Exploring differences in self-control across sex, race, age, education, and language: Considering a bifactor MIMIC model

Purpose: Two research avenues on self-control measurement have explored the factor structure and identified differential item functioning (DIF) in the Grasmick et al. (1993) scale. This work integrates and extends this research by considering the consequences of factor structure for the detection of biased items across age, sex, race, education, and language. Methods: Within a structural equation modeling framework, unidimensional and bifactor multiple indicator, multiple causes (MIMIC) models are employed to detect DIF in covariates under alternative factor structures. Effects of covariates on item responses are decomposed into general, specific, and DIF effects and mean difference tests are conducted. Results: Factor structure contributed to an overestimation of DIF; nonetheless, 32% of all possible covariate-to-item effects exhibited DIF, which was most common across race and language. Bias due to factor structure and DIF for mean difference tests in self-control was confined to race, where the effect was underestimated by half. Except for sex, there were generally larger implications of factor structure and DIF for mean difference tests of the elements. Conclusion: Apart from race, testing group differences in self-control with an observed scale score is largely unbiased. Testing group differences in elements using observed subscores is frequently biased and generally unsupported.