The Use of Discrete Latent Variables in Dyadic Data Analysis

Two topics of methodological research in the social sciences that have garnered recent attention are the topics of dyadic data analysis and the use of discrete latent variables. Dyadic data refers to data that were collected from two interdependent sources, such as data from identical twins or romantic partners. Data collected in this fashion violate the traditional independence assumption underlying many common statistical techniques. Discrete latent variables come in many commonly used models, such as the latent class, latent profile, and latent transition models. All these models share the goal of explaining observed relationships between variables using discrete categories (i.e. classification) in which observations are statistically similar to those in the same category, and dissimilar from those in separate categories. While both dyadic data analysis and categorical latent variables have seen countless articles (and even entire textbooks) written about their usage, these two techniques have formerly remained independent procedures. This dissertation will briefly review the conceptual and statistical details of both modeling techniques and then provide two substantive examples of how dyadic data and discrete latent variables can profitably be used together. The first example combines growth mixture modeling with the use of the common fate growth model to identify distinct trajectories of marital satisfaction among couples. The oft-observed decline in satisfaction in the years following marriage can largely be attributed to a sub-population that reports a large decrease in marital satisfaction. The second substantive example combines the latent profile, latent transition, and actor-partner interdependence model into a model examining the cross-lagged association of couple members political beliefs. The goal of this dissertation is to demonstrate how dyadic data analysis and discrete latent variables techniques can be used together with the hopes that these two modeling techniques will begin to be research, applied, and reference together