Links between binary and multi-category logit item response models and quasi-symmetric loglinear models

Alan Agresti

Annales de la Faculté des sciences de Toulouse : Mathématiques (2002)

  • Volume: 11, Issue: 4, page 443-454
  • ISSN: 0240-2963

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Agresti, Alan. "Links between binary and multi-category logit item response models and quasi-symmetric loglinear models." Annales de la Faculté des sciences de Toulouse : Mathématiques 11.4 (2002): 443-454. <http://eudml.org/doc/73587>.

@article{Agresti2002,
author = {Agresti, Alan},
journal = {Annales de la Faculté des sciences de Toulouse : Mathématiques},
language = {eng},
number = {4},
pages = {443-454},
publisher = {UNIVERSITE PAUL SABATIER},
title = {Links between binary and multi-category logit item response models and quasi-symmetric loglinear models},
url = {http://eudml.org/doc/73587},
volume = {11},
year = {2002},
}

TY - JOUR
AU - Agresti, Alan
TI - Links between binary and multi-category logit item response models and quasi-symmetric loglinear models
JO - Annales de la Faculté des sciences de Toulouse : Mathématiques
PY - 2002
PB - UNIVERSITE PAUL SABATIER
VL - 11
IS - 4
SP - 443
EP - 454
LA - eng
UR - http://eudml.org/doc/73587
ER -

