robmixglm {robmixglm}

Fits a Robust Generalized Linear Model and Variants

Description

Fits robust generalized linear models and variants described in Beath (2018).

Usage

robmixglm(formula, family = c("gaussian", "binomial", "poisson", 
"gamma", "truncpoisson", "nbinom"), data, offset = NULL, 
quadpoints = 21, notrials = 50, EMTol = 1.0e-4, cores  =  max(detectCores() %/% 2,  1), 
verbose = FALSE)

Arguments

formula

Model formula

family

Distribution of response

data

Data frame from which variables are obtained

offset

Offset to be incorporated in the linear predictor.

quadpoints

Number of quadrature points used in the Gauss-Hermite integration.

notrials

Number of random starting values to be used for EM

EMTol

Relative change in likelihood for completion of EM algorithm before switching to quasi-Newton

cores

Number of cores to be used for parallel evaluation of starting values

verbose

Print out diagnostic information? This includes the likelihood and parameter estimates for each EM run.

Details

Fits robust generalized models assuming that data is a mixture of standard observations and outlier abservations, which belong to an overdispersed model (Beath, 2018). For binomial, Poisson, truncated Poisson and gamma, the overdispersed component achieved through including a random effect as part of the linear predictor, as described by Aitkin (1996). For gaussian and negative binomial data the outlier component is also a gaussian and negative binomial model, respectively but with a higher dispersion. For gaussian this corresponds to a higher value of \sigma^2 but for negative binomial this is a lower value of \theta.

The method used is a generalised EM. Random starting values are determined by randomly allocating observations to either the standard or outlier class for the first iteration of the EM. The EM is then run to completion for all sets of starting values. The best set of starting values is then used to obtain the final results using a quasi-Newton method. Where the overdispersed data is obtained using a random effect, the likelihood is obtained by integrating out the random effect using Gauss-Hermite quadrature.

Value

robmixglm object. This contains

fit

Final model fit from quasi-Newton

prop

Posterior probability of observation in each class

logLik

final log likelihood

np

Number of parameters

nobs

Number of observations

coef.names

Coefficient names

call

Call to function

family

Family of model to be fitted

model

model

terms

terms

xlevels

Levels for factors.

quadpoints

Number of quadrature points used in the Gauss-Hermite integration.

notrials

Number of random starting values to be used for EM

EMTol

Relative change in likelihood for completion of EM algorithm before switching to quasi-Newton

verbose

Was verbose output requested?

Author(s)

Ken Beath

References

Beath, K. J. A mixture-based approach to robust analysis of generalised linear models, Journal of Applied Statistics, 45(12), 2256-2268 (2018) DOI: 10.1080/02664763.2017.1414164

Aitkin, M. (1996). A general maximum likelihood analysis of overdispersion in generalized linear models. Statistics and Computing, 6, 251262. DOI: 10.1007/BF00140869

Examples

if (requireNamespace("MASS", quietly = TRUE)) {
library(MASS)
data(forbes)
forbes.robustmix <- robmixglm(100*log10(pres)~bp, data = forbes, cores = 1)
}