This study examined how three item response models performed when they were applied to data collected from a conventionally developed Likert-type personality scale. Each model examined isbased on a different response assumption: the multiple linear factor analysis model (continuous responses), the TOBIT factor analysis model (censored responses), and the multidimensional graded response model. The item and examinee parameters of the models were estimated using different discrepancy functions and current software implementations. Comparisons were made in terms of the goodness-of-fit of the model, parameter estimates, and criterion-related validity. Results showed that the models’ response assumptions were reasonably tenable and that the solutions obtained in all cases were similar. More complex models did not lead to substantial improvement in predictive validity.
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References
1.
Aguilar, A. (1984). CAR cuestionario de ansiedad y rendimiento. Unpublished manuscript, University of Barcelona, Spain.
2.
Babakus, E. , Ferguson, C. E., & Jöreskog, K. 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.
Bartholomew, D. J. (1981). Posterior analysis of the factor model. British Journal of Mathematical and Statistical Psychology, 34, 93–99.
4.
Bentler, P. M. (1977). Factor simplicity index and transformations. Psychometrika, 42, 277–295.
5.
Bentler, P. M. (1990). Comparative fit indices in structural models. Psychological Bulletin, 107, 238–246.
6.
Bock, R. D. (1985). Contributions of empirical Bayes and marginal maximum likelihood methods to the measurement of individual differences. In E. E. Roskam (ed.), Measurement and personality assessment (pp. 75–99). New York: Elsevier.
7.
Bock, R. D. , & Mislevy, R. (1982). Adaptative EAP estimation of ability in a microcomputer environment. Applied Psychological Measurement, 6, 431–444.
8.
Bollen, K. A. , & Barb, K. H. (1981). Pearson’s r and coarsely categorized measures. American Sociological Review, 46, 232–239.
9.
Brown, R. L. (1989a). Using covariance modeling for estimating reliability on scales with ordered polytomous variables. Educational and Psychological Measurement, 49, 385–398.
10.
Brown, R. L. (1989b). Congeneric modeling of reliability using censored variables. Applied Psychological Measurement, 13, 151–159.
11.
Brown, R. L. (1992). Estimation problems with Type 1 censored response distributions in structural equation modeling. Educational and Psychological Measurement, 52, 325–336.
12.
Browne, M. W. (1982). Covariance structures. In D. M. Hawkins (Ed.), Topics in applied multivariate analysis (pp. 72–141). Cambridge MA: Cambridge University Press.
13.
Browne, M. W. (1984). Asymptotic distribution free methods in analysis of covariance structures. British Journal of Mathematical and Statistical Psychology, 37, 62–83.
14.
Browne, M. W. , & Cudeck, R. (1993). Alternative ways of assessing model fit. In K. A. Bollen & J. S. Long (Eds.), Testing structural equation models (pp. 136–162). Newbury Park CA: Sage.
15.
De Ayala, R. J. (1994). The influence of multidimensionality on the graded response model. Applied Psychological Measurement, 18, 155–170.
16.
Deffenbacher, J. L. (1980). Worry and Emotionality in test anxiety. In I. G. Sarason (Ed.), Test anxiety: Theory, research and applications (pp. 111–128). Hillsdale NJ: Erlbaum.
17.
Dolan, C. V. (1994). Factor analysis of variables with 2, 3, 5 and 7 response categories: A comparison of categorical variable estimators using simulated data. British Journal of Mathematical and Statistical Psychology, 47, 309–326.
18.
Drasgow, F. (1995). Introduction to the polytomous IRT special issue. Applied Psychological Measurement, 19, 1–3.
19.
Hembree, R. (1988). Correlates, causes, effects, and treatment of test anxiety. Review of Educational Research, 58, 47–79.
20.
Hu, L. , Bentler, P. M., & Kano, Y. (1992). Can test statistics in covariance structure analysis be trusted?Psychological Bulletin, 112, 351–362.
21.
Jöreskog, K. G. (1979). A general approach to confirmatory maximum likelihood factor analysis with addendum. In J. Magidson (Ed.), Advances in factor analysis and structural equation models (pp. 21–43). Cambridge MA: Abt Books.
22.
Jöreskog, K. G. , & Sörbom, D. (1996a). LISREL8: User’s Reference Guide. Chicago: Scientific Software.
