Penalized Likelihood Methods for Modeling of Reading Count Data
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The paper considers parameter estimation in count data models using penalized likelihood methods. The motivating data consists of multiple independent count variables with a moderate sample size per variable. The data were collected during the assessment of oral reading fluency (ORF) in school-aged children. Specifically, a sample of fourth-grade students was given one of ten possible to read with passages differing in length and difficulty. The observed number of words read incorrectly (WRI) is used to measure ORF. The goal of this paper is to efficiently estimate passage difficulty as measured by the expected proportion of words read incorrectly. Three models are considered for WRI scores, namely the binomial, the zero-inflated binomial, and the beta-binomial. Two types of penalty functions are considered for penalized likelihood, respectively with the goal of shrinking parameter estimates either closer to zero or closer to one another. A simulation study evaluates the efficacy of the shrinkage estimates using Mean Square Error (MSE) as a metric, with big reductions in MSE relative to maximum likelihood in some instances. The paper concludes by presenting an analysis of the motivating ORF data.
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