Latent variable GIMME using model implied instrumental variables (MIIVs)

Researchers across many domains of psychology increasingly wish to arrive at personalized and generalizable dynamic models of individuals' processes. This is seen in psychophysiological, behavioral, and emotional research paradigms, across a range of data types. Errors of measurement are inherent in most data. For this reason, researchers typically gather multiple indicators of the same latent construct and use methods, such as factor analysis, to arrive at scores from these indices. In addition to accurately measuring individuals, researchers also need to find the model that best describes the relations among the latent constructs. Most currently available data-driven searches do not include latent variables. We present an approach that builds from the strong foundations of group iterative multiple model estimation (GIMME), the idiographic filter, and model implied instrumental variables with two-stage least squares estimation (MIIV-2SLS) to provide researchers with the option to include latent variables in their data-driven model searches. The resulting approach is called latent variable GIMME (LV-GIMME). GIMME is utilized for the data-driven search for relations that exist among latent variables. Unlike other approaches such as the idiographic filter, LV-GIMME does not require that the latent variable model to be constant across individuals. This requirement is loosened by utilizing MIIV-2SLS for estimation. Simulated data studies demonstrate that the method can reliably detect relations among latent constructs, and that latent constructs provide more power to detect effects than using observed variables directly. We use empirical data examples drawn from functional MRI and daily self-report data.