Generalized Linear Models
Bibliography
This is a very idiosyncratic of bibliography of some of the recent
generalized linear model literature. See also Books.
New Response Distributions
Glms assume a response distribution which is a linear exponential family plus a
dispersion parameter. The following three references study the properties of this family
form, and answer questions like "How many glm families are there?"
- Jørgensen, B. (1997). The Theory of Dispersion Models. Chapman and Hall,
London.
- Smyth, G. K. (1996). Regression modelling of quantity data with exact zeroes.
Proceedings of the Second Australia-Japan Workshop on Stochastic Models in
Engineering, Technology and Management. Technology Management Centre, University of
Queensland, 572-580. (Postscript).
- Jørgensen, B. (1992). The theory of exponential dispersion models and analysis of
deviance. Monografias de Matemátika No. 51, Instituto de Mathemátika pura e
Aplicada, Rio de Janeiro.
- Jørgensen, B. (1987). Exponential dispersion models. J. Roy. Statist. Soc. B, 49,
127-162.
- Brockwell,
P. J., and Brown, B. M. (1978). Expansions for the positive stable laws. Z. Wahrsch.
Verw. Gebiete, 45, 213-224.
- Brockwell, P. J., and Brown, B. M. (1979). Estimation for the positive stable laws, I. Austral.
J. Statist., 21, 139-148.
- Feller, W. (1971). An Introduction to Probability Theory and Its Applications,
Volume II, Second Edition. Wiley, New York. Section XIII.6-7.
- Jorgensen, B. (1997), The Theory of Dispersion Models. Chapman and Hall,
London. Section 4.2.1.
- Nolan, J. P. (1997). Numerical calculation of stable densities and distribution
functions. Communications in Statistics - Stochastic Models, 13,
759-774.
Diagnostics and Residuals
- Breslow N. E. (1996). Generalized linear models: Checking assumptions and strengthening
conclusions. Statistica Applicata 8, 23-41. (Postscript)
- Cook, R. D., and Weisberg, S. (1994). ARES plots for generalized linear models. Computational
Statistics and Data Analysis, 17, 303-315.
- Dunn, K. P., and Smyth, G. K. (1996). Randomized quantile residuals. J. Comput.
Graph. Statist., 5, 236-244. (Abstract - Postscript)
- Pierce, D. A., and Schafer, D. W. (1986). Residuals in generalized linear models. Journal
of the American Statistical Assocation. 81
Robust Estimation
- Cantoni, E., and Ronchetti, E.(2001). "Resistant selection of the
smoothing parameter for smoothing splines", Statistics and Computing
11, 141-146.
- Cantoni, E., and Ronchetti, E. (2001). Robust inference for
generalized linear models. Journal of the American Statistical
Association 96, 1022-1030.
- Cantoni, E. (2001). Robust inference based on quasi-likelihoods for
generalized linear models and longitudinal data. Proceedings of the
International Conference on Robust Statistics 2001.
Generalized Nonlinear Models
- Hastie, T., and Tibshirani, R. (1997). Generalized Additive Models. Encyclopedia of
Statistical Science, Wiley. (Postscript)
- Czado, C. (1997). On Selecting Parametric Link Transformation Families in Generalized
Linear Models. Journal of Statistical Planning and Inference. To appear. (Postscript)
- Gay, D. M., and Welsh, R. E. (1988). Maximum likelihood and quasi-likelihood for
nonlinear exponential family models. Journal of the American Statistical Association,
83, 990-998.
- Rigby, R. and Stasinopoulos, M. (1992). Detecting break points in the Hazard Function in
Survival Analysis. In Statistical Modelling, eds B. Francis, G.U.H. Seeber, P.G.M. van der
Heyden and W. Jansen, pp 303-312. Elsevier Science Publishers B.V.
- Stasinopoulos, M. and Rigby, R. (1992). Detecting break points in Generalised Linear
Models. Computational Statistics and Data Analysis, 13, 461-471.
- Exponential
Family Nonlinear Models, Bo-Cheng Wei (Southeast University, Nanjing), Springer-Verlag
Sinpagore, 1998.
Dispersion Modelling
- Rigby, R., and Stasinopoulos, M. (1998). Mean and Dispersion Additive Models.
Technical Report.
- Benjamin M. A., Rigby R. A. and Stasinopoulos M. D. (1998). Modelling exponential family time
series data. In Statistical Modelling: Proceedings of the 13th International
Workshop on Statistical Modelling, eds B. Marx and H. Friedl. New Orleans.
