Multilevel models for ordinal and nominal variables

Handbook of Multilevel Analysis

Volumn , Issue , 2008, Pages 237-274

  Hedeker, Donald ^a  

^a UNIVERSITY OF ILLINOIS AT CHICAGO   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84892232319     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1007/978-0-387-73186-5_6     Document Type: Chapter

References (118)

1. R. J. Adams, M. Wilson, and M. Wu. Multilevel item response models: An approach to errors in variable regression. Journal of Educational and Behavioral Statistics, 22:47-76, 1997.
2. A. Agresti. Categorical Data Analysis. Wiley, New York, 1990.
3. A. Agresti, J. G. Booth, J. P. Hobart, and B. Caffo. Random-effects modeling of categorical response data. Sociological Methodology, 30:27-80, 2000.
4. A. Agresti and J. B. Lang. A proportional odds model with subject-specific effects for repeated ordered categorical responses. Biometrika, 80:527-534, 1993.
5. A. Agresti and R. Natarajan. Modeling clustered ordered categorical data: A survey. International Statistical Review, 69:345-371, 2001.
6. P. D. Allison. Discrete-time methods for the analysis of event histories. Sociological Methodology, 13:61-98, 1982.
7. P. D. Allison. Survival Analysis using the SAS System: A Practical Guide. SAS Institute, Cary, NC, 1995.
8. T. Amemiya. Qualitative response models: A survey. Journal of Economic Literature, 19:483-536, 1981.
9. D. A. Anderson and M. Aitkin. Variance component models with binary response: Interviewer variability. Journal of the Royal Statistical Society, Series B, 47:203-210, 1985.
10. K. J. Arrow. Social Choice and Individual Values. Wiley, New York, 1951.
11. D. J. Bartholomew and M. Knott. Latent Variable Models and Factor Analysis, 2nd edition. Oxford University Press, New York, 1999.
12. E. K. Berndt, B. H. Hall, R. E. Hall, and J. A. Hausman. Estimation and inference in nonlinear structural models. Annals of Economic and Social Measurement, 3:653-665, 1974.
13. C. R. Bhat. Quasi-random maximum simulated likelihood estimation of the mixed multinomial logit model. Transportation Research, Part B, 35:677-693, 2001.
14. R. D. Bock. Estimating item parameters and latent ability when responses are scored in two or more nominal categories. Psychometrika, 37:29-51, 1972.
15. R. D. Bock. Multivariate Statistical Methods in Behavioral Research. McGraw-Hill, New York, 1975.
16. R. D. Bock and M. Aitkin. Marginal maximum likelihood estimation of item parameters: An application of the EM algorithm. Psychometrika, 46:443-459, 1981.
17. R. D. Bock and M. Lieberman. Fitting a response model for n dichotomously scored items. Psychometrika, 35:179-197, 1970.
18. R. D. Bock and S. Shilling. High-dimensional full-information item factor analysis. In M. Berkane, editor, Latent Variable Modeling and Applications to Causality, pages 163-176. Springer, New York, 1997.
19. N. E. Breslow and X. Lin. Bias correction in generalised linear mixed models with a single component of dispersion. Biometrika, 82:81-91, 1995.
20. G. Camilli and L. A. Shepard. Methods for Identifying Biased Test Items. Sage, Thousand Oaks, CA, 1994.
21. M. R. Conaway. Analysis of repeated categorical measurements with conditional likelihood methods. Journal of the American Statistical Association, 84: 53-61, 1989.
22. C. Corcoran, B. Coull, and A. Patel. Egret for Windows User Manual. Cytel Software Corporation, Cambridge, MA, 1999.
23. L. A. Cupples, R. B. D'Agostino, K. Anderson, and W. B. Kannel. Comparison of baseline and repeated measure covariate techniques in the Framingham Heart Study. Statistics in Medicine, 7:205-218, 1985.
