Inference for error-prone count data: estimation under a binomial convolution framework

doi:10.1080/02664763.2026.2646574

Inference for error-prone count data: estimation under a binomial convolution framework

2026-03-01

0

PRE

AI

C

Christina Vu *

P

Potgieter, Cornelis J.

DOI：10.1080/02664763.2026.2646574

Original

Original request for help

Save

Abstract

En 中文

Measurement error in count data is common but often overlooked, particularly when scores are bounded and arise from discrete processes. Motivated by oral reading fluency assessments, we propose a binomial convolution model that generalizes binary misclassification frameworks to integer-valued outcomes, allowing for both overcounting and undercounting. The model distinguishes between true positive and true negative rates and respects the finite support of the data. Assuming a subset of cases with both contaminated and gold-standard scores, we develop three estimation methods: maximum likelihood estimation (MLE), linear regression, and generalized method of moments (GMM). Simulation studies show that MLE performs best under correct model specification, while regression is more robust but less precise; GMM balances model flexibility and efficiency but is sensitive to outliers. Applied to real data comparing two error-prone scoring mechanisms, our framework is able to reveal differences in scoring accuracy and consistency. Findings highlight the practical implications of estimator choice and underscore the importance of explicitly modeling asymmetric measurement error in count data.

Keywords:

Binomial convolution

measurement error

misclassification

oral reading fluency

sensitivity

specificity

Inference for error-prone count data: estimation under a binomial convolution framework

Abstract

Journal

Organization