Specifying exogeneity and bilinear effects in data-driven model searches

Abstract

Data-driven model searches provide the opportunity to quantify person-specific processes using ambulatory assessment data. Here, the search space typically includes all potential relations among variables, meaning that all variables can potentially explain variability in all other variables. Oftentimes, this is unrealistic. For example, weather is unlikely to be predicted by someone's emotional state, whereas the reverse might be true. Allowing for specification of exogenous variables, or variables that are not predicted within the system, permits more realistic models and allows the researcher to model contextual change processes via the use of moderation variables. We use two sets of daily diary data to demonstrate the capabilities of allowing for the specification of exogenous variables in GIMME (Group Iterative Multiple Model Estimation), a model search algorithm that allows for models with idiographic, individual-level as well as subgroup- and group-level processes with intensive longitudinal data. First, using data collected from individuals diagnosed with personality disorders, we show results where weather-related and temporal basis variables are specified as exogenous, and reports on affect and behavior are endogenous. Next, we demonstrate the modeling of treatment effects in an intervention study, looking at data from a 6-week meditation workshop in midlife adults. Finally, we use the meditation intervention data to demonstrate modeling moderation effects, where relationships between two endogenous variables are dependent on the current stage of the study for a given participant (i.e., currently attending meditation classes or not). We end by presenting adaptive LASSO as a method for probing results obtained from GIMME.

Keywords: Daily diary; Data-driven; Exogenous; Gimme; Model search; Moderator; Sem; Time series.

Figure 1.

Example of representation of an exogenous variable in a path diagram. Temperature is “outside the system” and can predict positive and negative affects but cannot be predicted by any variables inside the system. Autoregressive relations for the endogenous variables and error/variance depictions omitted for clarity.

Figure 2.

Example summary plot from gimme model search. Group-level paths (i.e., paths that improve model fit for a majority of individuals) are in black, subgroup-level paths in green, and individual-level paths in gray. Lagged paths are indicated by a dashed line, and contemporaneous paths are indicated by a solid line.

Figure 3.

Summary plot showing results from Example 1. No group-level paths were recovered. Subgroup level paths are indicated in green, and individual level paths are indicated in gray. Dashed lines represent a lagged effect, and solid lines represent a contemporaneous effect.

Figure 4.

Summary plot for Example 1 broken down by subgroup. Colored lines indicate paths found at the subgroup level for each subgroup. n indicates the number of individuals assigned to each subgroup.

Figure 5.

Summary plot showing results from Example 2

Figure 6.

Summary plot showing results from Example 3