Beta-Binomial Model for Count Data: An Application in Estimating Model-Based Oral Reading Fluency

Abstract

In this article, the beta-binomial model for count data is proposed and demonstrated in terms of its application in the context of oral reading fluency (ORF) assessment, where the number of words read correctly (WRC) is of interest. Existing studies adopted the binomial model for count data in similar assessment scenarios. The beta-binomial model, however, takes into account extra variability in count data that have been neglected by the binomial model. Therefore, it accommodates potential overdispersion in count data compared to the binomial model. To estimate model-based ORF scores, WRC and response times were jointly modeled. The full Bayesian Markov chain Monte Carlo method was adopted for model parameter estimation. A simulation study showed adequate parameter recovery of the beta-binomial model and evaluated the performance of model fit indices in selecting the true data-generating models. Further, an empirical analysis illustrated the application of the proposed model using a dataset from a computerized ORF assessment. The obtained findings were consistent with the simulation study and demonstrated the utility of adopting the beta-binomial model for count-type item responses from assessment data.