Penalized Likelihood Methods for Modeling Count Data

TL;DR

This paper develops penalized likelihood methods for estimating parameters in count data models, demonstrating significant MSE reduction in simulations and applying the approach to oral reading fluency data.

Contribution

It introduces penalized likelihood techniques tailored for count data models, improving parameter estimation accuracy over traditional methods.

Findings

Significant MSE reduction with penalized estimates in simulations

Effective estimation of passage difficulty from ORF data

Application to real-world ORF data demonstrates practical utility

Abstract

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. 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. Three models are considered for WRI scores, namely the binomial, the zero-inflated binomial, and the beta-binomial. We aim to efficiently estimate passage difficulty, a quantity expressed as a function of the underlying model parameters. Two types of penalty functions are considered for penalized likelihood with respective goals of shrinking parameter estimates closer to zero or closer to one another. A simulation study evaluates the efficacy of the shrinkage estimates using Mean Square Error (MSE) as metric. Big reductions in MSE relative to unpenalized maximum likelihood are observed. The paper concludes with an analysis of the motivating ORF data.