- McCullagh, P., and Nelder, J. A. (1989). Generalized Linear Models, Second
Edition. Chapman and Hall, London. (Chapter 10)
- Nelder, J. A., and Lee, Y. (1991). Generalized linear models for the analysis of
Taguchi-type experiments. Applied Stochastic Models and Data Analysis, 7,
107-120.
- Rigby, R. A. and Stasinopoulos, D. M. (1994). Robust fitting of an Additive model for
the variance Heterogeneity. In COMPSTAT Proceedings in Computational Statistics, eds R.
Dutter and W. Grossmann, pp 261-268, Physica-Verlag.
- Rigby R. A. and Stasinopoulos M. D. (1995). Mean and Dispersion Additive Models:
Applications and Diagnostics. In Statistical Modelling: Proceedings of the 10th
International Workshop on Statistical Modelling, eds G.U.H Seeber, B.J Francis, R
Hatzinger, G. Steckel-Berger, Springer-Verlag.
- Rigby, R. A., and Stasinopoulos, D. M. (1996). Mean and Dispersion Additive Models. In
Statistical Theory and Computational Aspects of Smoothing eds. W Hardle and M.G. Schimek,
pp 215-230, Physica-Verlag.
- Rigby, R. A. and Stasinopoulos, D. M. (1996). A Semi-parametric Additive model for
variance heterogeneity. Statistics and Computing, 6, 57-65..
- Stasinopoulos, D. M. and Francis, B. (1993). Generalised Additive Models in GLIM4. GLIM
Newsletter, 22, pp 30-36.
- Smyth, G. K. (1989). Generalized linear models with varying
dispersion. Journal
of the Royal Statistical Society B 51, 47-60. (Abstract
and Full Text)
- Smyth, G. K., and Verbyla, A. P.(1996). A conditional approach to residual maximum
likelihood estimation in generalized linear models. J. Roy. Statist. Soc. B, 58,
565-572. (Abstract - Postscript).
- Smyth, G. K., and Verbyla, A. P. (1999). Adjusted likelihood methods for modelling
dispersion in generalized linear models. Environmetrics. To appear. (Abstract - Zipped PostScript)
- Tran G., Stasinopoulos, D. M. (1995). Plotting additive fits in Generalised Additive
Models. GLIM Newsletter, 24, pp 10-15.
Overdispersion
- Albert, P. S. (1991). A two-state Markov model for a time series of epileptic seizure
counts. Biometrics 47, 1371-1381.
- Altham, P. M. E. (1976). Discrete variable analysis for individuals grouped into
families. Biometrika 63, 263-269.
- Altham, P. M. E. (1978). Two generalizations of the binomial distribution. Journal
of the Royal Statistical Society C27, 162-167.
- Andersen, D. A. (1988). Some models for overdispersed binomial data. Australian
Journal of Statistics 30, 125-148.
- Barnwall, R. K., and Paul, S. R. (1988). Analysis of a one-way layout of count data with
negative binomial variation. Biometrika 75, 215-222.
- Bateman, G. I. (1950). The power of the c^{2} index
of dispersion when Neyman's contagious distribution is the alternative hypothesis. Biometrika
37, 59-63.
- Bennett, S. (1988). An extension of William's method of overdisperion models. GLIM
Newsletter 17, 12-18.
- Bissell, A. F. (1972). A negative binomial model with varying element sizes. Biometrika
59, 435-441.
- Böhning, D. (1995). A review of reliable maximum likelihood algorithms for
semiparametric mixture models. Journal of Statistical Planning and Inference, 47,
5-28.
- Breslow, N. E. (1984). Extra-Poisson variation in log-linear models. Journal of the
Royal Statistical Society C33, 38-44.
- Breslow, N. E. (1989). Score tests in overdispersed GLMs. In Workshop on Statistical
Modelling, A. Decarli, B. J. Francis, R Gilchrist and G. U. H. Seeber, eds.,
Springer-Verlag, New York, pages 64-74.
- Breslow, N. E. (1990). Tests of hypotheses in overdispersed Poisson regression and other
quasi-likelihood models. Journal of the American Statistical Association 85,
565-571.
- Breslow, N. E. (1996). Generalized linear models: checking assumptions and strengthening
conclusions. Statistica Applicata, 8, 23-41.
- Breslow, N. E., and Clayton, D. G. (1993). Approximate inference in generalized linear
mixed models. Journal of the American Statistical Association, 88,
9-25.
- Breslow, N. E. and Lin, X. (1995). Bias correction in generalized linear models with a
single component of dispersion. Biometrika, 82, 81-91.
