The purpose of the present study was to extend the model of measurement invariance by simultaneously estimating invariance across multiple populations in the dichotomous instrument case using multi-group confirmatory factor analytic and multiple indicator multiple causes (MIMIC) methodologies. Using the Arabic version of the General Aptitude Test (GAT), invariance was tested at the configural, metric, and scalar levels. Results indicated that the hybrid model that incorporates both the multi-group case and the MIMIC model provide a viable alternative to the measurement of invariance between variables when they interact. Metric and scalar invariance were supported for all of GAT’s subscales with the exception of Word Meaning for which lack of invariance was likely caused by model misspecification. Subtle effects were observed in favor of public school testees, but they did not exceed significance levels.
AlharbiA. K. (in press). The performance of secondary education graduates in the Kingdom of Saudi Arabia in basic cognitive abilities and skills. Journal of Education and Psychology.
2.
AlqataeeA. A.AlharbiK. A. (2012). The ability of admission criteria to predict the first-year college grade point average in some Saudi universities (Technical Report No. TR009-2012). Riyadh, Saudi Arabia: The National Center for Assessment in Higher Education.
3.
BollenK. (1989). Structural equations with latent variables. New York, NY: Wiley.
4.
CheungG. W.RensvoldR. B. (2002). Evaluating goodness of fit indexes for testing measurement invariance. Structural Equation Modeling: A Multidisciplinary Journal, 9, 233-255.
5.
CochranW. G. (1952). The chi-square test of goodness of fit. Annals of Mathematical Statistics, 23, 315-345.
6.
ColeN. S.ZiekyM. J. (2001). The new faces of fairness. Journal of Educational Measurement, 38, 369-382.
7.
FinchH. (2005) The mimic model as a method for detecting DIF: Comparison with Mantel–Haenszel, Sibtest, and the IRT likelihood ratio. Applied Psychological Measurement, 29, 278-295.
8.
FrenchB. F.FinchW. H. (2006). Confirmatory factor analytic procedures for the determination of measurement invariance. Structural Equation Modeling, 13, 378-402.
9.
FrenchB. F.FinchW. H. (2011). Model misspecification and invariance testing using confirmatory factor analytic procedures. Journal of Experimental Education, 79, 404-428.
10.
HuL.BentlerP. M. (1998). Fit indices in covariance structure modeling: Sensitivity to underparameterized model misspecification. Psychological Methods, 3, 424–453.
11.
HuL.-T.BentlerP. M. (1999). Cutoff criteria for fit indexes in covariance structure analysis: Conventional criteria versus new alternatives. Structural Equation Modeling: A Multidisciplinary Journal, 6, 1-55.
12.
JoreskogK. (1973). A general method for estimating a linear structural equation system. In GoldbergerA. S.DuncanO. D. (Eds.), Structural equation models in the social sciences (pp. 85-112). New York, NY: Seminar Press.
13.
KimE. S.YoonM.LeeT. (2012). Testing measurement invariance using MIMIC: Likelihood ratio test with a critical value adjustment. Educational and Psychological Measurement, 72, 469-492.
14.
MacCallumR. C.BrowneM. W.SugawaraH. M. (1996). Power analysis and determination of sample size for covariance structure modeling. Psychological Methods, 1, 130-149.
15.
MakranskyG.BilenbergN. (2014). Psychometric Properties of the Parent and Teacher ADHD Rating Scale (ADHD-RS) Measurement Invariance Across Gender, Age, and Informant. Assessment, 21, 694-705.
16.
MarshH. W.NagengastB.MorinA. J. S. (2013). Measurement invariance of big-five factors over the life span: ESEM tests of gender, age, plasticity, maturity, and la dolce vita effects. Developmental Psychology, 49, 1194-1218. doi:10.1037/a0026913
17.
MuellerR. (1996). Basic principles of structural equation modeling: An introduction to Lisrel and EQS. New York, NY: Springer.
18.
MuthénB.ChristoffersonA. (1981). Simultaneous factor analysis of dichotomous variables in several groups. Psychometrika, 46, 407-419.
19.
MuthénL. K.MuthénB. O. (2007). Mplus user’s guide 4. Los Angeles, CA: Author.
20.
MuthénL. K.MuthénB. O. (2002). How to use a Monte Carlo study to decide on sample size and determine power. Structural Equation Modeling: A Multidisciplinary Journal, 4, 599-620.
PreacherK. J.CoffmanD. L. (2006). Computing power and minimum sample size for RMSEA [Computer software]. Available from http://quantpsy.org/
23.
RandallJ.EngelhardG. (2010). Using confirmatory factor analysis and the Rasch model to assess measurement invariance in a high stakes reading assessment. Applied Measurement in Education, 23, 286-306.
24.
RaykovT.MarcoulidesG.LiC. (2012). Measurement invariance for latent constructs in multiple populations: A critical review and refocus. Educational and Psychological Measurement, 72, 954-974.
25.
ReiseS.WidamanK.PughR. (1993). Confirmatory factor analysis and item response theory: Two approaches for exploring measurement invariance. Psychological Bulletin, 114, 552-566.
26.
RigdonE. E. (1994). Calculating degrees of freedom for a structural equation model. Structural Equation Modeling: A Multidisciplinary Journal, 1, 274-278.
27.
StarkS.ChernyshenkoO.DrasgowF. (2006). Detecting differential item functioning with confirmatory factor analysis and item response theory. Toward a unified strategy. Journal of Applied Psychology, 91, 1292-1306.
28.
TanakaJ. S. (1993). Multifaceted conceptions of fit in structural equation models. In BollenK. A.LongJ. S. (Eds.), Testing structural equation models (pp. 10-40). Newbury Park, CA: Sage.
29.
VandenbergR. J.LanceC. E. (2000). A review and synthesis of the measurement invariance literature: Suggestions, practices, and recommendations for organizational research. Organizational Research Methods, 3, 4-70.
