ml_glm function

A function to fit generalized linear models using maximum likelihood.

This function fits generalized linear models by maximizing the joint log-likeliood, which is set in a separate function. Only single-parameter members of the exponential family are covered. The post-estimation output is designed to work with existing reporting functions.

ml_glm(formula, data, family, link, offset = 0, start = NULL, verbose =
FALSE, ...)

Arguments

• formula: an object of class '"formula"' (or one that can be coerced to that class): a symbolic description of the model to be fitted. (See the help for 'glm' for more details).
• data: a data frame containing the variables in the model.
• family: a description of the error distribution be used in the model. This must be a character string naming a family.
• link: a description of the link function be used in the model. This must be a character string naming a link function.
• offset: this can be used to specify an a priori known component to be included in the linear predictor during fitting. This should be 0 or a numeric vector of length equal to the number of cases.
• start: optional starting points for the parameter estimation.
• verbose: logical flag affecting the detail of printing. Defaults to FALSE.
• ...: optional arguments to pass within the function.

Details

The containing package, msme, provides the needed functions to use the ml_glm function to fit the Poisson and Bernoulli families, and supports the use of the identity, log, logit, probit, and complementary log-log link functions. The object returned by the function is designed to be reported by the print.glm function.

Returns

• fit: the output of optim.

• X: the design matrix.

• y: the response variable.

• call: the call used for the function.

• obs: the number of observations.

• df.null: the degrees of freedom for the null model.

• df.residual: the residual degrees of freedom.

• deviance: the residual deviance.

• null.deviance: the residual deviance for the null model.

• residuals: the deviance residuals.

• coefficients: parameter estimates.

• se.beta.hat: standard errors of parameter estimates.

• aic: Akaike's Information Criterion.

• i: the number of iterations required for convergence.

References

Hilbe, J.M., and Robinson, A.P. 2013. Methods of Statistical Model Estimation. Chapman & Hall / CRC.

Author(s)

Andrew Robinson and Joe Hilbe.

Note

This function is neither as comprehensive nor as stable as the inbuilt glm function. It is a lot easier to read, however.

See Also

irls, glm, ml_glm2

Examples

data(medpar)

ml.poi <- ml_glm(los ~ hmo + white,
                 family = "poisson",
                 link = "log",
                 data = medpar)
ml.poi
summary(ml.poi)