Latent Variable Modeling

Latent variable models link observed (or manifest) variables to unobserved (or latent) constructs. They comprise of two parts: a measurement model specifying the relationship between manifest and latent variables, and a structural model delineating the relationships among the latent variables themselves. Both the manifest and the latent variables can be either discrete or continuous in nature. When both are continuous, one obtains the factor analytic models used widely in psychology, e.g., to measure latent constructs such as human intelligence. When both are discrete, one obtains the latent class models used to categorize observations into distinct groups, e.g., to classify individuals into diseased vs. non-diseased according to their constellation of symptoms. Widely used in educational testing are Item Response Theory models (also known as Latent Trait models) that relate a group of categorical manifest variables to a continuous latent variable, e.g., using answers to a multiple choice test to measure mastery of a particular academic subject. Finally, finite mixture models  (also known as Latent Profile Analysis) relate a set of continuous manifest variables to underlying categorical constructs, e.g., by partitioning clinical trial participants into homogeneous groups across behavioral and cognitive dimensions of engagement with physical activity interventions. Originally developed for cross-sectional data, latent variable models have recently been generalized to longitudinal data. For example, Latent Transition Analysis has been used to model movement across stages of change in studies of smoking cessation. An example of latent variable modeling by our faculty is given by the 2-parameter logistic IRT models fit to the DSM-IV criteria for nicotine dependence by Dr. Papandonatos and his students. They uncovered a 2-dimensional structure with two positively correlated latent factors, thus contradicting conventional wisdom that DSM-IV symptoms measure a single dimension of liability to nicotine dependence.

George Papandonatos

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