Likelihood-Based Estimation of Model-Derived Oral Reading Fluency Under Overdispersed Count-Time Data

This is the authors' abstract. We don't add key points for this paper.

Model-derived word read correctly per minute (WCPM) scores have been shown to exhibit better psychometric properties than observed WCPM scores for assessing oral reading fluency. These model-derived WCPM scores are estimated by jointly modeling reading count data and time data. Potgieter et al. (2026) showed that it is critical to take into account the potential overdispersion in the reading count data to obtain accurate and precise model parameter estimates in the calibration stage. However, likelihood-based estimators of model-derived WCPM scores that account for such overdispersion are lacking in the scoring stage. This study fills this gap by deriving the maximum likelihood (ML), the maximum a posteriori (MAP), and the expected a posteriori (EAP) estimators for model-derived WCPM scores under overdispersed count data. In addition, we investigate the impact of ignoring overdispersion in implementing likelihood-based estimators using a simulation study and real data analysis. We also compare the performance of likelihood-based estimators to a Bayesian Markov Chain Monte Carlo approach in these studies. Results show that the proposed likelihood-based estimators perform well, while neglecting overdispersion leads to underestimated standard errors in model-derived WCPM scores.