Bayesian multilevel logistic regression models: a case study applied to the results of two questionnaires administered to university students

Cristian David Correa-Álvarez (), Juan Carlos Salazar-Uribe () and Luis Raúl Pericchi-Guerra ()
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Cristian David Correa-Álvarez: Instituto Tecnológico Metropolitano (ITM)
Juan Carlos Salazar-Uribe: Universidad Nacional de Colombia (Medellín campus)
Luis Raúl Pericchi-Guerra: University of Puerto Rico

Computational Statistics, 2023, vol. 38, issue 4, No 11, 1810 pages

Abstract: Abstract Bayesian multilevel models—also known as hierarchical or mixed models—are used in situations in which the aim is to model the random effect of groups or levels. In this paper, we conduct a simulation study to compare the predictive ability of 1-level Bayesian multilevel logistic regression models with that of 2-level Bayesian multilevel logistic regression models by using the prior Scaled Beta2 and inverse-gamma distributions to model the standard deviation in the 2-level. Then, these models are employed to estimate the correct answers in two questionnaires administered to university students throughout the first academic semester of 2018. The results show that 2-level models have a better predictive ability and provide more precise probability intervals than 1-level models, particularly when the prior Scaled Beta2 distribution is used to model the standard deviation in the second level. Moreover, the probability intervals of 1-level Bayesian multilevel logistic regression models proved to be more precise when Scaled Beta2 distributions, rather than an inverse-gamma distribution, are employed to model the standard deviation or when 1-level Bayesian multilevel logistic regression models, are used.

Keywords: Bayesian inference; Prior distributions; Multilevel models; Bayesian logistic models (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s00180-022-01287-4

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