GEE: GEE (Generalized Estimating Equations)

Description

GEE provides GEE-based methods from the packages gee and geepack to account for spatial autocorrelation in multiple linear regressions

Usage

GEE(formula, family, data, coord, corstr = "fixed", cluster = 3,
  moran.params = list(), plot = FALSE, scale.fix = FALSE,
  customize_plot = NULL)

Arguments

formula

Model formula. Variable names must match variables in data.

family

gaussian, binomial, or poisson are supported. Called using a quoted character string (i.e. family = "gaussian").

data

A data frame with variable names that match the variables specified in formula.

coord

A matrix of two columns with corresponding cartesian coordinates. Currently only supports integer coordinates.

corstr

Expected autocorrelation structure: independence, fixed, exchangeable, and quadratic are possible.

independence - This is the same as a GLM, i.e. correlation matrix = identity matrix.
fixed - Uses an adapted isotropic power function specifying all correlation coefficients.
exchangeable and quadratic for clustering, i.e. the correlation matrix has a block diagonal form:
- exchangeable - All intra-block correlation coefficients are equal.
- quadratic - Intra-block correlation coefficients for different distances can be different.

cluster

Cluster size for cluster models exchangeable and quadratic. Values of 2, 3, and 4 are allowed.

2 - a 2*2 cluster
3 - a 3*3 cluster
4 - a 4*4 cluster

moran.params

A list of parameters for calculating Moran's I.

lim1 Lower limit for first bin. Default is 0.
increment Step size for calculating I. Default is 1.

plot

A logical value indicating whether autocorrelation of residuals should be plotted.

scale.fix

A logical indicating whether or not the scale parameter should be fixed. The default is FALSE. Use TRUE when planning to use stepwise model selection procedures in step.spind.

customize_plot

Additional plotting parameters passed to ggplot

Value

An object of class GEE. This consists of a list with the following elements:

call: Call
formula: Model formula
family: Family
coord: Coordinates used for the model
corstr: User-selected correlation structure
b: Estimate of regression parameters
s.e.: Standard errors of the estimates
z: Depending on the family, either a z or t value
p: p-values for each parameter estimate
scale: Scale parameter (dispersion parameter) of the distribution's variance
scale.fix: Logical indicating whether scale has fixed value
cluster: User-specified cluster size for clustered models
fitted: Fitted values from the model
resid: Normalized Pearson residuals
w.ac: Working autocorrelation parameters
Mat.ac: Working autocorrelation matrix
QIC: Quasi Information Criterion. See qic.calc for further details
QLik: Quasi-likelihood. See qic.calc for further details
plot: Logical value indicating whether autocorrelation should be plotted
moran.params: Parameters for calculating Moran's I
v2: Parameter variance of the GEE model
var.naive: Paramter variance of the independence model
ac.glm: Autocorrelation of GLM residuals
ac.gee: Autocorrelation of GEE residuals

Elements can be viewed using the summary.GEE methods included in the package.

Details

GEE can be used to fit linear models for response variables with different distributions: gaussian, binomial, or poisson. As a spatial model, it is a generalized linear model in which the residuals may be autocorrelated. It accounts for spatial (2-dimensional) autocorrelation of the residuals in cases of regular gridded datasets and returns corrected parameter estimates. The grid cells are assumed to be square. Futhermore, this function requires that all predictor variables be continuous.

References

Carl G & Kuehn I, 2007. Analyzing Spatial Autocorrelation in Species Distributions using Gaussian and Logit Models, Ecol. Model. 207, 159 - 170

Carey, V. J., 2006. Ported to R by Thomas Lumley (versions 3.13, 4.4, version 4.13)., B. R. gee: Generalized Estimation Equation solver. R package version 4.13-11.

Yan, J., 2004. geepack: Generalized Estimating Equation Package. R package version 0.2.10.

Examples

Run this code

# NOT RUN {
data(musdata)
coords<- musdata[,4:5]

# }
# NOT RUN {
mgee<-GEE(musculus ~ pollution + exposure, "poisson", musdata,
      coord=coords, corstr="fixed", plot=TRUE,scale.fix=FALSE,
      customize_plot = scale_color_manual("Custom legend", values = c('blue','red')))

summary(mgee,printAutoCorPars=TRUE)
# }

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