Misleading effects in relational event models

Abstract

In a broad field of applications, high-dimensional problems occur, i.e. problems where the number of parameters in a regression-type model is too high compared to the sample size or can even exceed it. Especially in presence of categorical explanatory variables (i.e. factors), such problems can occur easily even if the number of candidate factors is moderate. While penalized regression approaches enable a simultaneous variable selection and regression coefficients’ estimation, the implementation of further statistical inference procedures, e.g., likelihood ratio tests (LRT), is not straightforward, due to the high-dimensionality of the problem. For this, we propose a two-stage penalized logistic regression approach for a penalty function enforcing both factor selection and levels fusion simultaneously. In particular, we extend the (multiple) sample splitting approach, which is introduced for penalization methods performing only variable selection, to a method performing factor selection as well as levels fusion. We specify and adjust the regularity conditions for penalization methods of this type, considering two different approaches for multiplicity adjustments, i.e. the Benjamini- Hochberg procedure and Bonferroni correction.We further investigate asymptotic properties, such as type-I-error control, concluding that the proposed two-stage approach is adequate for applications