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

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.