Abstract
This chapter deals with several useful variants of LMs and binomial GLMs. For example, LMs have been generalized to varying coefficient models, seemingly unrelated regressions (SUR), the Tobit model (censored LM), and AR(1) time series model (correlated data over time). And for logistic regression, this can be extended to bivariate binary responses, a two-stage sequential binomial process, and double-exponential family models.
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Agresti, A. 2013. Categorical Data Analysis (Third ed.). Hoboken: Wiley.
Amemiya, T. 1984. Tobit models: a survey. Journal of Econometrics 24(1–2):3–61.
Amemiya, T. 1985. Advanced Econometrics. Oxford: Blackwell.
Ashford, J. R. and R. R. Sowden 1970. Multi-variate probit analysis. Biometrics 26(3):535–546.
Christensen, R. 1997. Log-linear Models and Logistic Regression (Second ed.). New York: Springer-Verlag.
Crowder, M. and T. Sweeting 1989. Bayesian inference for a bivariate binomial distribution. Biometrika 76(3):599–603.
Efron, B. 1986. Double exponential families and their use in generalized linear regression. Journal of the American Statistical Association 81(395):709–721.
Fan, J. and Q. Yao 2003. Nonlinear Time Series: Nonparametric and Parametric Methods. New York: Springer.
Freedman, D. A. and J. S. Sekhon 2010. Endogeneity in probit response models. Political Analysis 18(2):138–150.
Goldberger, A. S. 1964. Econometric Theory. New York: Wiley.
Greene, W. H. 2012. Econometric Analysis (Seventh ed.). Upper Saddle River: Prentice Hall.
Hastie, T. and R. Tibshirani 1993. Varying-coefficient models. Journal of the Royal Statistical Society, Series B 55(4):757–796.
Johnson, N. L., S. Kotz, and N. Balakrishnan 1994. Continuous Univariate Distributions (Second ed.), Volume 1. New York, USA: Wiley.
McCullagh, P. and J. A. Nelder 1989. Generalized Linear Models (Second ed.). London: Chapman & Hall.
Palmgren, J. 1989. Regression models for bivariate binary responses. Technical Report 101, Biostatistics Dept, University of Washington, Seattle, USA.
Park, B. U., E. Mammen, Y. K. Lee, and E. R. Lee 2015. Varying coefficient regression models: a review and new developments. International Statistical Review 83(1):36–64.
Smith, M. and R. Kohn 2000. Nonparametric seemingly unrelated regression. Journal of Econometrics 98(2):257–281.
Smithson, M. and E. C. Merkle 2013. Generalized Linear Models for Categorical and Continuous Limited Dependent Variables. London: Chapman & Hall/CRC.
Smyth, G. K. 1989. Generalized linear models with varying dispersion. Journal of the Royal Statistical Society, Series B 51(1):47–60.
Srivastava, V. K. and T. D. Dwivedi 1979. Estimation of seemingly unrelated regression equations: A brief survey. Journal of Econometrics 10(1):15–32.
Srivastava, V. K. and D. E. A. Giles 1987. Seemingly Unrelated Regression Equations Models: Estimation and Inference. New York, USA: Marcel Dekker.
Tobin, J. 1958. Estimation of relationships for limited dependent variables. Econometrica 26(1):24–36.
von Eye, A. and E.-E. Mun 2013. Log-linear Modeling: Concepts, Interpretation, and Application. Hoboken, NJ, USA: Wiley.
Wooldridge, J. M. 2006. Introductory Econometrics: A Modern Approach (5th ed.). Mason, OH, USA: South-Western.
Zellner, A. 1962. An efficient method of estimating seemingly unrelated regressions and tests for aggregation bias. Journal of the American Statistical Association 57(298):348–368.
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Yee, T.W. (2015). Some LM and GLM Variants. In: Vector Generalized Linear and Additive Models. Springer Series in Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-2818-7_10
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DOI: https://doi.org/10.1007/978-1-4939-2818-7_10
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