov & Muthén, 2014;Muthén & Asparouhov, 2014).…”

“…Valid comparisons across different measurement occasions and countries requires that the administered instruments function comparably and capture identical constructs in similar ways. Therefore, measurement invariance was examined across the three measurements waves in 2012, 2014, and 2017 using a multi-group confirmatory factor analysis for orderedcategorical data with a mean and variance adjusted diagonally weighted least square estimator (Liu, Millsap, West, Tein, Tanaka, & Grimm, 2017). For each wave, an independent group was specified that modeled a single latent factor with three items.…”

Testing Measurement Invariance with Ordinal Missing Data: A Comparison of Estimators and Missing Data Techniques

“…Limited research in the past has shown that multiple imputation combined with WLSMV will produce accurate parameter and standard error estimates (Asparouhov & Muthén, 2010a;Teman, 2012). However, there is so far no good way to pool the 2 test statistics across the imputed data sets when WLSMV is used (Liu et al, 2017). Given that 2 tests are critical for ME/I testing, this is an indisputable limitation.…”

Short Index of Job Satisfaction: Validity evidence from Portugal and Brazil

“…In this cross-sectional study, no information can be extracted regarding the temporal stability of the SIJS structure. In future research, researchers might address this issue by testing longitudinal measurement invariance [149]. Research with other samples (i.e.…”