Building marginal models for multiple ordinal measurements

Journal of the Royal Statistical Society. Series C: Applied Statistics

Volumn 51, Issue 1, 2002, Pages 37-57

  Huang, Guan Hua ^a,d   Bandeen Roche, Karen ^b   Rubin, Gary S ^c  

^a UNIVERSITY OF WISCONSIN MADISON   (United States)

^b JOHNS HOPKINS UNIVERSITY   (United States)

^c UNIVERSITY COLLEGE LONDON   (United Kingdom)

^d UNIVERSITY OF WISCONSIN SCHOOL OF MEDICINE AND PUBLIC HEALTH   (United States)

Author keywords

Generalized estimating equation; Global odds ratio; Graphical diagnosis; Model building; Partial residual plot; Proportional odds model

Indexed keywords

EID: 0036431047     PISSN: 00359254     EISSN: None     Source Type: Journal    
DOI: 10.1111/1467-9876.04739     Document Type: Article

References (42)

1. Bailey, I.L., Bullimore, M.A., Raasch, T.W. and Taylor, H.R. (1991) Clinical grading and the effects of scaling. Invest. Ophth. Vis. Sci., 32, 422-432.
2. Bandeen-Roche, K., Huang, G.H., Munoz, B. and Rubin, G.S. (1999) On determining risk factor associations with questionnaire outcomes: a methods case study. Am. J. Epidem., 150, 1165-1178.
3. Bandeen-Roche, K., Miglioretti, D.L., Zeger, S.L. and Rathouz, P.J. (1997) Latent variable regression for multiple outcomes. J. Am. Statist. Ass., 92, 1375-1386.
4. Bartholomew, D.J. (1987) Latent Variable Models and Factor Analysis. London: Griffin.
5. Bryk, A.S. and Raudenbush, S.W. (1992) Hierarchical Linear Models: Applications and Data Analysis Methods. Newbury Park: Sage.
6. Carey, V.J., Zeger, S.L. and Diggle, P. (1993) Modelling multivariate binary data with logistic regressions. Biometrika, 80, 517-526.
7. Cook, R.D. and Weisberg, S. (1997) Graphics for assessing the adequacy of regression models. J. Am. Statist. Ass., 92, 490-499.
8. Dale, J.R. (1986) Global cross-ratio models for bivariate, discrete, ordered responses. Biometrics, 42, 909-917.
9. Fitzmaurice, G.M. and Laird, N.M. (1993) A likelihood-based method for analysing longitudinal binary responses. Biometrika, 80, 141-151.
10. Folstein, M.F., Folstein, S.E. and McHugh, P.R. (1975) Mini-mental state: a practical method for grading the cognitive state of patients for the clinician. J. Psychiatr. Res., 12, 189-198.
11. Goldberg, D. (1972) GHQ: the Selection of Psychiatric Illness by Questionnaire. London: Oxford University Press.
12. Hall, C.B. (1995) Diagnosis for dependent data regression models. PhD Thesis. Department of Biostatistics, Johns Hopkins University, Baltimore.
13. Heagerty, P.J. and Zeger, S.L. (1996) Marginal regression models for clustered ordinal measurements. J. Am. Statist. Ass., 91, 1024-1036.
14. Hosmer, D.W. and Lemeshow, S. (1989) Applied Logistic Regression. New York: Wiley.
15. Jacquez, J.A., Mather, F.J. and Crawford, C.R. (1968) Linear regression with non-constant, unknown error variances: sampling experiments with least squares, weighted least squares and maximum likelihood estimators. Biometrics, 24, 607-626.
16. Katz, S., Ford, A.B., Moskowitz, R.W., Jackson, B.A. and Jaffer, M.W. (1963) Studies of illness in the age. The index of ADL: a standardized measure of biological and psychosocial function. J. Am. Med. Ass., 185, 914-918.
17. Laird, N.M. and Ware, J.H. (1982) Random-effects models for longitudinal data. Biometrics, 38, 963-974.
18. Landwehr, J.M., Pregibon, D. and Shoemaker, C. (1984) Graphical methods for assessing logistic regression models. J. Am. Statist. Ass., 79, 61-71.
19. Larsen, W.A. and McCleary, S.J. (1972) The use of partial residual plots in regression analysis. Technometrics, 14, 781-790.
