fitjoint {JointGLM}R Documentation

Joint Modelling Fitting

Description

Fit two interlinked GLMs or GAMS to model dependently the Mean and the Dispersion.

Usage

fitjoint(model, form.mean, form.disp, data, family.mean =
gaussian, family.disp = Gamma(link='log'), eps = 10^(-6), iter.max =
100, maxit = 50, reml = TRUE)

Arguments

model A character string. Must be one of ``glm'' and ``gam'' for GLMs and GAMs models respectively.
form.mean, form.disp R formula put in a character type way which specifies the linear model for the mean and the dispersion respectively.
data A data.frame for the data. The first column corresponds to the response observations, while others to the explicative variables.
family.mean, family.disp The family for the mean and dispersion. See family.
eps Optional numeric. The precision for the convergence test.
iter.max, maxit Numerics. The maximum number of iteration in the Joint Modelling algorithm and glm.fit function respectively.
reml Logical. If TRUE - the default, the Restricted Maximum Likelihood Estimation is used.

Details

The estimation procedure of the Joint Model is based on the see-saw algorithm. This procedure is explained in McCullagh and Nelder, 1987. The pair of models is fitting thanks to the Extended Quasi-Deviance criterion. We start by setting the dispersion parameter for the mean to 1 and fitting the model for the mean. We then form d the response variable for dispersion and fit the dispersion GLM/GAM. From the fitted values of the dispersion GLM/GAM, we form prior weights given by the inverse of these fitted values and refit the model for the mean. The alternation of fits continues until stability is reached. We say that stability is reached when the EQD variation - in percent - between two iteration in lower than an ε.

Value

This function returns an object of class c("joint", mod) where mod is either "glm" or "gam". In particular this object is a list with four components. The first two are glm/gam ocbjects corresponding to the final estimate of the mean and dispersion GLMs/GAMs component. A component iterations corresponding to the number of iterations in the Joint Modelling fitting algorithm. And a component eql corresponding to the Extended Quasi-Likelihood for this Joint Model Object.

Author(s)

Mathieu Ribatet and Bertrand Iooss

References

Lee, Y and Nelder, J. A. (2003). Robust Design via Generalized Linear Models. Journal of Quality Technology, 35:2-12. McCullagh P. and Nelder J. A. (1987). Generalized Linear Models Second Edition. London: Chapman and Hall. ISBN 0-412-31760-5.

Examples

X <- rnorm(500, 5)
mu <- 2*X + 1
sigma2 <- exp(-X)
Y <- rnorm(500, mu, sqrt(sigma2))
data.frm <- data.frame(Y=Y, X=X)
ajust <- fitjoint("glm", 'Y~X', 'd~X', data = data.frm)
ajust

[Package JointGLM version 1.0-3 Index]