| Abstract | This thesis considers parameter estimation for different statistical models used on count data. 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. A sample of fourth-grade students were given one of ten available passages to read with these differing in length and difficulty. The observed number of words read incorrectly (WRI) is used to measure ORF. Five models are considered for WRI scores, namely the binomial, the Poisson, the zero-inflated binomial, the zero-inflated Poisson, and the beta-binomial distributions. We aim to efficiently estimate passage difficulty, a quantity expressed as a function of the underlying model parameters. In addition to considering ordinary maximum likelihood, two types of penalty functions are considered for penalized likelihood. The goal of shrinkage is to encourage 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. Big reductions in MSE relative to unpenalized maximum likelihood are observed. The thesis concludes with an analysis of the motivating ORF data. |
