Statistical Science

Discussion of Likelihood Inference for Models with Unobservables: Another View

Geert Molenberghs, Michael G. Kenward, and Geert Verbeke

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Statist. Sci., Volume 24, Number 3 (2009), 273-279.

First available in Project Euclid: 31 March 2010

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Molenberghs, Geert; Kenward, Michael G.; Verbeke, Geert. Discussion of Likelihood Inference for Models with Unobservables: Another View. Statist. Sci. 24 (2009), no. 3, 273--279. doi:10.1214/09-STS277B.

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  • Aerts, M., Geys, H., Molenberghs, G. and Ryan, L. (2002). Topics in Modelling of Clustered Data. Chapman & Hall, London.
  • Aitkin, M. (1999). A general maximum likelihood analysis of variance components in generalized linear models. Biometrics 55 117–128.
  • Alfò, M. and Aitkin, M. (2000). Random coefficient models for binary longitudinal responses with attrition. Statist. Comput. 10 279–288.
  • Bahadur, R. R. (1961). A representation of the joint distribution of responses to n dichotomous items. In Studies in Item Analysis and Prediction (H. Solomon, ed.). Stanford Mathematical Studies in the Social Sciences VI. Stanford Univ. Press, Stanford, CA.
  • Booth, J. G., Casella, G., Friedl, H. and Hobert, J. P. (2003). Negative binomial loglinear mixed models. Statist. Model. 3 179–181.
  • Butler, J. S. and Moffit, R. (1982). A computationally efficient quadrature procedure for the one-factor multinomial probit model. Econometrica 50 761–765.
  • Duchateau, L. and Janssen, P. (2007). The Frailty Model. Springer, New York.
  • Fitzmaurice, G. M. and Laird, N. M. (1993). A likelihood-based method for analysing longitudinal binary responses. Biometrika 80 141–151.
  • Gibbons, R. D. and Hedeker, D. (1997). Random effects probit and logistic regression models for three-level data. Biometrics 53 1527–1537.
  • Guilkey, D. K. and Murphy, J. L. (1993). Estimation and testing in the random effects probit model. J. Econometrics 59 301–317.
  • Harville, D. A. (1974). Bayesian inference for variance components using only error contrasts. Biometrika 61 383–385.
  • Hedeker, D. and Gibbons, R. D. (1994). A random-effects ordinal regression model for multilevel analysis. Biometrics 51 933–944.
  • Henderson, C. R. (1984). Applications of Linear Models in Animal Breeding. Univ. Guelph Press, Guelph, Canada.
  • Heitjan, D. F. and Rubin, D. B. (1991). Ignorability and coarse data. Ann. Statist. 19 2244–2253.
  • Lin, T. I. and Lee, J. C. (2008). Estimation and prediction in linear mixed models with skew-normal random effects for longitudinal data. Stat. Med. 27 1490–1507.
  • Liu, L. and Yu, Z. (2008). A likelihood reformulation method in non-normal random-effects models. Stat. Med. 27 3105–3124.
  • Lee, Y. and Nelder, J. A. (1996). Hierarchical generalized linear models (with discussion). J. Roy. Statist. Soc. Ser. B 58 619–678.
  • Lee, Y. and Nelder, J. A. (2001). Hierarchical generalized linear models: A synthesis of generalized linear models, random-effect models and structured dispersions. Biometrika 88 987–1006.
  • Lee, Y. and Nelder, J. A. (2003). Extended-REML estimators. J. Appl. Statist. 30 845–856.
  • Molenberghs, G., Beunckens, C., Sotto, C. and Kenward, M. G. (2008). Every missing not at random model has got a missing at random counterpart with equal fit. J. Roy. Statist. Soc. Ser. B 70 371–388.
  • Molenberghs, G. and Kenward, M. G. (2007). Missing Data in Clinical Studies. Wiley, New York.
  • Molenberghs, G. and Kenward, M. G. (2010). Generalized estimating equations and their corresponding full models. Comput. Statist. Data Anal. 54 585–597.
  • Molenberghs, G. and Lesaffre, E. (1994). Marginal modelling of correlated ordinal data using a multivariate Plackett distribution. J. Amer. Statist. Assoc. 89 633–644.
  • Molenberghs, G. and Ritter, L. (1996). Likelihood and quasi-likelihood based methods for analysing multivariate categorical data, with the association between outcomes of interest. Biometrics 52 1121–1133.
  • Molenberghs, G. and Verbeke, G. (2005). Models for Discrete Longitudinal Data. Springer, New York.
  • Molenberghs, G. and Verbeke, G. (2010). A note on a hierarchical interpretation for negative variance components. To appear.
  • Molenberghs, G., Verbeke, G., Demétrio, C. G. B. and Vieira, A. (2009). A family of generalized linear models for repeated measures with normal and conjugate random effects. To appear.
  • Nelder, J. A. (1954). The interpretation of negative components of variance. Biometrika 41 544–548.
  • Nelson, K. P., Lipsitz, S. R., Fitzmaurice, G. M., Ibrahim, J., Parzen, M. and Strawderman, R. (2006). Use if the probability integral transformation to fit nonlinear mixed-effects models with nonnormal random effects. J. Comput. Graph. Statist. 15 39–57.
  • Renard, D., Molenberghs, G. and Geys, H. (2004). A pairwise likelihood approach to estimation in multilevel probit models. Comput. Statist. Data Anal. 44 649–667.
  • Schall, R. (1991). Estimation in generalized linear models with random effects. Biometrika 78 719–729.
  • Verbeke, G. and Molenberghs, G. (2000). Linear Mixed Models for Longitudinal Data. Springer, New York.
  • Verbeke, G. and Molenberghs, G. (2010). Arbitrariness of models for augmented and coarse data, with emphasis on incomplete-data and random-effects models. Stat. Model. To appear.
  • Zhang, J. and Heitjan, D. F. (2007). Impact of nonignorable coarsening on Bayesian inference. Biostatistics 8 722–743.
  • Zeger, S. L., Liang, K.-Y. and Albert, P. S. (1988). Models for longitudinal data: A generalized estimating equation approach. Biometrics 44 1049–1060.