Added Variable Plot for Point Process Model
Computes the coordinates for an Added Variable Plot for a fitted point process model.
addvar(model, covariate, ...,
subregion=NULL,
bw="nrd0", adjust=1,
from=NULL, to=NULL, n=512,
bw.input = c("points", "quad"),
bw.restrict = FALSE,
covname, crosscheck=FALSE)model |
Fitted point process model (object of class |
covariate |
The covariate to be added to the model. Either a
pixel image, a |
subregion |
Optional. A window (object of class |
bw |
Smoothing bandwidth or bandwidth rule
(passed to |
adjust |
Smoothing bandwidth adjustment factor
(passed to |
n, from, to |
Arguments passed to |
... |
Additional arguments passed to |
bw.input |
Character string specifying the input data used for automatic bandwidth selection. |
bw.restrict |
Logical value, specifying whether bandwidth selection is performed using
data from the entire spatial domain or from the |
covname |
Optional. Character string to use as the name of the covariate. |
crosscheck |
For developers only. Logical value indicating whether to perform cross-checks on the validity of the calculation. |
This command generates the plot coordinates for an Added Variable Plot for a spatial point process model.
Added Variable Plots (Cox, 1958, sec 4.5; Wang, 1985) are commonly used in linear models and generalized linear models, to decide whether a model with response y and predictors x would be improved by including another predictor z.
In a (generalised) linear model with response y and predictors x, the Added Variable Plot for a new covariate z is a plot of the smoothed Pearson residuals from the original model against the scaled residuals from a weighted linear regression of z on x. If this plot has nonzero slope, then the new covariate z is needed. For general advice see Cook and Weisberg(1999); Harrell (2001).
Essentially the same technique can be used for a spatial point process model (Baddeley et al, 2012).
The argument model should be a fitted spatial point process
model (object of class "ppm").
The argument covariate
identifies the covariate that is to be considered for addition to
the model. It should be either a pixel image (object of class
"im") or a function(x,y) giving the values of the
covariate at any spatial location. Alternatively covariate
may be a character string, giving the name of a covariate that was
supplied (in the covariates argument to ppm)
when the model was fitted, but was not used in the model.
The result of addvar(model, covariate) is an object belonging
to the classes "addvar" and "fv". Plot this object to
generate the added variable plot.
Note that the plot method shows the pointwise significance bands for a test of the null model, i.e. the null hypothesis that the new covariate has no effect.
The smoothing bandwidth is controlled by the arguments
bw, adjust, bw.input and bw.restrict.
If bw is a numeric value, then
the bandwidth is taken to be adjust * bw.
If bw is a string representing a bandwidth selection rule
(recognised by density.default)
then the bandwidth is selected by this rule.
The data used for automatic bandwidth selection are
specified by bw.input and bw.restrict.
If bw.input="points" (the default) then bandwidth selection is
based on the covariate values at the points of the original point
pattern dataset to which the model was fitted.
If bw.input="quad" then bandwidth selection is
based on the covariate values at every quadrature point used to
fit the model.
If bw.restrict=TRUE then the bandwidth selection is performed
using only data from inside the subregion.
An object of class "addvar" containing the coordinates
for the added variable plot. There is a plot method.
In a large dataset, computation can be very slow if the default
settings are used, because the smoothing bandwidth is selected
automatically. To avoid this, specify a numerical value
for the bandwidth bw. One strategy is to use a coarser
subset of the data to select bw automatically.
The selected bandwidth can be read off the print output for
addvar.
The return value has an attribute "spatial" which contains
the internal data: the computed values of the residuals,
and of all relevant covariates,
at each quadrature point of the model. It is an object of class
"ppp" with a data frame of marks.
Adrian Baddeley Adrian.Baddeley@curtin.edu.au, Rolf Turner r.turner@auckland.ac.nz, Ya-Mei Chang and Yong Song.
Baddeley, A., Chang, Y.-M., Song, Y. and Turner, R. (2013) Residual diagnostics for covariate effects in spatial point process models. Journal of Computational and Graphical Statistics, 22, 886–905.
Cook, R.D. and Weisberg, S. (1999) Applied regression, including computing and graphics. New York: Wiley.
Cox, D.R. (1958) Planning of Experiments. New York: Wiley.
Harrell, F. (2001) Regression Modeling Strategies. New York: Springer.
Wang, P. (1985) Adding a variable in generalized linear models. Technometrics 27, 273–276.
X <- rpoispp(function(x,y){exp(3+3*x)})
model <- ppm(X, ~y)
adv <- addvar(model, "x")
plot(adv)
adv <- addvar(model, "x", subregion=square(0.5))Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.