Three Approaches to Using Lengthy Ordinal Scales in Structural Equation Models

Lengthy scales or testlets pose certain challenges for structural equation modeling (SEM) if all the items are included as indicators of a latent construct. Three general approaches to modeling lengthy scales in SEM (parceling, latent scoring, and shortening) have been reviewed and evaluated. A hypothetical population model is simulated containing two exogenous constructs with 14 indicators each and an endogenous construct with four indicators. The simulation generates data sets with varying numbers of response options, two types of distributions, factor loadings ranging from low to high, and sample sizes ranging from small to moderate. The population model is varied to incorporate one of the following: (a) single parcels, (b) various parcels as indicators of two exogenous constructs, (c) latent scores as observed exogenous variables, and (d) four and six individual items as indicators of two exogenous constructs. The dependent variables evaluated are biases in the covariance and partial covariance population parameters. Biases in these parameters are found to be minimal under the following conditions: (a) when parcels of indicators of five response options are used as indicators of two latent exogenous constructs, (b) when latent scores are used as observed variables at sample sizes above 100 and with indicators that are relatively less skewed in the case of dichotomous indicators, and (c) when four or six individual items with high or diverse factor loadings are used as indicators of two exogenous constructs. These findings provide guidelines for resolving the inconsistency of findings from applying various approaches to empirical data.