A note on structured means analysis for a single group

TL;DR

This paper examines how structured means analysis (SMM) estimates factor means in a single group, highlighting the implications of assumptions about unique factors and proposing more flexible estimation practices.

Contribution

It reveals the relationship between factor loadings and observed means in SMM and recommends estimating observed expectations freely when proportionality assumptions are invalid.

Findings

Larger observed means are associated with larger absolute factor loadings in SMM.

Smaller factor loadings can lead to larger estimated common factor means.

Proportionality between loadings and observed means should be critically evaluated in SMM.

Abstract

The calculation of common factor means in structured means analysis (SMM) is considered. The SMM equations imply that the unique factors are defined as having zero means. It was shown within the one factor solution that this definition implies larger absolute common factor loadings to co-occur with larger absolute expectations of the observed variables in the single group case. This result was illustrated by means of a small simulation study. It is argued that the proportionality of factor loadings and observed means should be critically examined in the context of SMM. It is recommended that researchers should freely estimate the observed expectations, whenever, the proportionality of loadings and observed means does not make sense. It was also shown that for a given size of observed expectations, smaller common factor loadings result in larger common factor mean estimates. It should therefore be checked whether variables with very small factor loadings occur when SMM results in very large absolute common factor means.