scaleWMRR: Scaling by wavelet multiresolution regression (WMRR)
In spind: Spatial Methods and Indices

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

scaleWMRR performs a scale-specific regression based on a wavelet multiresolution analysis.

scaleWMRR(
  formula,
  family,
  data,
  coord,
  scale = 1,
  detail = TRUE,
  wavelet = "haar",
  wtrafo = "dwt",
  b.ini = NULL,
  pad = list(),
  control = list(),
  moran.params = list(),
  trace = FALSE
)

`formula`	With specified notation according to names in data frame.
`family`	`gaussian`, `binomial`, or `poisson`.
`data`	Data frame.
`coord`	Corresponding coordinates which have to be integer.
`scale`	0 (which is equivalent to GLM) or higher integers possible (limit depends on sample size).
`detail`	Remove smooth wavelets? If `TRUE`, only detail components are analyzed. If set to `FALSE`, smooth and detail components are analyzed. Default is `TRUE`.
`wavelet`	Type of wavelet: `haar` or `d4` or `la8`
`wtrafo`	Type of wavelet transform: `dwt` or `modwt`.
`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 the `formula` includes an intercept and has 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.
`trace`	A logical value indicating whether to print parameter estimates to the console

This function fits generalized linear models while taking the two-dimensional grid structure of datasets into account. The following error distributions (in conjunction with appropriate link functions) are allowed: gaussian, binomial, or poisson. The model provides scale-specific results for data sampled on a contiguous geographical area. The dataset is assumed to be regular gridded and the grid cells are assumed to be square. A function from the package 'waveslim' is used for the wavelet transformations (Whitcher, 2005). Furthermore, this function requires that all predictor variables be continuous.

scaleWMRR returns a list containing the following elements

call: Model call
b: Estimates of regression parameters
s.e.: Standard errors of the parameter estimates
z: Z values (or corresponding values for statistics)
p: p-values for each parameter estimate
df: Degrees of freedom
fitted: Fitted values
resid: Pearson residuals
converged: Logical value whether the procedure converged
trace: Logical. If TRUE:

ac.glm Autocorrelation of glm.residuals
ac Autocorrelation of wavelet.residuals

Gudrun Carl

Carl G, Doktor D, Schweiger O, Kuehn I (2016) Assessing relative variable importance across different spatial scales: a two-dimensional wavelet analysis. Journal of Biogeography 43: 2502-2512.

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

waveslim,mra.2d

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

## Not run: 

# scaleWMRR at scale = 0 is equivalent to GLM

ms0 <- scaleWMRR(carlina.horrida ~ aridity + land.use,
                 family = "poisson",
                 data = carlinadata,
                 coord = coords,
                 scale = 0,
                 trace = TRUE)

# scale-specific regressions for detail components
ms1 <- scaleWMRR(carlina.horrida ~ aridity + land.use,
                 family = "poisson",
                 data = carlinadata,
                 coord = coords,
                 scale = 1,
                 trace = TRUE)

ms2 <- scaleWMRR(carlina.horrida ~ aridity + land.use,
                 family = "poisson",
                 data = carlinadata,
                 coord = coords,
                 scale = 2,
                 trace = TRUE)

ms3<- scaleWMRR(carlina.horrida ~ aridity + land.use,
                 family = "poisson",
                 data = carlinadata,
                 coord = coords,
                 scale = 3,
                 trace = TRUE)


## End(Not run)