A graphical comparison of empirical versus simu lated residual variation is presented as one way to as sess the goodness of fit of an item response theory model. The two forms of residual variation were gen erated through the separate calibration of empirical data and data "tailored" to fit the model, given the empirical parameter estimates. A variety of techniques illustrate the utility of using tailored residuals as a specific baseline against which empirical residuals may be understood.
Get full access to this article
View all access options for this article.
References
1.
Andrich, D. (1978). A rating formulation for ordered response categories . Psychometrika, 43, 561-573.
2.
Anscombe, F.J., & Tukey, J.W. (1963). The examination and analysis of residuals. Technometrics, 5, 141-160.
3.
Bachi, R. (1968). Graphical rational patterns. New York: Israel Universities Press.
4.
Barnett, V., & Lewis, T. (1978). Outliers in statistical data. New York: Wiley.
5.
Blom, G. (1958). Statistical estimates and transformed beta variables . New York: Wiley.
6.
Chambers, J.M., Cleveland, W.S., Kleiner, B., & Tukey, P.A. (1983). Graphical methods of data analysis. Boston: Duxbury Press.
7.
Cleveland, W.S. (1984). Graphical methods for data presentation: Full scale breaks, dot charts, and multibased logging. The American Statistician, 38, 270-280.
8.
Cleveland, W.S. (1985). The elements of graphing data. Monterey CA: Wadsworth.
9.
Collet, D., & Lewis, T. (1976). The subjective nature of outlier rejection procedures . Applied Statistician, 25, 228-237.
10.
Cook, R.D., & Weisberg, S. (1982). Residuals and influence in regression. New York: Chapman and Hall.
11.
Courington, S.M., Lambert, R.W., Ludlow, L.H., Wright, B.D., & Becker, S.W. (1983). The measurement of attitudes toward blindness and its importance for rehabilitation. International Journal of Rehabilitation Research, 6, 67-72.
12.
Daniel, C., & Wood, F.S. (1980). Fitting equations to data (2nd ed.). New York: Wiley.
13.
Draper, N.R., & Smith, H. (1981). Applied regression analysis (2nd ed.). New York: Wiley.
14.
Embretson, S. (1984). A general latent trait model for response processes . Psychometrika, 49, 175-186.
15.
Fischer, G.H. (1973). Linear logistic test model as an instrument in educational research. Acta Psychologica, 37, 359-374.
16.
Gnanadesikan, R. (1977). Methods for statistical data analysis of multivariate observations. New York: Wiley.
17.
Hahn, G.J., & Shapiro, S.S. (1967). Statistical models in engineering. New York: Wiley.
18.
Hambleton, R.K., & Murray, L. (1983). Some goodness of fit investigations for item response models. In R. K. Hambleton (Ed.), Applications of item response theory (pp. 71-94). Vancouver, British Columbia: Education Research Institute of British Columbia .
