Abstract:
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Psychometric modeling techniques are used to describe a person’s latent ability or trait and how that latent trait changes over time based on a specific measurement tool. However, there may be multiple instruments with varying scales that can be used to capture various aspects of the latent quality of interest, and as an individual’s skill grows over time some measurement tools may become too easy and thus non-informative. We present a Bayesian hierarchical mixed model approach which combines information from several instruments with different scoring schemes to examine growth in one latent trait over time. The model does not require subjects to have responses on each instrument, nor to be measured on the same instrument over the entire study period. Similar to a typical item response theory (IRT) model, the proposed model produces a new measurement scale of the latent ability. The proposed method is demonstrated on a study that captured responses to eight instruments on various aspects of language development in children from ages one to ten. Researchers were interested in identifying children that had faster or slower than average language growth.
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