Deriving Expected Values of Model Parameters when Using Sum Scores in Simulation Research

There is increasing interest in using factor scores in structural equation models and there have been numerous methodological papers on the topic. Nevertheless, sum scores, which are computed from adding up item responses, continue to be ubiquitous in practice. It is therefore important to compare simulation results involving factor scores to those of sum scores so that applied researchers can understand the advantages. Yet, researchers do not often compare sum scores and factor scores in terms of bias, a common simulation outcome. A reason for this is that sum scores are on a different scale and it is unclear how to compare sum scores to other types of scores. The purpose of this paper is to provide guidance for methodological researchers who wish to conduct research on scoring how to compute bias for sum scores by obtaining the expected values of their model parameters under a sum score model.