🤖 AI Summary
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.
📝 Abstract
We introduce a new equivalence test to show sufficiently good agreement of observed data with a binary generalized linear model (GLM). The test statistic is constructed via the minimum distance method. The test is developed for the important special case where all covariates are categorical. The critical values can be calculated using an asymptotic approximation or by means of bootstrapping. The application of the test to logistic regression is illustrated on two real data sets. The finite sample performance of the proposed test is studied by simulations which are based on these two data sets.