Psychometric test data are useful for predicting a variety of important life outcomes and personality characteristics. The Cognitive Reflection Test (CRT) is a short, well-validated rationality test, designed to assess subjects' ability to override intuitively appealing but incorrect responses to a series of math- and logic-based questions. The CRT is predictive of many other cognitive abilities and tendencies, such as verbal intelligence, numeracy, and religiosity. Cognitive psychologists and psychometricians are concerned with whether subjects improve their scores on the test with repeated exposure, as this may threaten the test's predictive validity. This project uses the first publicly available longitudinal dataset derived from subjects who took the CRT multiple times over a predefined period. The dataset includes a multitude of predictors, including number of previous exposures to the test (our variable of primary interest). Also included are two response variables measured with each test exposure: CRT score and time taken to complete the CRT. These responses serve as a proxy for underlying latent variables, "rationality" and "reflectiveness", respectively. We propose methods to describe the relationship between the responses and selected predictors. Specifically, we employ a bivariate longitudinal model to account for the presumed dependence between our two responses. Our model also allows for subpopulations ("clusters") of individuals whose responses exhibit similar patterns. We estimate the parameters of our one- and two-cluster models via adaptive Gaussian quadrature. We also develop an Expectation-Maximization algorithm for estimating models with greater numbers of clusters. We use our fitted models to address a range of subject-specific questions in a formal way (building on earlier work relying on ad hoc methods). In particular, we find that test exposure has a greater estimated effect on test scores than previously reported and we find evidence of at least two subpopulations. Additionally, our work has generated numerous avenues for future investigation.
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