# 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 a `plot`

method.

##### Slow computation

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`

.

##### 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., 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.

##### See Also

##### Examples

```
# NOT RUN {
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))
# }
```

*Documentation reproduced from package spatstat, version 1.63-0, License: GPL (>= 2)*