vis.pfr: Visualization of PFR objects

Description

Produces perspective or contour plot views of an estimated surface corresponding smooths over two or more dimensions. Alternatively plots slices of the estimated surface or estimated second derivative surface with one of its arguments fixed. Corresponding twice-standard error Bayesian confidence bands are constructed using the method in Marra and Wood (2012). See the details.

Usage

vis.pfr(object, select = 1, xval = NULL, tval = NULL, deriv2 = FALSE,
  theta = 50, plot.type = "persp", ticktype = "detailed", ...)

Arguments

object

an pfr object, produced by pfr

select

index for the smooth term to be plotted, according to its position in the model formula (and in object$smooth). Not needed if only one multivariate term is present.

xval

a number in the range of functional predictor to be plotted. The surface will be plotted with the first argument of the estimated surface fixed at this value

tval

a number in the domain of the functional predictor to be plotted. The surface will be plotted with the second argument of the estimated surface fixed at this value. Ignored if xval is specified.

deriv2

logical; if TRUE, plot the estimated second derivative surface along with Bayesian confidence bands. Only implemented for the "slices" plot from either xval or tval being specified

theta

numeric; viewing angle; see persp

plot.type

one of "contour" (to use levelplot) or "persp" (to use persp). Ignored if either xval or tval is specif

ticktype

how to draw the tick marks if plot.type="persp". Defaults to "detailed"

...

other options to be passed to persp, levelplot, or plot

Value

Simply produces a plot

Details

The confidence bands used when plotting slices of the estimated surface or second derivative surface are the ones proposed in Marra and Wood (2012). These are a generalization of the "Bayesian" intevals of Wahba (1983) with an adjustment for the uncertainty about the model intercept. The estimated covariance matrix of the model parameters is obtained from assuming a particular Bayesian model on the parameters.

References

McLean, M. W., Hooker, G., Staicu, A.-M., Scheipl, F., and Ruppert, D. (2014). Functional generalized additive models. Journal of Computational and Graphical Statistics, 23(1), pp. 249-269. Available at http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3982924. Marra, G., and Wood, S. N. (2012) Coverage properties of confidence intervals for generalized additive model components. Scandinavian Journal of Statistics, 39(1), pp. 53--74. Wabha, G. (1983) "Confidence intervals" for the cross-validated smoothing spline. Journal of the Royal Statistical Society, Series B, 45(1), pp. 133--150.

Examples

Run this code

################# DTI Example #####################
data(DTI)

## only consider first visit and cases (since no PASAT scores for controls),
## and remove missing data
DTI <- DTI[DTI$visit==1 & DTI$case==1 & complete.cases(DTI$cca),]

## Fit the PFR using FA measurements along corpus
## callosum as functional predictor with PASAT as response
## using 8 cubic B-splines for each marginal bases with
## third order marginal difference penalties.
## Specifying gamma>1 enforces more smoothing when using GCV
## to choose smoothing parameters
fit <- pfr(pasat ~ af(cca, basistype="te", k=c(8,8), m=list(c(2,3),c(2,3)), bs="ps"),
           method="GCV.Cp", gamma=1.2, data=DTI)

## contour plot of the fitted surface
vis.pfr(fit, plot.type='contour')

## similar to Figure 5 from McLean et al.
## Bands seem too conservative in some cases
xval <- runif(1, min(fit$pfr$ft[[1]]$Xrange), max(fit$pfr$ft[[1]]$Xrange))
tval <- runif(1, min(fit$pfr$ft[[1]]$xind), max(fit$pfr$ft[[1]]$xind))
par(mfrow=c(2, 2))
vis.pfr(fit, deriv2=FALSE, xval=xval)
vis.pfr(fit, deriv2=FALSE, tval=tval)
vis.pfr(fit, deriv2=TRUE, xval=xval)
vis.pfr(fit, deriv2=TRUE, tval=tval)

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