24. R. B. D'Agostino, M.-L. Lee, A. J. Belanger, L. A. Cupples, K. Anderson, and W. B. Kannel. Relation of pooled logistic regression to time dependent Cox regression analysis: The Framingham Heart Study. Statistics in Medicine, 9: 1501-1515, 1990.
25. M. J. Daniels and C. Gatsonis. Hierarchical polytomous regression models with applications to health services research. Statistics in Medicine, 16:2311-2325, 1997.
26. K. A. Doksum and M. Gasko. On a correspondence between models in binary regression analysis and in survival analysis. International Statistical Review, 58:243-252, 1990.
27. D. M. Drukker. Maximum simulated likelihood: Introduction to a special issue. The Stata Journal, 6:153-155, 2006.
28. J. Engel. On the analysis of grouped extreme-value data with GLIM. Applied Statistics, 42:633-640, 1993.
29. F. Ezzet and J. Whitehead. A random effects model for ordinal responses from a crossover trial. Statistics in Medicine, 10:901-907, 1991.
30. A. Fielding, M. Yang, and H. Goldstein. Multilevel ordinal models for examination grades. Statistical Modelling, 3:127-153, 2003.
31. G. M. Fitzmaurice, N. M. Laird, and A. G. Rotnitzky. Regression models for discrete longitudinal responses. Statistical Science, 8:284-309, 1993.
32. S. A. Freels, R. B. Warnecke, T. P. Johnson, and B. R. Flay. Evaluation of the effects of a smoking cessation intervention using the multilevel thresholds of change model. Evaluation Review, 26:40-58, 2002.
33. S. Geman and D. Geman. Stochastic relaxation, Gibbs distributions and the Bayesian restoration of images. IEEE Transactions on Pattern Analysis and Machine Intelligence, 6:721-741, 1984.
34. R. D. Gibbons and R. D. Bock. Trend in correlated proportions. Psychometrika, 52:113-124, 1987.
35. R. D. Gibbons and D. Hedeker. Random-effects probit and logistic regression models for three-level data. Biometrics, 53:1527-1537, 1997.
36. G. Glasgow. Mixed logit models for multiparty elections. Political Analysis, 9: 116-136, 2001.
37. H. Goldstein. Nonlinear multilevel models, with an application to discrete response data. Biometrika, 78:45-51, 1991.
38. H. Goldstein. Multilevel Statistical Models, 3rd edition. Edward Arnold, London, 2003.
39. H. Goldstein and J. Rasbash. Improved approximations for multilevel models with binary responses. Journal of the Royal Statistical Society, Series A, 159: 505-513, 1996.
40. W. H. Greene. LIMDEP Version 8.0 User's Manual, 4th edition. Econometric Software, Plainview, NY, 2002.
41. P. Haan and A. Uhlendorff. Estimation of multinomial logit models with unobserved heterogeneity using maximum simulated likelihood. The Stata Journal, 6:229-245, 2006.
42. A. Han and J. A. Hausman. Flexible parametric estimation of duration and competing risk models. Journal of Applied Econometrics, 5:1-28, 1990.
43. J. Hartzel, A. Agresti, and B. Caffo. Multinomial logit random effects models. Statistical Modelling, 1:81-102, 2001.
44. D. A. Harville and R. W. Mee. A mixed-model procedure for analyzing ordered categorical data. Biometrics, 40:393-408, 1984.
45. P. J. Heagerty and S. L. Zeger. Marginalized multilevel models and likelihood inference. Statisical Science, 15:1-26, 2000. (with discussion)
46. D. Hedeker. MIXNO: A computer program for mixed-effects nominal logistic regression. Journal of Statistical Software, 4(5):1-92, 1999.
47. D. Hedeker. A mixed-effects multinomial logistic regression model. Statistics in Medicine, 21:1433-1446, 2003.
48. D. Hedeker and R. D. Gibbons. A random-effects ordinal regression model for multilevel analysis. Biometrics, 50:933-944, 1994.
49. D. Hedeker and R. D. Gibbons. MIXOR: A computer program for mixed-effects ordinal regression analysis. Computer Methods and Programs in Biomedicine, 49:157-176, 1996.
