Explaining Constraint Interaction: How to Interpret Estimated Model Parameters under Alternative Scaling Methods

TL;DR

This paper investigates how different scaling methods affect the interpretation of estimated model parameters, explaining the phenomenon of constraint interaction and providing guidelines for correct interpretation.

Contribution

It introduces a detailed explanation of constraint interaction caused by scaling methods and offers rules for interpreting parameters under various scaling approaches.

Findings

Scaling methods influence which parameters are estimated.

Constraint interaction depends on the choice of scaling.

Guidelines for correct interpretation of parameters are proposed.

Abstract

In this paper, we explain the reasons behind constraint interaction, which is the phenomenon that the results of testing equality constraints may depend heavily on the scaling method used. We find that the scaling methods interfere with the testing procedures because scaling methods determine which transformations of population quantities model parameters actually estimate. We therefore also develop rules on how to correctly interpret estimates of model parameters under alternative scaling methods.