Abstract
Linear models are well suited for regression analyses when the response variable is continuous and at least approximately normal. In some cases, an appropriate transformation is needed to ensure approximate normality of the response. In addition, the expectation of the response is assumed to be a linear combination of covariates. Again, these covariates may be transformed before being included in the linear predictor.
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Bibliography
Albert, J., & Chib, S. (1993). Bayesian analysis of binary and polychotomous response data. Journal of the American Statistical Association, 88, 669–679.
Anderson, T. W. (2003). An introduction to multivariate statistical analysis. Dordrecht: Kluwer.
Cameron, A. C., & Trivedi, P. K. (1998). Regression analysis of count data. Cambridge: Cambridge University Press.
Cameron, A. C., & Trivedi, P. K. (2005). Microeconometrics: Methods and applications. Cambridge: Cambridge University Press.
Carroll, R. J., Ruppert, D., Stefanski, L. A., & Crainiceanu, C. M. (2006). Measurement error in nonlinear models (2nd ed.). New York/Boca Raton: Chapman & Hall/CRC.
Collett, D. (1991). Modelling binary data. New York/Boca Raton: Chapman & Hall/CRC.
Collett, D. (2003). Modelling survival data in medical research (2nd ed.). New York/Boca Raton: Chapman & Hall/CRC.
Dellaportas, P., & Smith, A. F. M. (1993). Bayesian inference for generalized linear and proportional hazards models via Gibbs sampling. Applied Statistics, 42, 443–459.
Dey, D., Gosh, S. K., & Mallick, B. K. (2000). Generalized linear models: A Bayesian Perspective. New York: Marcel Dekker.
Diggle, P. J., Heagerty, P., Liang, K. L., & Zeger, S. L. (2002). Analysis of longitudinal data (2nd ed.). Oxford: Oxford University Press.
Fahrmeir, L., Hamerle, A., & Tutz, G. (1996). Multivariate Statistische Verfahren (second edition), De Gruyter.
Fahrmeir, L., & Kaufmann, H. (1985). Consistency and asymptotic normality of the maximum likelihood estimator in generalized linear models. The Annals of Statistics, 13, 342–368.
Fahrmeir, L., & Tutz, G. (2001). Multivariate statistical modelling based on generalized linear models (2nd ed.). Berlin: Springer.
Friedman, J., Hastie, T., & Tibshirani, R. (2000). Additive logistic regression: A statistical view of boosting. The Annals of Statistics, 28, 337–407.
Frühwirth-Schnatter, S., & Frühwirth, R. (2010). Data augmentation and MCMC for binary and multinomial logit models. In T. Kneib, & G. Tutz (Eds.), Statistical modelling and regression structures: Festschrift in honour of Ludwig Fahrmeir (pp. 111–132). Heidelberg: Springer.
Frühwirth-Schnatter, S., Frühwirth, R., Held, L., & Rue, H. (2009). Improved auxiliary mixture sampling for hierarchical models of non-Gaussian data. Statistics and Computing, 19, 479–492.
Frühwirth-Schnatter, S., & Wagner, H. (2006). Gibbs sampling for parameter-driven models of time series of small counts with application to state space modelling. Biometrika, 93, 827–841.
Gamerman, D. (1997). Efficient sampling from the posterior distribution in generalized linear mixed models. Statistics and Computing, 7, 57–68.
Geweke, J. (1991). Efficient simulation from the multivariate normal and student-t distribution subject to linear constraints. Computer science and statistics: Proceedings of the twenty-third symposium on the interface (pp. 571–578). Alexandria.
Holmes, C. C., & Held, L. (2006). Bayesian auxiliary variable models for binary and multinomial regression. Bayesian Analysis, 1, 145–168.
Hosmer, D. W., Lemeshow, S., & May, S. (2008). Applied survival analysis: Regression modeling of time to event data. New York: Wiley.
Joe, H. (1997). Multivariate models and dependence concepts. New York/Boca Raton: Chapman & Hall/CRC.
Kleiber, C., & Zeileis, A. (2008). Applied econometrics with R. New York: Springer.
Klein, J. P., & Moeschberger, M. L. (2005). Survival analysis (2nd edn.). New York: Springer.
Lenk, P., & DeSarbo, W. (2000). Bayesian inference for finite mixtures of generalized linear models with random effects. Psychometrika, 65, 93–119.
McCullagh, P., & Nelder, J. A. (1989). Generalized linear models (2nd ed.). New York/ Boca Raton: Chapman & Hall/CRC.
Nelder, J. A., & Wedderburn, R. W. M. (1972). Generalized linear models. Journal of the Royal Statistical Society A, 135, 370–384.
Rigby, R. A., & Stasinopoulos, D. M. (2005). Generalized additive models for location, scale and shape. Applied Statistics, 54, 507–554.
Robert, C. P. (1995). Simulation of truncated normal variables. Statistics and Computing, 5, 121–125.
Skrondal, A., & Rabe-Hesketh, S. (2004). Generalized latent variable modelling. New York/ Boca Raton: Chapman & Hall/CRC.
Therneau, T., & Grambsch, P. (2000). Modeling survival data: Extending the Cox model. New York: Springer.
Tutz, G. (2011). Regression for categorical data. Cambridge: Cambridge University Press.
Winkelmann, R. (2010a). Analysis of microdata (2nd ed.). Heidelberg: Springer.
Winkelmann, R. (2010b). Econometric analysis of count data (5th ed.). Berlin: Springer.
Zeileis, A., Kleiber, C., & Jackman, S. (2008). Regression models for count data in r. Journal of Statistical Software, 27(8), 1–25.
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Fahrmeir, L., Kneib, T., Lang, S., Marx, B. (2013). Generalized Linear Models. In: Regression. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-34333-9_5
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DOI: https://doi.org/10.1007/978-3-642-34333-9_5
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