- Cameron, A. C., and Trivedi, P. K. (1990). Regression-based tests for overdispersion in
the Poisson model. Journal of Econometrics 46, 347-364.
- Davidian, M., and Carroll, R. J. (1987). Variance function estimation. Journal of
the American Statistical Association, 82, 1079-1081.
- Cox, D. R. (1983). Some remarks on overdispersion. Biometrika 70,
269-274.
- Dean, C. B. (1991). Estimating equations for mixed Poisson models. In Estimating
Functions, V. P. Godambe, ed., Oxford University Press, Oxford, pages 35-46.
- Dean, C. B. (1992). Testing for overdispersion in Poisson and binomial regression
models. Journal of the American Statistical Association, 87,
451-457.
- Dean, C. B. (1998). Overdispersion. In: Encyclopedia
of Biostatistics, P. Armitage and T. Colton (eds.), Wiley, London,
pages 3226-3232.
- Dean, C., and Lawless, J. F. (1989). Tests for detecting overdispersion in Poisson
regression models. Journal of the American Statistical Association, 84,
467-472.
- Diggle, P., Liang, K. Y., and Zeger, S. L. (1994). Analysis of Longitudinal Data.
Oxford University Press, New York.
- Fisher, R. A. (1950). The significance of deviations from expectation in a Poisson
series. Biometrics, 6, 17-24.
- Godambe, V. P., and Thompson, M. E. (1989). An extension of quasi-likelihood estimation
(with discussion). Journal of Statistical Planning and Inference, 22,
137-152.
- Lesperance, M. L., and Kalbfleisch, J. D. (1992). An algorithm for computing the
non-parametric MLE of a mixing distribution. Journal of the American Statistical
Association, 87, 120-126.
- Lindsay, B. (1995). Mixture Models: Theory, Geometry and Applications. NSF-CBMS
Regional Conference Series in Probability and Statistics, Vol. 5, Institute of
Mathematical Statistics, Hayward.
- Lindsey, J. K. (1993). Models for Repeated Measurements. Oxford University
Press, New York. (Chapter 5)
- Lindsey, J. K. (1999). On the use of corrections for overdispersion. Applied
Statistics 48, 553-561. (Argues for use of mixture models and AIC
rather than use of dispersion parameter without a probabilistic foundation.)
- McCullagh, P., and Nelder, J. A. (1989). Generalized Linear Models, Second
Edition. Chapman and Hall, London. (Sections 4.5, 5.5, 6.2)
- O'Hara Hines, R. J., Lawless, J. F., and Carter, E. M. (1992). Diagnostics for a
cumulative multinomial generalized linear model, with applications to grouped toxilogical
mortality data. Journal of the American Statistical Assocation, 87,
1059-1069.
- Prentice, R. L. (1986). Binary regression using an extended beta-binomial distribution,
with discussion of correlation induces by covariate measurement errors. Journal of the
American Statistical Assocation, 81, 321-327.
- Smith, P. J., and Heitjan, D. F. (1993). Testing and adjusting for departures from
nominal dispersion in generalized linear models. Applied Statistics, 42,
31-41.
- "Student" (1919). An explanation of deviations from Poisson's law in practice.
Biometrika, 12, 211-215.
- Tarone, R. E. (1979). Testing the goodness-of-fit of the binomial distribution. Biometrika,
66, 585-590.
- Thall, P. F., and Vail, S. C. (1990). Some covariance models for longitudinal count data
with overdispersion. Biometrics, 46, 657-671.
Random Effects
- Breslow, N. E., and Clayton, D. G. (1993). Approximate inference in generalized linear
mixed models. Journal of the American Statistical Association 88,
9-25.
- Firth, D., and Harris, I. R. (1991). Quasi-likelihood for multiplicative random effects.
Biometrika, 78, 545- 555.
- Gilks, W.R., Wang, C.C., Yvonnet, B. und Coursaget, P. (1993). Random-effects models for
longitudinal data using Gibbs sampling. Biometrics 49, 441-453.
- Gilmour, A. R., Anderson, R. D., and Rae, A. L. (1985). The analysis of binomial data by
a generalized linear mixed model. Biometrika 72, 593-599.
- Ibrahim, J.G. and Kleinman, K.P. (1998). Semiparametric Bayesian methods for random
effects models. Practical Nonparametric and Semiparmetric bayesian Statistics,
89-114, Lecture Notes in Statistics 133, Springer-Verlag, New York.
