WRM: Wavelet-revised models (WRMs)
In spind: Spatial Methods and Indices

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

A wavelet-based method to remove spatial autocorrelation in multiple linear regressions. Wavelet transforms are implemented using waveslim (Whitcher, 2005).

WRM(
  formula,
  family,
  data,
  coord,
  level = 1,
  wavelet = "haar",
  wtrafo = "dwt",
  b.ini = NULL,
  pad = list(),
  control = list(),
  moran.params = list(),
  plot = FALSE,
  customize_plot = NULL
)

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

## S3 method for class 'WRM'
summary(object, ...)

## S3 method for class 'WRM'
predict(object, newdata, sm = FALSE, newcoord = NA, ...)

`formula`	Model formula. Variable names must match variables in `data`.
`family`	`gaussian`, `binomial`, or `poisson` are supported.
`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.
`level`	An integer specifying the degree of wavelet decomposition 0 - Without autocorrelation removal (equivalent to a GLM) 1 - For best autocorrelation removal ... - Higher integers possible. The limit depends on sample size
`wavelet`	Name of wavelet family. `haar`, `d4`, and `la8`. are possible. `haar` is the default.
`wtrafo`	Type of wavelet transform. Either `dwt` or `modwt`. `dwt` is the default.
`b.ini`	Initial parameter values. Default is NULL.
`pad`	A list of parameters for padding wavelet coefficients. padform - 0, 1, and 2 are possible. `padform` is automatically set to 0 when either `level`=0 or a `formula` including an intercept and a non-gaussian family 0 - Padding with 0s. 1 - Padding with mean values. 2 - Padding with mirror values. padzone - Factor for expanding the padding zone
`control`	a list of parameters for controlling the fitting process. `eps` - Positive convergence tolerance. Smaller values of `eps` provide better parameter estimates, but also reduce the probability of the iterations converging. In case of issues with convergence, test larger values of `eps`. Default is 10^-5. `denom.eps` - Default is 10^-20. `itmax` - Integer giving the maximum number of iterations. Default is 200.
`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 Moran's I. Default is 1.
`plot`	A logical value indicating whether to plot autocorrelation of residuals by distance bin. NOW DEPRECATED in favor of `plot.WRM` method.
`customize_plot`	Additional plotting parameters passed to `ggplot`. NOW DEPRECATED in favor of `plot.WRM` method.
`x`	An object of class `GEE` or `WRM`
`...`	Not used
`object`	An object of class `WRM`
`newdata`	A data frame containing variables used to make predictions.
`sm`	Logical. Should part of smooth components be included?
`newcoord`	New coordinates corresponding to observations in `newdata`.

WRM can be used to fit linear models for response vectors of different distributions: gaussian, binomial, or poisson. As a spatial model, it is a generalized linear model in which the residuals may be autocorrelated. It corrects for 2-dimensional residual autocorrelation for regular gridded data sets using the wavelet decomposition technique. The grid cells are assumed to be square. Furthermore, this function requires that all predictor variables be continuous.

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

call: Call
formula: Model formula
family: Family
coord: Coordinates used in the model
b: Estimate of regression parameters
s.e.: Standard errors
z: Depending on the family, either a z or t value
p: p-values
fitted: Fitted values from the model
resid: Pearson residuals
b.sm: Parameter estimates of neglected smooth part
fitted.sm: Fitted values of neglected smooth part
level: Selected level of wavelet decomposition
wavelet: Selected wavelet
wtrafo: Selected wavelet transformation
padzone: Selected padding zone expansion factor
padform: Selected matrix padding type
n.eff: Effective number of observations
AIC: Akaike information criterion
AICc: AIC score corrected for small sample sizes
LogLik: Log likelihood of the model
ac.glm: Autocorrelation of GLM residuals
ac.wrm: Autocorrelation of WRM residuals
b.ini: Initial parameter values
control: Control parameters for the fitting process
moran.params: Parameters for calculating Moran's I
pad: List of parameters for padding wavelet coefficients
plot: An object of class ggplot containing information on the autocorrelation of residuals from the fitted WRM and a GLM

For those interested in multimodel inference approaches, WRM with level = 1 is identical to mmiWMRR with scale = 1.

Gudrun Carl, Sam Levin

Carl, G., Kuehn, I. (2010): A wavelet-based extension of generalized linear models to remove the effect of spatial autocorrelation. Geographical Analysis 42 (3), 323 - 337

Whitcher, B. (2005) Waveslim: basic wavelet routines for one-, two- and three-dimensional signal processing. R package version 1.5.

mmiWMRR, predict.WRM, summary.WRM, aic.calc

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

## Not run: 
mwrm <- WRM(musculus ~ pollution + exposure,
            family = "poisson",
            data = musdata,
            coord = coords,
            level = 1)

pred <- predict(mwrm, newdata = musdata)

summary(mwrm)

plot(mwrm)

library(ggplot2)

my_wrm_plot <- mwrm$plot

# increase axis text size
print(my_wrm_plot + ggplot2::theme(axis.text = element_text(size = 15)))


## End(Not run)