Title: Binomial logistic modelling for aggregate binary data: application to preschoolers' alphabet knowledge

Authors: Seongah Im; Barbara D. DeBaryshe

Addresses: Department of Educational Psychology, University of Hawai'i at Mānoa, Honolulu, HI 96822, USA ' Center on the Family, University of Hawai'i at Mānoa, Honolulu, HI 96822, USA

Abstract: This study investigated the use of different binomial logistic models as alternatives to the normal model when analysing non-normal aggregate outcomes that are sums of correlated binary responses. The outcome variables provided in the two illustrative examples were preschoolers' uppercase and lowercase letter naming knowledge with different shapes of non-normal distributions. The binomial, beta-binomial, and mixed binomial models with logit links were examined and compared to each other and to the normal linear model. Results were consistent in both examples. Among the models compared, the beta-binomial and mixed binomial models with overdispersion parameters captured interdependence among correlated binary responses. In addition, the mixed binomial model further explained remaining overdispersion and best fitted the data. Implications including advocating for the use of the binomial models with overdispersion parameters for clustered data were further discussed.

Keywords: correlated binary responses; non-normal; aggregate data; mixed binomial; overdispersion; beta-binomial; test scores; alphabet knowledge.

DOI: 10.1504/IJQRE.2020.106566

International Journal of Quantitative Research in Education, 2020 Vol.5 No.1, pp.67 - 85

Received: 08 Oct 2018
Accepted: 14 Apr 2019

Published online: 15 Apr 2020 *

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