Preprint Article Version 1 This version is not peer-reviewed

# $L_p$ Loss Functions in Invariance Alignment and Haberman Linking

Version 1 : Received: 3 June 2020 / Approved: 4 June 2020 / Online: 4 June 2020 (13:25:49 CEST)

How to cite: Robitzsch, A. $L_p$ Loss Functions in Invariance Alignment and Haberman Linking. Preprints 2020, 2020060034 (doi: 10.20944/preprints202006.0034.v1). Robitzsch, A. $L_p$ Loss Functions in Invariance Alignment and Haberman Linking. Preprints 2020, 2020060034 (doi: 10.20944/preprints202006.0034.v1).

## Abstract

The comparison of group means in latent variable models plays a vital role in empirical research in the social sciences. The present article discusses extensions of invariance alignment and Haberman linking concerning the choice of linking functions for comparisons of many groups. Robust linking functions are proposed for invariance alignment and robust Haberman linking that are particularly suited to item response data under partial invariance. In a simulation study, it is shown that both linking approaches have comparable performance, and in some conditions, the newly proposed robust Haberman linking outperforms invariance alignment.

## Subject Areas

factor model; 2PL model; linking; invariance alignment; Haberman linking; partial invariance; item response model; structural equation model; differential item functioning