50. D. Hedeker and R. D. Gibbons. Application of random-effects pattern-mixture models for missing data in longitudinal studies. Psychological Methods, 2:64-78, 1997.
51. D. Hedeker and R. D. Gibbons. Longitudinal Data Analysis. Wiley, New York, 2006.
52. D. Hedeker and R. J. Mermelstein. A multilevel thresholds of change model for analysis of stages of change data. Multivariate Behavioral Research, 33: 427-455, 1998.
53. D. Hedeker and R. J. Mermelstein. Analysis of longitudinal substance use outcomes using random-effects regression models. Addiction, 95(Supplement 3):S381-S394, 2000.
54. D. Hedeker, O. Siddiqui, and F. B. Hu. Random-effects regression analysis of correlated grouped-time survival data. Statistical Methods in Medical Research, 9:161-179, 2000.
55. R. L. Hough, S. Harmon, H. Tarke, S. Yamashiro, R. Quinlivan, P. Landau-Cox, M. S. Hurlburt, P. A. Wood, R. Milone, V. Renker, A. Crowell, and E. Morris. Supported independent housing: Implementation issues and solutions in the San Diego McKinney homeless demonstration research project. In W. R. Breakey and J. W. Thompson, editors, Mentally Ill and Homeless: Special Programs for Special Needs, pages 95-117. Harwood, New York, 1997.
56. M. S. Hurlburt, P. A. Wood, and R. L. Hough. Providing independent housing for the homeless mentally ill: A novel approach to evaluating long-term longitudinal housing patterns. Journal of Community Psychology, 24:291-310, 1996.
57. H. Ishwaran. Univariate and multirater ordinal cumulative link regression with covariate specific cutpoints. Canadian Journal of Statistics, 28:715-730, 2000.
58. J. Jansen. On the statistical analysis of ordinal data when extravariation is present. Applied Statistics, 39:75-84, 1990.
59. E. Läärä and J. N. S. Matthews. The equivalence of two models for ordinal data. Biometrika, 72:206-207, 1985.
60. N. M. Laird. Missing data in longitudinal studies. Statistics in Medicine, 7: 305-315, 1988.
61. E. Lesaffre and B. Spiessens. On the effect of the number of quadrature points in a logistic random-effects model: An example. Applied Statistics, 50:325-335, 2001.
62. J. K. Lindsey and P. Lambert. On the appropriateness of marginal models for repeated measurements in clinical trials. Statistics in Medicine, 17:447-469, 1998.
63. L. C. Liu and D. Hedeker. A mixed-effects regression model for longitudinal multivariate ordinal data. Biometrics, 62:261-268, 2006.
64. Q. Liu and D. A. Pierce. A note on Gauss-Hermite quadrature. Biometrika, 81:624-629, 1994.
65. J. S. Long. Regression Models for Categorical and Limited Dependent Variables. Sage, Thousand Oaks, CA, 1997.
66. F. M. Lord. Applications of Item Response Theory to Practical Testing Problems. Erlbaum, Hillside, NJ, 1980.
67. R. D. Luce. Individual Choice Behavior. Wiley, New York, 1959.
68. G. S. Maddala. Limited-Dependent and Qualitative Variables in Econometrics. Cambridge University Press, Cambridge, UK, 1983.
69. J. R. Magnus. Linear Structures. Charles Griffin, London, 1988.
70. E. C. Marshall and D. Spiegelhalter. Institutional performance. In A. H. Leyland and H. Goldstein, editors, Multilevel Modelling of Health Statistics, pages 127-142. Wiley, New York, 2001.
71. P. McCullagh. Regression models for ordinal data. Journal of the Royal Statistical Society, Series B, 42:109-142, 1980. (with discussion)
72. P. McCullagh and J. A. Nelder. Generalized Linear Models, 2nd edition. Chapman & Hall, London, 1989.
73. D. McFadden. Conditional logit analysis of qualitative choice behavior. In P. Zarembka, editor, Frontiers in Econometrics. Academic Press, New York, 1973.
