leroux.inla: Fit Leroux et al's spatial model.

Description

This function fits the model by Leroux et al. for a given value of the parameter lambda, i.e., the mixture parameter that appears in the variance..

Usage

leroux.inla(formula, d, W, lambda, improve = TRUE, fhyper = NULL, ...)

Arguments

formula

Formula of the fixed effects.

A data.frame with the data to be used.

Adjacency matrix.

lambda

Parameter used in the mixture of the two precission matrices.

improve

Logical. Whether to improve the fitted models to obtain better estimates of the marginal likelihoods.

fhyper

Extra arguments passed to the definition of the hyperparameters.

...

Extra arguments passed to function inla.

Value

An INLA object.

Details

This function fits the model proposed by Leroux et al. (1999) for a given value of parameter lambda. This parameter controls the mixture between a diagonal precission (lambda=1) and an intrinsic CAR precission (lambda=0).

The marginal log-likelihood is corrected to add half the log-determinant of the precission matrix.

References

Leroux B, Lei X, Breslow N (1999). Estimation of Disease Rates in Small Areas: A New Mixed Model for Spatial Dependence. In M Halloran, D Berry (eds.), Statistical Models in Epidemiology, the Environment and Clinical Trials, pp. 135-178. Springer-Verlag, New York.

Roger S. Bivand, Virgilio Gmez-Rubio, Hvard Rue (2014). Approximate Bayesian inference for spatial econometrics models. Spatial Statistics, Volume 9, 146-165.

Roger S. Bivand, Virgilio Gmez-Rubio, Hvard Rue (2015). Spatial Data Analysis with R-INLA with Some Extensions. Journal of Statistical Software, 63(20), 1-31. URL http://www.jstatsoft.org/v63/i20/.