Open AccessTesting measurement invariance in longitudinal data with ordered-categorical measures.
Author(s) -
Yu Liu,
Roger E. Millsap,
Stephen G. West,
Jenn Yun Tein,
Rika Tanaka,
Kevin J. Grimm
Publication year - 2017
Publication title -
psychological methods
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 6.981
H-Index - 151
eISSN - 1939-1463
pISSN - 1082-989X
DOI - 10.1037/met0000075
Subject(s) - categorical variable , measurement invariance , item response theory , latent variable , latent variable model , metric (unit) , psychology , local independence , econometrics , structural equation modeling , statistics , psychometrics , confirmatory factor analysis , mathematics , operations management , economics
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 article 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 3 major latent variable programs (lavaan, Mplus, OpenMx) and computer scripts for addressing longitudinal measurement invariance. (PsycINFO Database Record