A Time-Varying Dynamic Partial Credit Model to Analyze Polytomous and Multivariate Time Series Data

Abstract

The accessibility to electronic devices and the novel statistical methodologies available have allowed researchers to comprehend psychological processes at the individual level. However, there are still great challenges to overcome as, in many cases, collected data are more complex than the available models are able to handle. For example, most methods assume that the variables in the time series are measured on an interval scale, which is not the case when Likert-scale items were used. Ignoring the scale of the variables can be problematic and bias the results. Additionally, most methods also assume that the time series are stationary, which is rarely the case. To tackle these disadvantages, we propose a model that combines the partial credit model (PCM) of the item response theory framework and the time-varying autoregressive model (TV-AR), which is a popular model used to study psychological dynamics. The proposed model is referred to as the time-varying dynamic partial credit model (TV-DPCM), which allows to appropriately analyze multivariate polytomous data and nonstationary time series. We test the performance and accuracy of the TV-DPCM in a simulation study. Lastly, by means of an example, we show how to fit the model to empirical data and interpret the results.