References

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  1. [1] Agresti ( A.). — A simple diagonals-parameter symmetry and quasisymmetry model, Statistics and Probability Letters, 1 (1983), 313-316. Zbl0528.62050MR721443
  2. [2] Agresti ( A.). - Computing conditional maximum likelihood estimates for generalized Rasch models using simple loglinear models with diagonals parameters, Scandinavian Journal of Statistics, 20 (1993a), 63-72. Zbl0770.62095MR1221962
  3. [3] Agresti ( A.). - Distribution-free fitting of logit models with random effects for repeated categorical responses, Statistics in Medicine, 12 (1993b), 1969-1987. 
  4. [4] Agresti ( A.). - Simple capture-recapture models permitting unequal catchability and variable sampling effort, Biometrics, 50 (1994), 494-500. 
  5. [5] Agresti ( A.). - Logit models and related quasi-symmetric loglinear models for comparing responses to similar items in a survey, Sociological Methods in Research, 50 (1995), 68-95. 
  6. [6] Agresti ( A.). - An Introduction to Categorical Data Analysis, Wiley, New York, 1996. Zbl0868.62008MR1394195
  7. [7] Agresti ( A.). - A model for repeated measurements of a multivariate binary response, Journal of the American Statistical Association, 92 (1997), 315-321. Zbl0890.62087
  8. [8] Agresti ( A.), Lang ( J.B.). - Quasi-symmetric latent class models, with application to rater agreement, Biometrics, 49 (1993a), 131-139. 
  9. [9] Agresti ( A.), Lang ( J.B.). — A Proportional odds model with subject-specific effects for repeated ordered categorical responses, Biometrika, 80 (1993b), 527-534. Zbl0800.62750MR1248018
  10. [10] Andersen ( E.B.). - Conditional inference for multiple-choice questionnaires, British Journal of Mathematical and Statistical Psychology, 26 (1973), 31-44. MR451601
  11. [11] Andrich ( D.). - A rating formulation for ordered response categories, Psychometrika, 43 (1978), 561-573. Zbl0438.62086
  12. [12] Becker ( M.P.). - Quasisymmetric models for the analysis of square contingency tables, Journal of the Royal Statistical Society, Series B, 52 (1990), 369-378. MR1064423
  13. [13] Bishop ( Y.M.M.), Fienberg ( S.E.), Holland ( P.W.). - Discrete Multivariate Analysis: Theory and Practice, MIT Press, Cambridge, MA, 1975. Zbl0332.62039MR381130
  14. [14] Caussinus ( H.). - Contribution à l'analyse statistique des tableaux de corrélation, Annales de la Faculté des Sciences de l'Université de Toulouse, 29 (année 1965), (1966), 77-183. Zbl0168.39904MR242341
  15. [15] Conaway ( M.). - Analysis of repeated categorical measurements with conditional likelihood methods, Journal of the American Statistical Association, 84 (1989), 53-62. MR999664
  16. [16] Darroch ( J.N.). - The Mantel-Haenszel test and tests of marginal symmetry; fixed-effects and mixed models for a categorical response, International Statistical Review, 49 (1981), 285-307. Zbl0484.62067MR651475
  17. [17] Darroch ( J.N.), Fienberg ( S.E.), Glonek ( G.F.V.), Junker ( B.W.). — A Three-sample multiple-recapture approach to census population estimation with heterogeneous catchability, Journal of the American Statistical Association, 88 (1993), 1137-1148. 
  18. [18] Darroch ( J.N.), Mccloud ( P.I.). - Category distinguishability and observer agreement, The Australian Journal of Statistics, 28 (1986), 371-388. Zbl0609.62140MR876747
  19. [19] De Leeuw ( J.), Verhelst ( N.). - Maximum likelihood estimation in generalized Rasch models, Journal of Educational Statistics, 11 (1986), 183-196. 
  20. [20] Duncan ( O.D.). - Rasch measurement: further examples and discussion, in Turner Charles F. and Martin Elizabeth, editors, Surveying Subjective Phenomena, volume 2, chapter 12, pages 367-403, Russell Sage Foundation, New York, 1984. 
  21. [21] Erosheva ( E.E.), Fienberg ( S.E.), Junker ( B.J.). - Alternative statistical models and representations for large sparse multi-dimensional contingency tables, Annales de la Faculté des Sciences de L'Université de Toulouse, Mathématiques, 2002, This issue. Zbl1042.62057MR2032354
  22. [22] Fienberg ( S.E.). - Recent advances in theory and methods for the analysis of categorical data: Making the link to statistical practice, in Bulletin of the International Statistical Institute, volume 49, Book 2 (1981), 763-791. Zbl0521.62048MR820977
  23. [23] Fienberg ( S.E.), Johnson ( M.S.), Junker ( B.W.). - Classical multilevel and Bayesian approaches to population size estimation using multiple lists, Journal of the Royal Statistical Society, Series A, 162 (1999), 383-405. 
  24. [24] Fienberg ( S.E.), Larntz ( K.). - Loglinear representation for paired and multiple comparisons models, Biometrika, 63 (1976), 245-254. Zbl0339.62051MR431541
  25. [25] Fienberg ( S.E.), Meyer ( M.M.). - Loglinear models and categorical data analysis with psychometric and econometric applications, Journal of Econometrics, 22 (1983), 191-214. Zbl0511.62057MR719131
  26. [26] Fischer ( G.W.), Kamlet ( M.S.), Fienberg ( S.E.), Schkade ( D.). - Risk preferences for gains and losses in multiple objective decisionmaking, Management Science, 32 (1986), 1065-1086. 
  27. [27] Goodman ( L.A.). - Multiplicative models for square contingency tables with ordered categories, Biometrika, 66 (1979), 413-418. 
  28. [28] Goodman ( L.A.). - Contributions to the statistical analysis of contingency tables : Notes on quasi-symmetry, quasi-independence, log-linear models, log-bilinear models, and correspondence analysis models, Annales de la Faculté des Sciences de l'Université de Toulouse, 2002, This issue. Zbl1122.62316MR2032356
  29. [29] Hatzinger ( R.). - The Rasch model, some extensions and their relation to the class of generalized linear models, in Statistical Modelling: Proceedings of GLIM89 and the 4th International Workshop on Statistical Modelling, volume 57 of Lecture Notes in Statistics, Berlin, Springer, 1989. Zbl0717.62058
  30. [30] Hedeker ( D.), Gibbons ( R.D.). - A random-effects ordinal regression model for multilevel analysis, Biometrics, 50 (1994), 933-944. Zbl0826.62049
  31. [31] Hout ( M.), Duncan ( O.D.), Sobel ( M.E.). - Association and heterogeneity : Structural models of similarities and differences, Sociological Methodology, 17 (1987), 145-184. 
  32. [32] Kelderman ( H.). - Loglinear Rasch model tests, Psychometrika, 49 (1984), 223-245. Zbl0573.62097
  33. [33] Kelderman ( H.), Rijkes ( C.P.M.). - Loglinear multidimensional IRT models for polytomously scored items, Psychometrika, 59 (1994), 149-176. Zbl0825.62936
  34. [34] Lang ( J.B.), Agresti ( A.). - Simultaneously modeling joint and marginal distributions of multivariate categorical responses, Journal of the American Statistical Association, 89 (1994), 625-632. Zbl0799.62063
  35. [35] Lindsay ( B.), Clogg ( C.C.), Grego ( J.). - Semiparametric estimation in the Rasch model and related exponential response models, including a simple latent class model for item analysis, Journal of the American Statistical Association, 86 (1991), 96-107. Zbl0735.62107MR1137102
  36. [36] Masters ( G.N.). - A Rasch model for partial credit scoring, Psychometrika, 47 (1982), 149-174. Zbl0493.62094
  37. [37] Mccullagh ( P.). - A logistic model for paired comparisons with ordered categorical data, Biometrika, 64 (1977), 449-453. Zbl0374.62069MR478469
  38. [38] Mccullagh ( P.). - Some applications of quasisymmetry, Biometrika, 69 (1982), 303-308. Zbl0497.62051MR671967
  39. [39] Neuhaus ( J.M.), Kalbfleisch ( J.D.), Hauck ( W.W.). - Conditions for consistent estimation in mixed-effects models for binary matched-pairs data, Canadian Journal of Statistics, 22 (1994), 139-148. Zbl0800.62113MR1271451
  40. [40] Rasch ( G.). - On general laws and the meaning of measurement in psychology, in J. Neyman, editor, Proceedings of the 4th Berkeley Symp. Math. Statist. Probab., volume 4, pages 321-333, Berkeley, 1961, University of California Press. Zbl0107.36805MR135196
  41. [41] Samejima ( F.). - Estimation of latent ability using a response pattern of graded scores, volume 17, Psychometrika, Monograph Supplement, Psychometric Society, Iowa City, 1969. 
  42. [42] Ten Have ( T.R.), Becker ( M.P.). — Multivariate contingency tables and the analysis of exchangeability, Biometrics, 51 (1995), 1001-1016. Zbl0867.62084
  43. [43] Tjur ( T.). - A Connection between Rasch's Item analysis model and a multiplicative Poisson model, Scandinavian Journal of Statistics, 9 (1982), 23-30. Zbl0484.62115MR651857
  44. [44] Tutz ( G.). - Sequential item response models with an ordered response, British Journal of Mathematical and Statistical Psychology, 43 (1990), 39-55. Zbl0718.62263MR1065199

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