Discriminating Between Measurement Scales Using Nonnested Tests and 2SLS: Monte Carlo Evidence

How should researchers choose between competing scales in predicting a criterion variable? This article proposes the use of nonnested tests for the 2SLS estimator of latent variable models to discriminate between scales. The finite sample performance of these tests is compared to structural equation modeling information-based criteria such as root mean squared error of approximation (RMSEA) and Akaike's Information Criterion (AIC). The Cox and encompassing tests and augmented versions of these tests are compared to the inconsistent ordinary least squares (OLS) J test. An augmented version of the encompassing test performs best for sample sizes of 100 or more and can be recommended for use on scales with high reliability (0.9) and sample sizes of 200 or more, under varying regressor and error distributions. The OLS J test performs best for small samples of N = 50 and can be recommended for use in small samples when scales have high reliability (0.9). Relative to the nonnested tests, the information-based criteria perform poorly.