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)

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.

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

parres, rhohat, rho2hat.

Aliases

• addvar

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))