This paper examines the implications of violating assumptions concerning the continuity and distributional properties of data in establishing measurement models in social science research. The General Health Questionnaire-12 uses an ordinal response scale. Responses to the GHQ-12 from 201 Hong Kong immigrants on arrival in Australia showed that the data were not normally distributed. A series of confirmatory factor analyses using either a Pearson product-moment or a polychoric correlation input matrix and employing either maximum likelihood, weighted least squares or diagonally weighted least squares estimation methods were conducted on the data. The parameter estimates and goodness-of-fit statistics provided support for using polychoric correlations and diagonally weighted least squares estimation when analyzing ordinal, nonnormal data.
Get full access to this article
View all access options for this article.
References
1.
AndersonJ. C.GerbingD. W. (1984) The effect of sampling error on convergence, improper solutions, and goodness-of-fit indices for maximum likelihood confirmatory factor analysis. Psychometrika, 49, 155–173.
2.
BabakusE.FergusonJ. C. E.JöreskogK. G. (1987) The sensitivity of confirmatory maximum likelihood factor analysis to violations of measurement scale and distributional assumptions. Journal of Marketing Research, 24, 222–228.
3.
BrowneM. W. (1984) Asymptotically distribution-free methods for the analysis of covariance structures. British Journal of Mathematical and Statistical Psychology, 37, 62–83.
4.
FrenchD. J.TaitR. J. (2004) Measurement invariance in the General Health Questionnaire-12 in young Australian adolescents. European Child and Adolescent Psychiatry, 13, 17.
5.
GoldbergD.WilliamsP. (1988) A user's guide to the General Health Questionnaire. Windsor: NFER-Nelson.
6.
GraetzB. (1991) Multidimensional properties of the General Health Questionnaire. Social Psychiatry and Psychiatric Epidemiology, 26, 132–138.
7.
GurejeO. (1991) Reliability and the factor structure of the Yoruba version of the 12-item General Health Questionnaire. Acta Psychiatrica Scandinavica, 84, 125–129.
8.
HuL.BentlerR. M. (1992) Can test statistics in covariance structure analysis be trusted?Psychological Bulletin, 112, 351–362.
9.
JöreskogK. G. (1990) New developments in LISREL: Analysis of ordinal variables using polychoric correlations and weighted least squares. Quality and Quantity, 24, 387–404.
10.
JöreskogK. G.SörbomD. (1981) LISREL: Analysis of linear structural relationships by the method of maximum likelihood (Version V). Chicago, IL: National Educational Resources, Inc.
KlineR. B. (1998) Principles and practice of structural equation modeling. New York: Guilford.
14.
Maydeu-OlivaresA. (2001) Limited information estimation and testing of Thurstonian models for paired comparison data under multiple judgment sampling. Psychometrika, 66, 209–228.
15.
MuthénB. O. (1993) Goodness of fit with categorical and other nonnormal variables. In BollenK. A.LongJ. S. (Eds.), Testing structural equation models. Newbury Park, CA: Sage. Pp. 205–234.
16.
MuthénB. O.du ToitS. H. C.SpisicD. (1997) Robust inference using weighted least squares and quadratic estimating equations in latent variable modeling with categorical and continuous outcomes. (Unpublished manuscript)
17.
MuthénB. O.KaplanD. (1985) A comparison of some methodologies for the factor analysis of non-normal Likert variables. British Journal of Mathematical and Statistical Psychology, 38, 171–189.
18.
MuthénB. O.KaplanD. (1992) A comparison of some methodologies for the factor analysis of non-normal Likert variables: A note on the size of the model. British Journal of Mathematical and Statistical Psychology, 45, 19–30.
19.
OlssonU. (1979) Maximum likelihood estimates for the polychoric correlation coefficient. Psychometrika, 44, 443–460.
20.
PanP. C.GoldbergD. P. (1990) A comparison of the validity of GHQ-12 and GHQ-12 in Chinese primary care patients in Manchester. Psychological Medicine, 20, 931–940.
21.
SchmitzN.KruseJ.TressW. (1999) Psychometric properties of the General Health Questionnaire (GHQ-12) in a German primary care sample. Acta Psychiatrica Scandinavica, 100, 462–468.
22.
SchumackerR. E.BeyerleinS. T. (2000) Confirmatory factor analysis with different correlation types and estimation methods. Structural Equation Modeling, 7, 629–636.
