Testing equivalence to binary generalized linear models with application to logistic regression
This study addresses the problem of assessing whether observed data are “sufficiently close” to a binary generalized linear model—such as logistic regression—with fully categorical covariates, rather than requiring exact model fit. To this end, the authors propose a formal equivalence testing framework based on minimum distance methodology. The approach leverages both asymptotic theory and bootstrap procedures to compute critical values, thereby filling a critical gap left by conventional goodness-of-fit tests, which are ill-suited for evaluating practical equivalence. Through extensive simulation studies and analyses of two real-world datasets, the proposed method demonstrates strong finite-sample performance and practical utility, offering a robust tool for model adequacy assessment in applied settings.