Abstract
When time-intensive longitudinal data are used to study daily-life dynamics of psychological constructs (e.g., well-being) within persons over time (e.g., by means of experience sampling methodology), the measurement model (MM)—indicating which constructs are measured by which items—can be affected by time- or situation-specific artifacts (e.g., response styles and altered item interpretation). If not captured, these changes might lead to invalid inferences about the constructs. Existing methodology can only test for a priori hypotheses on MM changes, which are often absent or incomplete. Therefore, we present the exploratory method “latent Markov factor analysis” (LMFA), wherein a latent Markov chain captures MM changes by clustering observations per subject into a few states. Specifically, each state gathers validly comparable observations, and state-specific factor analyses reveal what the MMs look like. LMFA performs well in recovering parameters under a wide range of simulated conditions, and its empirical value is illustrated with an example.
Highlights
Time-intensive longitudinal data for studying daily-life dynamics of psychological constructs within persons allow to delve into time- or situation-specific effects on the experiences of a large number of subjects (Larson & Csikszentmihalyi, 2014)
We present latent Markov factor analysis (LMFA),1 which combines two building blocks to model measurement model (MM) changes within subjects over time: (1) latent Markov modeling (LMM; Bartolucci, Farcomeni, & Pennoni, 2014; Collins & Lanza, 2010) clusters time-points into states according to the MMs and (2) FA (Lawley & Maxwell, 1962) evaluates which MM applies for each state
The multistart procedure increases the chance to find a global maximum likelihood (ML) solution, and in the simulation study—where the global maximum is unknown due to violations of FA assumptions, sampling fluctuations and residuals—we can compare the best solution of the multistart procedure to an approximation of the global ML solution, which we obtain by providing the model estimation with the true parameter values as starting values
Summary
Time-intensive longitudinal data for studying daily-life dynamics of psychological constructs (such as well-being and positive affect) within persons allow to delve into time- or situation-specific effects (e.g., stress) on the (e.g., emotional) experiences of a large number of subjects (Larson & Csikszentmihalyi, 2014). Color versions of one or more of the figures in the article can be found online at www.tandfonline.com/hsem. The MM is the model underlying a participant’s answers and indicates which unobservable or latent variables (i.e., psychological constructs) are measured by which items. It is evaluated by factor analysis (FA; Lawley & Maxwell, 1962), where the factors correspond—ideally— to the hypothesized constructs.
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