20. Lawton, M.P. and Brody, E.M. (1969) Assessment of older people: self-maintaining and instrumental activities of daily living. Gerontologist, 9, 179-186.
21. Liang, K.Y. and Zeger, S.L. (1986) Longitudinal data and analysis using generalized linear models. Biometrika, 73, 13-22.
22. _(1993) Regression analysis for correlated data. A. Rev. Publ. Hlth, 14, 43-68.
23. Liang, K.-Y., Zeger, S.L. and Qaqish, B. (1992) Multivariate regression analyses for categorical data (with discussion). J. R. Statist. Soc. B, 54, 3-40.
24. Lipsitz, S.R., Laird, N.M. and Harrington, D.P. (1991) Generalized estimating equations for correlated binary data: using the odds ratio as a measure of association. Biometrika, 78, 153-160.
25. Little, R.J.A. and Rubin, D.B. (1987) Statistical Analysis with Missing Data. New York: Wiley.
26. Mangione, C.M., Phillips, R.S., Seddon, J.M., Lawrence, M.G., Cook, E.F., Dailey, R. and Goldman, L. (1992) Development of the "Activities of Daily Vision" scale: a measurement of visual functional status. Med. Care, 30, 1111-1126.
27. McCullagh, P. (1980) Regression models for ordinal data (with discussion). J. R. Statist. Soc. B, 42, 109-142.
28. McCullagh, P. and Nelder, J.A. (1989) Generalized Linear Models, 2nd edn. London: Chapman and Hall.
29. Morrison, D.F. (1990) Multivariate Statistical Methods, 3rd edn. New York: McGraw-Hill.
30. O'Hara Hines, R.J. and Carter, E.M. (1993) Improved added variable and partial residual plots for the detection of influential observation in generalized linear models (with comments). Appl. Statist., 42, 3-20.
31. Pelli, D.G., Robson, J.G. and Wilkins, A.J. (1988) The design of a new letter chart for measuring contrast sensitivity. Clin. Vis. Sci., 2, 187-199.
32. Prentice, R.L. and Zhao, L.P. (1991) Estimating equations for parameters in means and covariances of multivariate discrete and continuous responses. Biometrics, 47, 825-839.
33. Rubin, G.S., Bandeen-Roche, K., Orasadarao, P. and Fried, L.P. (1994) Visual impairment and disability in older adults. Optom. Vis. Sci., 71, 750-760.
34. Rubin, G.S., West, S.K., Munoz, B., Bandeen-Roche, K., Zeger, S.L., Schein, O. and Fried, L.P. (1997) A comprehensive assessment of visual impairment in an older american population: SEE study. Invest. Ophth. Vis. Sci., 38, 557-568.
35. Scheffé, H. (1959) The Analysis of Variance. New York: Wiley.
36. Steinberg, E.P., Tielsch, J.M., Schein, O.D., Javitt, J.C., Sharkey, P., Cassard, S.D., Legro, M.W., Dienerwest, M., Bass, E.B., Damiano, A.M., Steinwachs, D.M. and Sommer, A. (1994) The VF-14: an index of functional impairment in patients with cataract. Arch. Ophth., 112, 630-638.
37. Stewart, A.L. and Ware, J.E. (1992) Measuring Functioning and Well-being: the Medical Outcomes Study Approach, pp. 73-85. Durham: Duke University Press.
38. Stiratelli, R., Laird, N. and Ware, J.H. (1984) Random-effects models for serial observations with binary response. Biometrics, 40, 961-971.
39. Ware, J.H. (1985) Linear models for the analysis of several measurements in longitudinal studies. Am. Statistn, 39, 95-101.
40. West, S.K., Munoz, B., Rubin, G.S., Schein, O.D., Bandeen-Roche, K., Zeger, S.L., German, P.S. and Fried, L.P. (1997) Function and visual impairment in a population-based study of older adults: SEE project. Invest. Ophth. Vis. Sci., 38, 72-82.
41. Zellner, A. (1962) An efficient method of estimating seemingly unrelated regressions and tests for aggregation bias. J. Am. Statist. Ass., 57, 348-368.
42. Zhao, L.P. and Prentice, R.L. (1990) Correlated binary regression using a quadratic exponential model. Biometrika, 77, 642-648.