# 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.

##### 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))
```

*Documentation reproduced from package spatstat, version 1.31-2, License: GPL (>= 2)*