74. D. McFadden. Qualitative response models. In W. Hildenbrand, editor, Advances in Econometrics, pages 1-37. Cambridge University Press, Cambridge, UK, 1980.
75. J. M. Neuhaus, J. D. Kalbfleisch, and W. W. Hauck. A comparison of clusterspecific and population-averaged approaches for analyzing correlated binary data. International Statistical Review, 59:25-35, 1991.
76. J. F. Pendergast, S. J. Gange, M. A. Newton, M. J. Lindstrom, M. Palta, and M. R. Fisher. A survey of methods for analyzing clustered binary response data. International Statistical Review, 64:89-118, 1996.
77. B. Peterson and F. E. Harrell. Partial proportional odds models for ordinal response variables. Applied Statistics, 39:205-217, 1990.
78. J. C. Pinheiro and D. M. Bates. Approximations to the log-likelihood function in the nonlinear mixed-effects model. Journal of Computational and Graphical Statistics, 4:12-35, 1995.
79. R. L. Prentice and L. A. Gloeckler. Regression analysis of grouped survival data with application to breast cancer data. Biometrics, 34:57-67, 1978.
80. S. Rabe-Hesketh, A. Skrondal, and A. Pickles. Reliable estimation of generalized linear mixed models using adaptive quadrature. The Stata Journal, 2: 1-21, 2002.
81. S. Rabe-Hesketh, A. Skrondal, and A. Pickles. GLLAMM manual. Working Paper 160, U.C. Berkeley Division of Biostatistics, Berkeley, CA, 2004. (Downloadable from http://www.bepress.com/ucbbiostat/paper160/)
82. S. Rabe-Hesketh, A. Skrondal, and A. Pickles. Maximum likelihood estimation of limited and discrete dependent variable models with nested random effects. Journal of Econometrics, 128:301-323, 2005.
83. R. Raman and D. Hedeker. A mixed-effects regression model for three-level ordinal response data. Statistics in Medicine, 24:3331-3345, 2005.
84. J. Rasbash, F. Steele, W. J. Browne, and B. Prosser. A User's Guide to MLwiN. Version 2.0. Centre for Multilevel Modelling, University of Bristol, Bristol, UK, 2005.
85. S. W. Raudenbush and A. S. Bryk. Hierarchical Linear Models: Applications and Data Analysis Methods, 2nd edition. Sage, Thousand Oaks, CA, 2002.
86. S. W. Raudenbush, A. S. Bryk, Y. F. Cheong, and R. Congdon. HLM 6: Hierarchical Linear and Nonlinear Modeling. Scientific Software International, Chicago, 2004.
87. S. W. Raudenbush, M.-L. Yang, and M. Yosef. Maximum likelihood for generalized linear models with nested random effects via high-order, multivariate Laplace approximation. Journal of Computational and Graphical Statistics, 9: 141-157, 2000.
88. D. Revelt and K. Train. Mixed logit with repeated choices: Household's choices of appliance efficiency level. Review of Economics and Statistics, 80:647-657, 1998.
89. F. Rijmen, F. Tuerlinckx, P. De Boeck, and P. Kuppens. A nonlinear mixed model framework for item response theory. Psychological Methods, 8:185-205, 2003.
90. G. Rodríguez and N. Goldman. An assessment of estimation procedures for multilevel models with binary responses. Journal of the Royal Statistical Society, Series A, 158:73-89, 1995.
91. D. B. Rubin. Inference and missing data. Biometrika, 63:581-592, 1976. (with discussion)
92. F. Samejima. Estimation of latent ability using a response pattern of graded scores. Psychometrika Monograph No. 17, 1969.
93. SAS/Stat. SAS/Stat User's Guide, version 9.1. SAS Institute, Cary, NC, 2004.
94. T. H. Scheike and T. K. Jensen. A discrete survival model with random effects: An application to time to pregnancy. Biometrics, 53:318-329, 1997.
