Parameter Shrinkage Estimation of Reading Count Data Models

The paper investigates the efficacy of parameter shrinkage on count data models through the use of penalized likelihood methods. The goal is to fit models to count data where multiple independent count variables are observed with only a moderate sample size per variable. The possibility of zero-inflated counts is also plausible for the data. In the context considered here, elementary school-aged kids were given passages of different lengths to read. We aim to find a suitable model that accurately captures their oral reading fluency (ORF) as measured by number of words read incorrectly (WRI) scores. The dataset contains information about the length of the passages (number of words) and WRI scores obtained from recorded reading sessions. The idea is to find passage-level parameter estimates with good MSE properties. Improvement over maximum likelihood MSE is considered by applying appending penalty functions to the negative log-likelihood. Three statistical models are considered for WRI scores, namely the binomial, zero-inflated binomial, and beta-binomial. The paper explores two types of penalty functions resulting in estimators that are either closer to $0$ or closer to the equivalent parameters corresponding to other passages. The efficacy of the shrinkage methods are explored in an extensive simulation study.