A "mixture" probability model that incorporates two component models defined by nonsubsuming sets of parameters is introduced, and a strategy for using this model in the selection of a preferred component model is developed. Example applications of the sug gested strategy are considered for the special case in which the Rasch item response model and a Latent State Mastery model are the component models com pared. Simulated data sets generated under each of these models were used to provide example applica tions of the proposed model selection strategy.
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References
1.
Atkinson, A.C. (1970). A method for discriminating between models. Journal of the Royal Statistical Society, 3, 323-345.
2.
Baker, F.B. (1981). Log-linear, Logit-linear models: A didactic. Journal of Educational Statistics, 6, 75-102.
3.
Conte, S.D., & deBoor, C. (1972). Elementary numerical analysis. New York: McGraw-Hill.
4.
Cox, D.R. (1961). Tests on separate families of hypotheses. Proceedings of the 4th Berkeley Symposium, 1, 105-123.
5.
Cox, D.R. (1962). Further results on tests of separate families of hypotheses. Journal of the Royal Statistical Society, Series B, 24, 406-424.
6.
Dayton, C.M., & Macready, G.B. (1976). A probabilistic model for validation of behavioral hierarchies. Psychometrika, 41, 189-204.
7.
Goodman, L.A. (1974). Exploratory latent structure analysis using both identified and unidentified models. Biometrika, 61, 215-231.
8.
Goodman, L.A. (1979). On the estimation of parameters in latent structure analysis. Psychometrika, 44, 123-128.
9.
Hambleton, R.K., & Swaminathan, H. (1983). Item response theory: Principles and applications. Boston: Kluwer-Nijhoff Publishers.
10.
Jöreskog, K.G., & Sörbom, D. (1979). Advances in factor analysis and structural equations models. Cambridge MA: Abt Books .
11.
Lord, F.M., & Novick, M.R. (1968). Statistical theories of mental test scores. Reading MA: Addison-Wesley.
12.
Macready, G.B., & Dayton, C.M. (1977). The use of probabilistic models in the assessment of mastery. Journal of Educational Statistics, 2, 99-120.
13.
Macready, G.B., & Dayton, C.M. (1980). The nature and use of state mastery models. Applied Psychological Measurement, 4, 493-516.
14.
Meskauskas, J.A. (1976). Evaluation models for criterion referenced testing: Views regarding mastery and standard setting. Review of Educational Research, 46, 133-158.
15.
Rao, C.R. (1973). Linear statistical inference and its applications (2nd ed.). New York: Wiley.
16.
Whitely, S.E., & Schneider, L.M. (1981). Information structure for geometric analogies: A test theory approach. Applied Psychological Measurement, 5, 383-397.
17.
Wilks, S.S. (1938). The large sample distribution of the likelihood ratio for testing composite hypotheses. Annals of Mathematical Statistics, 9, 60-62.
18.
Wright, B.D., & Douglas, G.A. (1977). Best procedures for sample free item analysis . Applied Psychological Measurement, 37, 573-586.
