ABSTRACT

This chapter focuses on the estimation of mean structures in confirmatory factor analysis. It examines the structure of a common intelligence measure, the Kaufman Assessment Battery for Children—Second Edition-II, for adolescent boys versus girls. When mean structures are estimated, common steps for establishing measurement invariance include: configural invariance, in which the same pattern of fixed and free loadings is tested across two or more groups. Metric invariance, also known as weak factorial invariance or factor loading invariance, in which the values of the factor loadings are constrained to be equal across groups. Intercept invariance, also known as scalar invariance, or strong factorial invariance, in which the values of the measured variable intercepts are constrained to be equal across the groups. Residual invariance, also known as strict measurement invariance, in which the measured variable residual variances are constrained to be equal across groups. Testing for invariance in measurement residuals completes the steps involved in testing for measurement invariance.