addvar
Added Variable Plot for Point Process Model
Computes the coordinates for an Added Variable Plot for a fitted point process model.
Usage
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)
Arguments
- model
- Fitted point process model (object of class
"ppm"
). - covariate
- The covariate to be added to the model. Either a
pixel image, a
function(x,y)
, or a character string giving the name of a covariate that was supplied when the model was fitted. - subregion
- Optional. A window (object of class
"owin"
) specifying a subset of the spatial domain of the data. The calculation will be confined to the data in this subregion. - bw
- Smoothing bandwidth or bandwidth rule
(passed to
density.default
). - adjust
- Smoothing bandwidth adjustment factor
(passed to
density.default
). - n, from, to
- Arguments passed to
density.default
to control the number and range of values at which the function will be estimated. - ...
- Additional arguments passed to
density.default
. - 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
subregion
. - 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.
Details
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
.
Value
- An object of class
"addvar"
containing the coordinates for the added variable plot. There is aplot
method.
Internal data
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.
References
Baddeley, A. and Chang, Y.-M. and Song, Y. and Turner, R. (2012) Residual diagnostics for covariate effects in spatial point process models. Submitted for publication. 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.
See Also
Examples
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))