refund (version 0.1-1)

predict.pfr: Prediction for penalized functional regression

Description

Given a pfr object and new data, produces fitted values on both a population and subject-specific scale.

Usage

## S3 method for class 'pfr':
predict(object, new.data=NULL, levels=NULL, ...)

Arguments

object

an object returned by pfr.

new.data

the covariate and functional predictor values for which predicted values are desired.

levels

currently not supported; both population- and subject-level fitted values are returned.

...

additional arguments.

Value

• A list with components
• fitted.vals.level.0
  predicted outcomes at population level
• fitted.vals.level.1
  predicted outcomes at subject-specific level (if applicable)

Details

Predicting for new data in a penalized functional regression setting takes care. Utilizing fpca.sc in both pfr and predict.pfr allows for the correct estimation of new scores using the original fit's basis functions. In the spirit of predict.lme, we can estimate for population and (if the subjects are in both the original and new data) subject-specific levels.

References

Goldsmith, J., Bobb, J., Crainiceanu, C., Caffo, B., and Reich, D. (2011). Penalized functional regression. Journal of Computational and Graphical Statistics, 20(4), 830-851. Goldsmith, J., Crainiceanu, C., Caffo, B., and Reich, D. (2012). Longitudinal penalized functional regression for cognitive outcomes on neuronal tract measurements. Journal of the Royal Statistical Society: Series C, 61(3), 453--469. Swihart, B. J., Goldsmith, J., and Crainiceanu, C. M. (2012). Testing for functional effects. Johns Hopkins University Dept. of Biostatistics Working Paper 247, available at http://biostats.bepress.com/jhubiostat/paper247

See Also

pfr, rlrt.pfr, predict.lme

Examples

##################################################################
#########               DTI Data Example                 #########
##################################################################


## load and reassign the data;
data(DTI2)
Y  <- DTI2$pasat ## PASAT outcome
id <- DTI2$id    ## subject id
W1 <- DTI2$cca   ## Corpus Callosum
W2 <- DTI2$rcst  ## Right corticospinal
V  <- DTI2$visit ## visit

## prep scalar covariate
visit.1.rest <- matrix(as.numeric(V > 1), ncol=1)
covar.in <- visit.1.rest 

## kz -- put it too high and the computation time bogs down.
pfr.obj <- pfr(Y = Y, covariates=covar.in, funcs = list(W1), subj = id, kz = 10, kb = 50)
## first column is not using random effects; second column is
head(cbind(pfr.obj$fitted.vals.level.0, pfr.obj$fitted.vals.level.1))

## do some predictions with predict.pfr()
## run predict.pfr() on all rows of data -- hope for same results as pfr fit above.
same.inputs <- predict.pfr(pfr.obj, new.data = list(subj=id, covariates=covar.in, funcs=list(W1)))
head(cbind(same.inputs[[1]], same.inputs[[2]]))
## run predict.pfr() on first 300 rows of data
subset.inputs <- predict.pfr(pfr.obj,
                             new.data = list(subj=head(id,300),
                                             covariates=head(covar.in,300),
                                             funcs=list(W1[1:300,])))
head(cbind(subset.inputs[[1]], subset.inputs[[2]]))
## compare the first 300 vs. the original full data
plot(subset.inputs[[1]], same.inputs[[1]][1:300]); abline(a=0,b=1,col="blue")
summary(subset.inputs[[1]] - same.inputs[[1]][1:300])

## try one where we have different subjects for predictions
## ids 7:12 are new
## and we just double-down the covariates and funcs from the first 6 to the second.
## check level.1 and level.0 predictions
subset.inputs <- predict.pfr(pfr.obj,
                             new.data = list(subj=c(head(id,6), 7:12),
                                             covariates=rbind(head(covar.in,6),head(covar.in,6)),
                                             funcs=list(rbind(W1[1:6,],W1[1:6,]))))
## first 6 have both levels; the last 6 do not have subject-specific
head(cbind(subset.inputs[[1]], subset.inputs[[2]]),12)

## see that whether predicted on subset or full data, the predicted
## values are the same for individuals regardless of who is in
## prediction set
## compare the first 6 vs. the original full data: 6 on the 45 degree line and 6 off.
plot(subset.inputs[[1]], same.inputs[[1]][1:12]); abline(a=0,b=1,col="blue")
summary(subset.inputs[[1]] - same.inputs[[1]][1:12])