Departure from normal assumptions: A promise for future psychometrics with substantive mathematical modeling

Psychometrika

Volumn 62, Issue 4, 1997, Pages 471-493

  Samejima, Fumiko ^a  

^a UNIVERSITY OF TENNESSEE   (United States)

Author keywords

Dichotomous responses; Item response theory; Latent trait models; Logistic positive exponent family of models; Substantive mathematical modeling; Task complexity

Indexed keywords

EID: 0031327506     PISSN: 00333123     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF02294639     Document Type: Article

References (24)

1. Birnbaum, A. (1968). Some latent trait models and their use in inferring an examinee's ability. In F. M. Lord & M. R. Novick (Eds.), Statistical theories of mental test scores (pp. 395-479). Reading, MA: Addison Wesley.
2. Bock, R. D. (1972). Estimating item parameters and latent ability when responses are scored in two or more nominal categories. Psychometrika, 37, 29-51.
3. Hemker, B. T., Sijtsma, K., Molenaar, I. W., & Junker, B. W. (1996). Polytomous IRT models and monotone likelihood ratio of the total test score. Psychometrika, 61, 679-693.
4. Huynh, H. (1994). A new proof for monotone likelihood ratio for the sum of independent Bernoulli random variables. Psychometrika, 59, 77-79.
5. Levine, M. (1984). An introduction to multilinear formula scoring theory (Office of Naval Research Report 84-4). Champaign, IL: University of Chicago.
6. Lord, F. M. (1952). A Theory of Test Scores. Psychometric Monograph, No. 7.
7. Lord, F. M. (1970). Item characteristic curves estimated without knowledge of their mathematical form: A confrontation of Birnbaum's logistical model. Psychometrika, 35, 43-50.
8. Lord, F. M. (1983). Unbiased estimators of ability parameters, of their variance, and of their parallel-forms reliability. Psychometrika, 48, 233-245.
9. Lord, F. M., & Novick, M. R. (1968). Statistical theories of mental test scores. Reading, MA: Addison Wesley.
10. Luce, R. D. (1959). Individual choice behavior. New York: Wiley.
11. Masters, G. N. (1982). A Rasch model for partial credit scoring. Psychometrika, 47, 149-174.
12. Muraki, E. (1992). A generalized partial credit model: Application of an EM algorithm. Applied Psychological Measurement, 16, 159-176.
13. Ramsay, J. O. (1991). Kernel smoothing approaches to nonparametric item characteristic curve estimation. Psychometrika, 56, 611-630.
14. Samejima, F. (1969). Estimation of latent ability using a response pattern of graded scores. Psychometrika Monograph, No. 17.
15. Samejima, F. (1972). A general model for free-response data. Psychometrika Monograph, No. 18.
16. Samejima, F. (1973). A comment on Birnbaum's three-parameter logistic model in the latent trait theory, Psychometrika, 38, 221-233.
17. Samejima, F. (1993a). An approximation for the bias function of the maximum likelihood estimate of a latent variable for the general case where the item responses are discrete. Psychometrika, 38, 119-138.
18. Samejima, F. (1993b). The bias function of the maximum likelihood estimate of ability for the dichotomous response level. Psychometrika, 58, 195-209.
19. Samejima, F. (1995). Acceleration model in the heterogeneous case of the general graded response model. Psychometrika, 60, 549-572.
20. Samejima, F. (1996). Evaluation of mathematical models for ordered polychotomous responses. Behaviormetrika, 23, 17-35.
21. Samejima, F. (in press). Rationale and actual procedures of efficient nonparametric approaches for estimating the operating characteristics of discrete item responses. Psychometrika.
22. Samejima, F. (accepted). Virtues of asymmetric item characteristic curves with the logistic model as a transition. Psychometrika.
23. Warm, T. A. (1989). Weighted likelihood estimation of ability in item response theory. Psychometrika, 54, 427-450.
24. Yen, W. M., Burket, G. R., & Sykes, R. C. (1991). Nonunique solutions to the likelihood equation for the three-parameter logistic model. Psychometrika, 56, 39-54.