- Karim, M. R., and Zeger, S. L. (1992). Generalized linear models with random effects;
salamander mating revisited. Biometrics 48, 631-644.
- Kuk, A.Y.C. (1995). Asymptotically unbiased estimation in generalized linear models with
random effects. Journal of the Royal Statistical Society B, 57,
395-407.
- Lee, Y., and Nelder, J. A. (1996). Heirarchical generalized linear models (with
discussion). Journal of the Royal Statistical Society B, 58,
619-678.
- Ma, R. (1999). An Orthodox BLUP Approach to Generalized Linear Mixed Models. Ph.D.
thesis, University of British Columbia.
- McCulloch, C. (1994). Maximum likelihood variance components estimation for binary data.
J. Amer. Statist. Assoc. 89, 330-335.
[Probit with random effects. EM, REML, Gibbs sampling.
Computations feasible for any number and structure of random effects and an arbitrary
number of fixed effects.]
- McCulloch, C.E. (1997). Maximum likelihood algorithms for generalized linear mixed
models. Journal of the American Statistical Association 92,
162-170.
- McGilchrist, C. A. (1994). Estimation in generalized mixed models. Journal of the
Royal Statistical Society B 56, 61-69.
- Morton, R. (1987). A generalized linear model with nested strata of extra-Poisson
variation. Biometrics 74, 247-257.
- Piegorsch, W. W., and Casella, G. (1996). Empirical Bayes estimation for logistic
regression and extended parametric regression models. Journal of Agricultural,
Biological, and Environmental Statistics 1, 231-249.
- Schall, R. (1991). Estimation in generalized linear models with random effects. Biometrika,
78, 719-727. Software
- Stiratelli, R., Laird, N., and Ware, J. H. (1984). Random-effects models for serial
observations with binary response. Biometrics 40, 961-971.
- Wolfinger, R. and O'Connel, M. (1993). Generalized linear mixed models: a
pseudo-likelihood approach. Journal of Statistical Computation and Simulation 48,
233-243.
- Wolfinger, R.D. (1999). Fitting nonlinear mixed models with the new NLMIXED procedure.
Paper 287, Proceedings of the 99 Joint Statistical Meetings.
- Wolfinger, R.D. (1999). Towards practical applications of generalized linear mixed
models.
- Zeger, S. L. and Karim, M. R. (1991). Generalized linear models with random effects; a
Gibbs sampling approach. Journal of the American Statistical Association 86,
79-86.
Bayesian
Time Series
- Albert, P. S. (1991). A two-state Markov model for a time series of epileptic seizure
counts. Biometrics 47, 1371-1381.
- Benjamin M. A., Rigby R. A. and Stasinopoulos M. D. (1998). Modelling exponential family time
series data. In Statistical Modelling: Proceedings of the 13th International
Workshop on Statistical Modelling, eds B. Marx and H. Friedl. New Orleans.
- Liang, K. Y., and Zeger, S. L. (1986). Longitudinal data analysis using generalized
linear models. Biometrika, 73, 13-22.
Multivariate
- Czado, C. (1997). Multivariate Probit Analysis of Binary Time Series with Missing
Responses. (Postscript)
Industrial Applications
- Chipman, H., and Hamada, M. (1996). Bayesian analysis of ordered categorical data from
industrial experiments. Technometrics, 38, 1-10.
- Engel, J. (1992). Modelling variation in industrial experiments. Appl. Statist.,
41, 579-593.
- Grego, J. (1993). Generalized linear models and process variation. J. Quality
Technology, 25, 288-295.
- Lee, Y., and Nelder, J. A. (1998). Generalized linear models for the analysis of
quality-improvement experiments. Canadian Journal of Statistics, 26,
95-105.
- Nair, V. N. (ed.) (1992). Taguchi's parameter design: a panel discussion. Technometrics,
34, 127-204.
- Nair, V. N., and Pregibon, D. (1986). A data analysis strategy for quality engineering
experiments. AT&T Technical J., 65, 73-84.
- Nair, V. N., and Pregibon, D. (1988). Analyzing dispersion effects from replicated
factorial experiments.
- Nelder, J. A. (1994). A re-analysis of the pump-failure data. Comment on:
"Conjugate likelihood distributions" [Scand. J. Statist. 20,
(1993), no. 2, 147-156] by E. I. George, U. E. Makov and A. F. M. Smith. With a reply by
George, Makov and Smith. Scand. J. Statist., 21, 187-191.
- Nielsen, L.K., Smyth, G.K., and Greenfield, P.F. (1991). Hemacytomer cell count
distributions: implications of non-Poisson behaviour. Biotechnology Progress, 7,
560-563.
