May 18, 2012

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You are here: Home / Dissertation Resources / Directory of Statistical Analyses / Generalized Linear Models and Estimating Equations

Generalized Linear Models and Estimating Equations

Generalized linear models are the generalization of certain general linear models.  These are namely ANOVA, ANCOVA, MANOVA and MANCOVA, as well as the regression models.  Generalized Linear Model supports non-normal distributions for dependent or criterion variables. Thus, it can be said that the generalized linear model involves logistic models for binary dependent variables, log linear analysis, Poisson regression, etc. In SPSS, generalized linear model can be performed by selecting “Generalized Linear Models” from the analyze of menu, and then selecting the type of model from which one wants to analyze as the Generalized Linear Models option.

Generalized Estimating Equations extends Generalized Linear Models further by involving dependent data for repeated measures, logistic regression and various other models for the time series or correlated data. In SPSS, Generalized Estimating Equations can be done by selecting “Generalized Linear Models” from the analyze menu, and then selecting the “Generalized Estimating Equations” from the Generalized Linear Models option.

The dependent variable in the implementation of Generalized Estimating Equations and Generalized Linear Models are distributed in the following distributions:

  • The dependent variable during the implementation of Generalized Estimating Equations and Generalized Linear Models takes the form of Normal distribution when the dependent variable is continuous (numeric).
  • The dependent variable during the implementation of Generalized Estimating Equations and Generalized Linear Models takes the form of Multinomial distribution when the dependent variable is ordinal (numeric or string).
  • The dependent variable during the implementation of Generalized Estimating Equations and Generalized Linear Models takes the form of Binomial distribution when the dependent variable is binary.
  • The dependent variable during the implementation of Generalized Estimating Equations and Generalized Linear Models takes the form of Poisson distribution when the dependent variable is count in nature or when the events are rare in nature.
  • The dependent or criterion variables in Generalized Estimating Equations and Generalized Linear Models are not distributed as free variables.
  • The link function in Generalized Linear Models relates the Generalized Linear Models in a specified design matrix.

There are certain assumptions in Generalized Estimating Equations and Generalized Linear Models.  These assumptions are as follows:

  • Generalized Estimating Equations and Generalized Linear Models do not assume that the dependent/independent variables are not normally distributed.
  • Generalized Estimating Equations and Generalized Linear Models neither assume linearity between the predictors and the dependent variables, nor homogeneity of variance for the range of the dependent variable.
  • There must be linearity in the link function as assumed by the Generalized Estimating Equations and Generalized Linear Models.
  • It is assumed in Generalized Estimating Equations and Generalized Linear Models that the multicollinearity is absent.
  • The data in Generalized Estimating Equations and Generalized Linear Models must be centered in order to reduce multicollinearity.
  • The dependent data in Generalized Estimating Equations and Generalized Linear Models are either interval or ordinal, and they are sometimes binary or count type.

Generalized Linear Model Resources

Ballinger, G. A. (2004). Using generalized estimating equations for longitudinal data analysis. Organizational Research Methods, 7(2), 127-150.

Beretvas, S. N., & Williams, N. J. (2004). The use of hierarchical generalized linear model for item dimensionality assessment. Journal of Educational Measurement, 41(4), 379-395.

Cardot, H., & Sarda, P. (2005). Estimation in generalized linear models for functional data via penalized likelihood. Journal of Multivariate Analysis, 92(1), 24-41.

Fox, J. (2008). Applied regression analysis and generalized linear models (2nd ed.). Thousand Oaks, CA: Sage Publications.

Hardin, J. W., & Hilbe, J. M. (2007). Generalized linear models and extensions (2nd ed.). College Station, TX: StataCorp LP.

Hoffman, J. P. (2003). Generalized linear models: An applied approach. Boston: Pearson, Allyn, & Bacon.

Hwang, H., & Takane, Y. (2005). Estimation of growth curve models with structured error covariances by generalized estimation equations. Behaviormetrika, 32(2), 155-163.

Johnson, T. R. (2006). Generalized linear models with ordinally-observed covariates. British Journal of Mathematical and Statistical Psychology, 59(2), 275-300.

Johnson, T. R., & Kim, J. -S. (2004). A generalized estimating equations approach to mixed-effects ordinal probit models. British Journal of Mathematical and Statistical Psychology, 57(2), 295-310.

McCullagh, P., & Nelder, J. A. (1989). Generalized linear models (2nd ed.). London: Chapman & Hall.

Mukherjee, B., & Liu, I. (2009). A note on bias due to fitting prospective multivariate generalized linear models to categorical outcomes ignoring retrospective sampling. Journal of Multivariate Analysis, 100(3), 459-472.

Nelder, J. A., & Wedderburn, R. W. M. (1972). Generalized linear models. Journal of the Royal Statistical Society, 135(3), 370-384.

Rogers, W. H. (1993). Comparison of nbreg and glm for negative binomial. Stata Technical Bulletin, 3(16), 1-32.

Schluchter, M. D. (2008). Flexible approaches to computing mediated effects in generalized linear models: Generalized estimating equations and bootstrapping. Multivariate Behavioral Research, 43(2), 268-288.