Dynamic Mixture Modeling with dynr

Abstract

Mixture modeling is commonly used to model sample heterogeneity by identifying unobserved classes of individuals with similar characteristics. Despite abundance of evidence in the literature suggesting that individuals are often characterized by different dynamic processes underlying their physiological, cognitive, psychological, and behavioral states, applications of dynamic mixture modeling are surprisingly lacking. We present here a proof-of-concept example of dynamic mixture modeling, where latent groups of individuals were identified based on different dynamic patterns in their time series. Our sample consists of 192 men who were in a heterosexual relationship. They were asked to complete a daily questionnaire involving emotions related to their relationship. Two latent groups were identified based on the strength of association between positive (e.g., loving) and negative (e.g., doubtful) affect. Men in the group characterized by a strong negative association ($\beta =-.67$) tended to be younger and had higher levels of anxiety toward their relationship than men in the other group, which was characterized by a weaker negative association ($\beta =-.31$). We illustrate the specification and estimation of dynamic mixture model using “dynr,” an R package capable of handling a broad class of linear and nonlinear discrete- and continuous-time models with regime-switching properties.

KEYWORDS:

• Dynamic processes
• mixture model
• autoregressive model
• intensive longitudinal data
• time series

Notes

1 There is no consensus regarding the definition of a qualitative difference in psychological research. This term could have different meanings in different contexts. In the context of dynamic mixture modeling, we adopt a definition similar to that in Bulteel et al. (2016) and define individuals as qualitatively different if they belong to different latent subgroups.

2 Following Ou et al. (2019), we only label the parameters, not the variables, with the regime indicators.

3 Currently dynr can only handle dependent variables that are assumed to be normally distributed. Dependent variables that are skewed can be incorporated after appropriate transformations (e.g., square root, log). At the moment, the program cannot handle discrete (e.g., binary) dependent variables.

4 We also conducted parallel analyses for women and found similar results. Specifically, the two-group model was selected because it fit better than the one-group model and models with more than two groups failed to converge. For both groups, there was a negative association between PA and NA. This association had different magnitudes for the two groups (–.38 vs. –.65)

5 It should be noted that the AR coefficient is not the only measure, and often not a sufficient one for emotional inertia. Other indicators of emotional inertia may include the level and variability of affect.

6 The residual variances were allowed to differ across groups, but they could also be constrained to be equal. We compared the latter restricted model with the model with freely estimated residual variances using log-likelihood ratio test and found that the less restricted model fit the data better significantly.