GEE: GEE (Generalized Estimating Equations)
In spind: Spatial Methods and Indices

Description Usage Arguments Details Value Note Author(s) References See Also Examples

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

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

## S3 method for class 'GEE'
plot(x, ...)

## S3 method for class 'GEE'
predict(object, newdata, ...)

## S3 method for class 'GEE'
summary(object, ..., printAutoCorPars = TRUE)

`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 22 cluster 3 - a 33 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. NOW DEPRECATED in favor of `plot.GEE` method.
`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`. NOW DEPRECATED in favor `plot.GEE` method.
`x`	An object of class `GEE` or `WRM`
`...`	Not used.
`object`	An object of class `GEE`.
`newdata`	A data frame containing variables to base the predictions on.
`printAutoCorPars`	A logical indicating whether to print the working autocorrelation parameters

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. Furthermore, this function requires that all predictor variables be continuous.

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: Parameter variance of the independence model
ac.glm: Autocorrelation of GLM residuals
ac.gee: Autocorrelation of GEE residuals
plot: An object of class ggplot containing information on the autocorrelation of residuals from the fitted GEE and a GLM

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

When using corstr = "fixed" on large data sets, the function may return an error, as the resulting variance-covariance matrix is too large for R to handle. If this happens, one will have to use one of the cluster models (i.e quadratic, exchangeable).

Gudrun Carl, Sam Levin

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.

qic.calc, summary.GEE, gee

data(musdata)
coords<- musdata[,4:5]

## Not run: 
mgee <- GEE(musculus ~ pollution + exposure,
            family = "poisson",
            data =  musdata,
            coord = coords,
            corstr = "fixed",
            scale.fix = FALSE)

summary(mgee, printAutoCorPars = TRUE)

pred <- predict(mgee, newdata = musdata)

library(ggplot2)

plot(mgee)

my_gee_plot <- mgee$plot

# move the legend to a new position
print(my_gee_plot + ggplot2::theme(legend.position = 'top'))


## End(Not run)

 Call: 
GEE(formula = musculus ~ pollution + exposure, family = "poisson", 
    data = musdata, coord = coords, corstr = "fixed", scale.fix = FALSE)
--- 
 Coefficients: 
            Estimate  Std.Err z value  Pr(>|z|)    
(Intercept) -1.90475  1.31091 -1.4530 0.1462252    
pollution    3.36216  0.91416  3.6779 0.0002352 ***
exposure    -1.46348  0.88010 -1.6629 0.0963410 .  
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
--- 
 QIC:  1139.159 
--- 
Autocorrelation of GLM residuals 
 [1]  0.685338504  0.509680590  0.363021118  0.247398654  0.144726020
 [6]  0.084220961  0.050228656  0.022369044 -0.001985639 -0.027296083

 Autocorrelation of GEE residuals 
 [1] -0.001277974 -0.004261554  0.045280260  0.022738750  0.005821352
 [6]  0.004289166  0.008311357  0.003437398  0.001030847 -0.010359040
--- 
 Autocorrelation parameters from  fixed  model 
[1] "a=alpha^(d^v)  , alpha=0.685 , v=1.093"