Two-Part Factor Mixture Modeling: Application to an Aggressive Behavior Measurement Instrument

Abstract

This study introduces a two-part factor mixture model as an alternative analysis approach to modeling data where strong floor effects and unobserved population heterogeneity exist in the measured items. As the names suggests, a two-part factor mixture model combines a two-part model, which addresses the problem of strong floor effects by decomposing the data into dichotomous and continuous response components, with a factor mixture model, which explores unobserved heterogeneity in a population by establishing latent classes. Two-part factor mixture modeling can be an important tool for situations in which ordinary factor analysis produces distorted results and can allow researchers to better understand population heterogeneity within groups. Building a two-part factor mixture model involves a consecutive model building strategy that explores latent classes in the data for each part as well as a combination of the two-part. This model building strategy was applied to data from a randomized preventive intervention trial in Baltimore public schools administered by the Johns Hopkins Center for Early Intervention. The proposed model revealed otherwise unobserved subpopulations among the children in the study in terms of both their tendency toward and their level of aggression. Furthermore, the modeling approach was examined using a Monte Carlo simulation.

FIGURE 1

Process of decomposing the skewed data into two parts and applying two-part modeling to a factor model.

FIGURE 2

Illustration of multistage strategy to build a two-part factor mixture model.

FIGURE 3

Distribution of 10 Teacher’s Observation of Classroom Adaptation Revised items.

FIGURE 4

Estimated probabilities for the dichotomous part and the estimated means for the continuous part.

FIGURE 5

Teacher’s Observation of Classroom Adaptation Revised items for two students in the low engagement/high activity level group. Note. Y-axis 0 = almost never, 1 = rarely, 2 = sometimes, 3 = often, 4 = very often, 5 = almost always.

FIGURE 6

Distribution of 10 items from simulated data.