- Smyth, G. K. (1996). Regression analysis of quantity data with exact zeros. Proceedings
of the 2nd Australia-Japan Workshop on Stochastic Models in Engineering, Technology and
Management, R. J. Wilson, D. N. P. Murthy and S. Osaki (eds.), Technology Management
Centre, University of Queensland, pp. 572-580.
- Vining, G. G., and Myers, R. H. (1990). Combining Taguchi and response surface
methodologies: a dual response approach. J. Quality Technology, 22,
38-45.
Biological Applications
- Hardy I. C. W., and Field S. A. (1998). Logistic analysis of animal contests.
Animal
Behaviour 56, 787-792.
Insurance Applications
- Smyth, G. K., and Jørgensen, B. (2002). Fitting Tweedie's compound Poisson model
to insurance claims data: dispersion modelling. ASTIN Bulletin 32,
143-157. (PDF) 6/2002
- McCullagh, P., and Nelder, J. A. (1983). Generalized Linear
Models. Chapman and Hall, London.
[Models claim size using gamma regression with reciprocal
link.]
- McCullagh, P., and Nelder, J. A. (1989). Generalized Linear
Models. Second Edition. Chapman and Hall, London.
[Car insurance claims are treated in Section 8.4.1. A
power variance function is estimated for this data data using extended
quasi-likelihood in Section 12.6.2.]
- Taylor, G. C. (1989). Use of spline functions for premium rating by
geographic area. ASTIN Bulletin 19, 91-122.
[Uses gamma responses and bivariate regression splines as
covariates.]
- Haberman, S., and Renshaw, A. E. (1990). Generalized linear models and
excess mortality from peptic ulcers. Insurance: Mathematics and
Economics 9, 147-154.
- Mack, T. (1991). A simple parametric model for rating
automobile insurance or estimating IBNR claims reserves. ASTIN
Bulletin 22, 93.
[Models claim size using gamma regression with log-link.]
- Renshaw, A. E. (1991). Actuarial graduation practice and generalized
linear and non-linear models. Journal of the Institute of Actuaries
119, 295-312.
- Brockman, M. J., and Wright, T. S. (1992). Statistical model rating:
making effective use of your data. Journal of the Institute of
Actuaries 119, 457.
[Models claim size using gamma regression with log-link.]
- Renshaw. A. E. (1993). An application of exponential dispersion
models in premium rating. ASTIN Bulletin 23, 145-147.
[Suggests use of compound Poisson responses using GLIM.]
- Renshaw, A. E. (1994). Modelling the claims process in the presence
of covariates. ASTIN Bulletin 24, 265-286.
[An overview of GLMs for modelling insurance claims
including Poisson regression for claims frequency, gamma regression for
claim size and compound Poisson for aggregrate claim value.]
- Nelder, J. A., and Verral, R. J. (1997). Credibility theory and
generalized linear models. ASTIN Bulletin 27, 71-82.
[Credibility estimates are obtained by including random
effects in a generalized linear model. Proposes to do this using
extended quasi h-likelihood.]
- Rolski, T., Schmidli, H., Schmidt, V., and Teugels, J. (1999).
Stochastic Processes for Insurance and Finance. John Wiley & Sons,
Chichester.
[Lots of material on distributions but no explicit
coverage of generalized linear models.]
- Haberman, S., and Renshaw, A. E. (1996). Generalized linear models and
actuarial science. The Statistician 45, 407-436.
[Nice review article including all of the above applications.]
- Haberman, S., and Renshaw, A. E. (1998). Actuarial applications of generalized
linear models. In Statistics in Finance, D. J. Hand and S. D. Jacka (eds),
Arnold, London.
[Similar to Haberman and Renshaw (1996).]
- Holler, K. D., Sommer, D., and Trahair, G. (1999). Something old,
something new in classificaiton ratemaking with a novel use of GLMs for
credit insurance. Casualty Actuarial Forum, Winter 1999.
- Millenhall, S. J. (1999). A systematic relationship between minimum
bias and generalized linear models.
1999
Proceedings of the Casualty Actuarial Society 86, 393-487.
[Very nice review of using generalized linear models to
set premium rates with particular reference to minimum bias models. Discusses Tweedie models with power variance functions
in Sections 8.3 and 8.4]
- Murphy, K. P., Brockman, M. J., and Lee, P. K. W. (2000). Using
generalized linear models to build dynamic pricing systems. Casualty
Actuarial Forum, Winter 2000.