On January 14th 2022 Leonie Vogelsmeier has defended her thesis
Latent Markov Factor Analysis: A mixture modeling approach for evaluating within- and between-person measurement model differences in intensive longitudinal data at the University of Tilburg
Studying dynamics in psychological constructs in intensive longitudinal data (ILD) becomes increasingly popular among researchers in the social and behavioral sciences. Technological advances facilitate gathering such ILD, for instance, with experience sampling methodology. However, before beginning with their analyses, researchers have to verify that the measured constructs are equivalent across subjects and time. To this end, the “measurement model” (MM) – indicating how items measure the constructs – needs to be invariant across subjects and time (i.e., “measurement invariance” (MI) must hold). If violations of MI are undetected or ignored, conclusions about (between-person differences in) within-person dynamics in the constructs may be invalid.
MI is often violated in ILD because response styles or item interpretation may not only differ across subjects, but subjects may also change in the way they respond to the questionnaire items over time. For instance, how subjects interpret an item could change depending on the context in which the questionnaire is completed, or subjects may start agreeing to all items once they are no longer motivated to complete the questionnaires. Existing methods could only test a priori assumptions about MI violations. However, these assumptions are usually absent or incomplete, leaving the social and behavioral scientists with no efficient approach to explore the tenability of the MI assumption in their ILD. This dissertation aims to solve this gap by presenting latent Markov factor analysis (LMFA) for unraveling MM differences/changes for many subjects and time-points simultaneously. In LMFA, a latent Markov model (i.e., a latent class model that allows subjects to transition between dynamic latent classes or “states” over time) classifies observations based on their underlying MM into a few states and exploratory factor analysis per state evaluates the structure of the state-specific MMs. Observations within the same state have the same underlying MM and are thus validly comparable.
In this dissertation, we first introduce LMFA and show that the method performs well in recovering the state memberships and the MMs per state under a wide range of conditions (Chapter 2). Then, we extend LMFA by means of a continuous-time latent Markov model to adequately handle typically encountered unequally-spaced observations (Chapter 3). Next, we propose a three-step maximum likelihood estimation as an alternative to the originally employed one-step full information maximum likelihood estimation because this facilitates the inclusion of explanatory variables and thus offers researchers the possibility to understand why MMs differ/change (Chapter 4). Thereafter, we extend LMFA into latent Markov latent trait analysis that adequately handles categorical data, which allows researchers to investigate MI in their ILD also if the data contain responses with only a few categories and skewed distributions (Chapter 5). Finally, we provide a tutorial on how to investigate MI with our R package lmfa, which is openly available to all researchers in the social and behavioral sciences (Chapter 6).
Dr Kim De Roover & Prof. Jeroen K. Vermunt
NWO Research Talent Grant
1 July 2017 to 14 January 2022