Characterizing a Latent Construct

Updated February 5, 2014

I encourage everyone to think of a latent construct (such as the CONSERVATIVISM construct in this entry) as the shared variation (or correlatedness) between the manifest indicators. My reasoning, loosely stated, followed these three steps.

1. The standardized factor loadings are based upon the correlations between any two manifest indicators. For example, if one indicator has a standardized loading of .70 and another has a loading of .80, the Pearson correlation between the two indicators will be .56 or thereabouts (i.e., the product of the two loadings). High loadings go along with high correlations.

2. High loadings, which are considered desirable for having a strong factor, thus signify correlatedness (or shared variation) among the indicators.

3. Taking a little leap from step 2, one can think of the factor itself as representing shared variation among its indicators. The "tiny bubbles" pointing to each manifest indicator thus represent variation in a given indicator that is not due to the common factor and are considered to represent error variance. Quoting from Barbara Byrne (2001; Structural Equation Modeling with AMOS):

Error associated with observed variables represents measurement error, which reflects on their adequacy in measuring the related underlying factors... Measurement error derives from two sources: random measurement error... and error uniqueness, a term used to describe error variance arising from some characteristic that is considered to be specific (or unique) to a particular indicator variable. (p. 9)

Going back to our example of the common cold as a common factor, uniqueness would refer to instances of, for example, sneezing due to allergies, not as part of a cold.