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.

Chronicle of a Measurement Unforetold

“…For example, the Rasch and the partial credit model were reformulated within the state-space modeling framework by Rijn et al (2010). The Rasch model was also extended to handle continuous time data by Hecht et al (2019), and recently, the partial credit model was extended to analyze categorical and multivariate time series data Castro-Alvarez et al (2022a). These models have been specially developed to handle intensive longitudinal data when the items are dichotomous or polytomous (e.g., Likert-scale items).…”

“…Furthermore, they also allow understanding the properties and the quality of the items and scales by means of the item parameters, the item characteristic function, and the item information function. In this chapter, we are specially interested in the time-varying dynamic partial credit model (TV-DPCM;Castro-Alvarez et al, 2022a) because this model is a promising approach that can handle non-stationary time series. The TV-DPCM is a combination of the partial credit model (PCM; Masters, 2016) and the time-varying autoregressive model (TV-AR; Bringmann et al, 2017).…”

“…Within the IRT framework, the PPMC method has been introduced for dichotomous IRT models by Glas and Meijer (2003) and Sinharay (2005Sinharay ( , 2006, and for polytomous IRT models by Li et al (2017) and Zhu and Stone (2011). Based on these previous studies, we adapt and extend existing test statistics and discrepancy measures to assess the goodness-of-fit of the TV-DPCM (Castro-Alvarez et al, 2022a). The PPMC tools presented in this chapter can also be generalized to other dynamic IRT models.…”

“…A popular set of tools to handling temporal dependence consists of autoregressive (AR) models, which are a family of statistical models in which the structure of the time-dependency in the data is explicitly modeled through regression equations (e.g., Bringmann et al, 2017;Rovine & Walls, 2006). A recent example of an AR model based on IRT is the time-varying dynamic partial credit model that was suggested by Castro-Alvarez et al (2022a).…”

“…Also, in contrast with Bringmann et al (2017), in the TV-DPCM, the autoregressive effect is not allowed to change over time. This constrain was kept because the authors of the TV-DPCM did not succeed on writing a working model that also included a time-varying autoregressive effect (Castro-Alvarez et al, 2022a).…”