95. J. D. Singer and J. B. Willett. It's about time: Using discrete-time survival analysis to study duration and the timing of events. Journal of Educational and Behavioral Statistics, 18:155-195, 1993.
96. J. D. Singer and J. B. Willett. Applied Longitudinal Data Analysis: Modeling Change and Event Occurrence. Oxford University Press, Oxford, UK, 2003.
97. A. Skrondal and S. Rabe-Hesketh. Multilevel logistic regression for polytomous data and rankings. Psychometrika, 68:267-287, 2003.
98. A. Skrondal and S. Rabe-Hesketh. Generalized Latent Variable Modeling: Multilevel, Longitudinal, and Structural Equation Models. Chapman & Hall/CRC, Boca Raton, FL, 2004.
99. T. A. B. Snijders and R. J. Bosker. Multilevel Analysis: An Introduction to Basic and Advanced Multilevel Modeling. Sage, Thousand Oaks, CA, 1999.
100. D. J. Spiegelhalter, A. Thomas, N. G. Best, and W. R. Gilks. BUGS: Bayesian Inference Using Gibbs Sampling, Version 0.50. Technical Report, MRC Biostatistics Unit, Cambridge, UK, 1995.
101. StataCorp. Stata Statistical Software: Release 9. Stata Corporation, College Station, TX, 2005.
102. S. Stern. Simulation-based estimation. Journal of Economic Literature, 35: 2006-2039, 1997.
103. R. Stiratelli, N. M. Laird, and J. H. Ware. Random-effects models for serial observations with binary response. Biometrics, 40:961-971, 1984.
104. A. H. Stroud and D. Secrest. Gaussian Quadrature Formulas. Prentice Hall, Englewood Cliffs, NJ, 1966.
105. M. A. Tanner. Tools for Statistical Inference: Methods for the Exploration of Posterior Distributions and Likelihood Functions, 3rd edition. Springer, New York, 1996.
106. T. R. Ten Have. A mixed effects model for multivariate ordinal response data including correlated discrete failure times with ordinal responses. Biometrics, 52:473-491, 1996.
107. T. R. Ten Have, A. R. Kunselman, and L. A. Tran. A comparison of mixed effects logistic regression models for binary response data with two nested levels of clustering. Statistics in Medicine, 18:947-960, 1999.
108. T. R. Ten Have and D. H. Uttal. Subject-specific and population-averaged continuation ratio logit models for multiple discrete time survival profiles. Applied Statistics, 43:371-384, 1994.
109. J. Terza. Ordinal probit: A generalization. Communications in Statistics: Theory and Methods, 14:1-11, 1985.
110. D. Thissen and L. Steinberg. A taxonomy of item response models. Psychometrika, 51:567-577, 1986.
111. L. L. Thurstone. Psychophysical analysis. American Journal of Psychology, 38:368-389, 1927.
112. K. E. Train. Discrete Choice Methods with Simulation. Cambridge University Press, Cambridge, UK, 2003.
113. G. Tutz and W. Hennevogl. Random effects in ordinal regression models. Computational Statistics & Data Analysis, 22:537-557, 1996.
114. M. A. Wakefield, F. J. Chaloupka, N. J. Kaufman, C. T. Orleans, D. C. Barker, and E. E. Ruel. Effect of restrictions on smoking at home, at school, and in public places on teenage smoking: Cross sectional study. British Medical Journal, 321:333-337, 2001.
115. G. Y. Wong and W. M. Mason. The hierarchical logistic regression model for multilevel analysis. Journal of the American Statistical Association, 80: 513-524, 1985.
116. B. D. Wright. Solving measurement problems with the Rasch model. Journal of Educational Measurement, 14:97-116, 1977.
117. H. Xie, G. McHugo, A. Sengupta, D. Hedeker, and R. Drake. An application of the thresholds of change model to the analysis of mental health data. Mental Health Services Research, 3:107-114, 2001.
118. S. L. Zeger, K.-Y. Liang, and P. S. Albert. Models for longitudinal data: A generalized estimating equation approach. Biometrics, 44:1049-1060, 1988.