Latent Markov Latent Trait Analysis for Exploring Measurement Model Changes in Intensive Longitudinal Data

Abstract

Drawing inferences about dynamics of psychological constructs from intensive longitudinal data requires the measurement model (MM)—indicating how items relate to constructs—to be invariant across subjects and time-points. When assessing subjects in their daily life, however, there may be multiple MMs, for instance, because subjects differ in their item interpretation or because the response style of (some) subjects changes over time. The recently proposed “latent Markov factor analysis” (LMFA) evaluates (violations of) measurement invariance by classifying observations into latent “states” according to the MM underlying these observations such that MMs differ between states but are invariant within one state. However, LMFA is limited to normally distributed continuous data and estimates may be inaccurate when applying the method to ordinal data (e.g., from Likert items) with skewed responses or few response categories. To enable researchers and health professionals with ordinal data to evaluate measurement invariance, we present “latent Markov latent trait analysis” (LMLTA), which builds upon LMFA but treats responses as ordinal. Our application shows differences in MMs of adolescents’ affective well-being in different social contexts, highlighting the importance of studying measurement invariance for drawing accurate inferences for psychological science and practice and for further understanding dynamics of psychological constructs.

How to explore within-person and between-person measurement model differences in intensive longitudinal data with the R package lmfa

“…Secondly, the factor analysis models in step 1 assume continuous item responses. If items are measured with only a few categories or if the item responses are heavily skewed, state-specific "latent trait" (or "item response theory") models should be employed in step 1 of the analysis to adequately deal with categorical data, as is done in the extension called latent Markov latent trait analysis (LMLTA; Vogelsmeier et al, 2020). Performing LMLTA is currently only possible in Latent GOLD, but advanced R users could theoretically specify their own state-specific models for step 1 (for instance, by using mixture models for categorical data from other packages) and use the posterior state-membership probabilities as input 34 for the step 3 analysis with lmfa.…”

“…Theoretically, it is possible to cluster subjects based on their transition behavior by adding a latent grouping variable to the LMFA in step 3 (e.g., see Crayen, Eid, Lischetzke, & Vermunt, 2017;Vogelsmeier et al, 2020). This is not possible with lmfa but advanced R users may consider using the depmix package in step 3 of LMFA by passing the modal state assignments and classification error probabilities as fixed parameters to the depmix() function.…”

“…Highly skewed responses with only a few response categories may lead to convergence problems and local optima (for a description of local optima, see Section 3.2.3). For such data, the LMFA extension to categorical data should be used, that is, latent Markov latent trait analysis (Vogelsmeier, Vermunt, Keijsers, & De Roover, 2020). month, subjects were randomly assigned to receiving an intervention to reduce anhedonia or not.…”

“…Note that the state-specific FA assumes continuous item responses (or responses that can be treated as such, say, with five or more categories; Dolan, Oort, Stoel, & Wicherts, 2009). It is possible to use a latent variable model for items with categorical item responses (Vogelsmeier et al, 2020) but this option is not included in the lmfa package. The second building block is the LMM that models the transitions between MMs over time (Bartolucci, Farcomeni, & Pennoni, 2015;Zucchini, MacDonald, & Langrock, 2016).…”

“…Furthermore, until now, LMFA was only available in the commercial software Latent GOLD (Vermunt & Magidson, 2016) and, thus, not all researchers had access to the novel method. The latter has now changed with the release of the package lmfa (Vogelsmeier & De Roover, 2020) that allows researchers to perform all necessary steps in the open-source software R (R Core Team, 2020). The aim of this paper is to provide a tutorial for the lmfa package that guides users through the different steps of performing the analysis and interpreting the results with the goal to increase researchers' confidence and ease in using LMFA.…”