23.
Jöreskog, K. G. , & Sörbom, D. (1996b). PRELIS2: User’s Reference Guide. Chicago: Scientific Software.
24.
Koch, W. R. (1983). Likert scaling using the graded response latent trait model. Applied Psychological Measurement, 7, 15–32.
25.
Liebert, R. M. ,& Morris, L. W. (1967). Cognitive and emotional components of test anxiety: A distinction and some initial data. Psychological Reports, 20, 975–978.
26.
MacCallum, R. J. ,& Tucker, L. R. (1991). Representing sources of error in the common-factor model: Implications for theory and practice. Psychological Bulletin, 109, 502–511.
27.
Mooijaart, A. (1983). Two kinds of factor analysis for ordered categorical variables. Multivariate Behavioral Research, 18, 423–441.
28.
Morris, L. W. , Davis, M. A., & Hutchings, C. H. (1981). Cognitive and emotional components of anxiety: Literature review and a revised worryemotionality scale. Journal of Educational Psychology, 73, 541–555.
29.
Morris, L. W. , & Fulmer, R. S. (1976). Test anxiety (worry and emotionality) changes during academic-testing as a function of feedback and test importance. Journal of Educational Psychology, 68, 817–824.
30.
Muraki, E. (1990). Fitting a polytomous item response model to Likert-type data. Applied Psychological Measurement, 14, 59–71.
31.
Muraki, E. , & Bejar, I. I. (1995, July). Fullinformation factor analysis of polytomous item responses of NCARB exams. Paper presented at the European meeting of the Psychometric Society, Leiden, the Netherlands.
32.
Muraki, E. , & Carlson, J. E. (1995). Full-information factor analysis for polytomous item responses. Applied Psychological Measurement, 19, 73–90.
33.
Muthén, B. (1984). A general structural equation model with dichotomous, ordered, categorical and continuous latent variable indicators. Psychometrika, 49, 115–132
34.
Muthén, B. (1987). LISCOMP: Analysis of linear structural equations with a comprehensive measurement model. Mooresville IN: Scientific Software.
35.
Muthén, B. (1989). Tobit factor analysis. British Journal of Mathematical and Statistical Psychology, 42, 241–250.
36.
Muthén, B. (1993). Goodness of fit with categorical and other nonnormal variables. In K. A. Bollen & J. S. Long (Eds.), Testing structural equation models (pp. 205–234). Newbury Park CA: Sage.
37.
Muthén, B. , & Kaplan, D. (1985). A comparison of some methodologies for the factor analysis of nonnormal Likert variables. British Journal of Mathematical and Statistical Psychology, 38, 171–189.
38.
Muthén, B. , & Kaplan, D. (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.
39.
Olsson, U. (1979). On the robustness of factor analysis against crude classification of the observations. Multivariate Behavioral Research, 14, 485–500.
40.
Potthast, M. J. (1993). Confirmatory factor analysis of ordered categorical variables with large models. British Journal of Mathematical and Statistical Psychology, 46, 273–286.
41.
Rigdon, E. E. , & Ferguson, C. E. (1991). The performance of the polychoric correlation coefficient and selected fitting functions in confirmatory factor analysis with ordinal data. Journal of Marketing Research, 28, 491–497.
42.
Samejima, F. (1969). Estimation of latent ability using a response pattern of graded scores.Psychometrika Monographs, 34, (4, Pt. 2).
43.
Stanley, J. C. , & Wang, M. D. (1970). Weighting test items and test-item options, an overview of the analytical and empirical literature. Educational and Psychological Measurement, 30, 21–35.
44.
Stroud, A. H. , & Secrest, D. (1966). Gaussian quadrature formulas. Englewood Cliffs NJ: Prentice-Hall.
45.
Takane, Y. ,& de Leeuw, J. (1987). Onthe relationship between item response theory and factor analysis of discretized variables. Psychometrika, 52, 393–408.
46.
Tanaka, J. S. (1993). Multifaceted conceptions of fit in structural models. In K. A. Bollen & J. S. Long (Eds.), Testing structural equation models (pp. 10–39). Newbury Park CA: Sage.
47.
Waller, N. G. ,& Muthén, B. (1992). GeneticTobit factor analysis: Quantitative genetic modeling with censored data. Behavior Genetics, 22, 265–292.
