Bootstrap based goodness-of-fit tests for binary multivariate regression models

• Published in: Journal of the Korean Statistical Society 2022, 51(1), , pp.308-335
• Main Authors: van Heel, Mareike, Dikta, Gerhard, Braekers, Roel
• Format: Article
• Language: English
• Subjects: Applied Statistics; Bayesian Inference; Mathematics and Statistics; Research Article; Statistical Theory and Methods; Statistics; Statistics and Computing/Statistics Programs; 통계학
• ISSN: 1226-3192; 2005-2863
• DOI: 10.1007/s42952-021-00142-4

We consider a binary multivariate regression model where the conditional expectation of a binary variable given a higher-dimensional input variable belongs to a parametric family. Based on this, we introduce a model-based bootstrap (MBB) for higher-dimensional input variables. This test can be used to check whether a sequence of independent and identically distributed observations belongs to such a parametric family. The approach is based on the empirical residual process introduced by Stute (Ann Statist 25:613–641, 1997). In contrast to Stute and Zhu’s approach (2002) Stute & Zhu (Scandinavian J Statist 29:535–545, 2002), a transformation is not required. Thus, any problems associated with non-parametric regression estimation are avoided. As a result, the MBB method is much easier for users to implement. To illustrate the power of the MBB based tests, a small simulation study is performed. Compared to the approach of Stute & Zhu (Scandinavian J Statist 29:535–545, 2002), the simulations indicate a slightly improved power of the MBB based method. Finally, both methods are applied to a real data set.