Implements longitudinal penalized functional regression (Goldsmith et al., 2012) for generalized linear functional models with scalar outcomes and subject-specific random intercepts.
lpfr(
Y,
subj,
covariates = NULL,
funcs,
kz = 30,
kb = 30,
smooth.cov = FALSE,
family = "gaussian",
method = "REML",
...
)vector of all outcomes over all visits
vector containing the subject number for each observation
matrix of scalar covariates
matrix or list of matrices containing observed functional predictors as rows. NA values are allowed.
dimension of principal components basis for the observed functional predictors
dimension of the truncated power series spline basis for the coefficient function
logical; do you wish to smooth the covariance matrix of observed functions? Increases computation time, but results in smooth principal components
generalized linear model family
method for estimating the smoothing parameters; defaults to REML
additional arguments passed to gam to fit
the regression model.
result of the call to gam
predicted outcomes
list of estimated coefficient functions
parameter estimates for scalar covariates
vector of subject-specific random intercepts
design matrix used in the model fit
list of truncated power series spline bases for the coefficient functions
list of principal components basis for the functional predictors
list containing covariance matrices for the estimated coefficient functions
list of bounds of a 95% confidence interval for the estimated coefficient functions
Functional predictors are entered as a matrix or, in the case of multiple
functional predictors, as a list of matrices using the funcs
argument. Missing values are allowed in the functional predictors, but it
is assumed that they are observed over the same grid. Functional
coefficients and confidence bounds are returned as lists in the same order
as provided in the funcs argument, as are principal component and
spline bases.
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.
# NOT RUN {
# }
# NOT RUN {
##################################################################
# use longitudinal data to regress continuous outcomes on
# functional predictors (continuous outcomes only recorded for
# case == 1)
##################################################################
data(DTI)
# subset data as needed for this example
cca = DTI$cca[which(DTI$case == 1),]
rcst = DTI$rcst[which(DTI$case == 1),]
DTI = DTI[which(DTI$case == 1),]
# note there is missingness in the functional predictors
apply(is.na(cca), 2, mean)
apply(is.na(rcst), 2, mean)
# fit two models with single functional predictors and plot the results
fit.cca = lpfr(Y=DTI$pasat, subj=DTI$ID, funcs = cca, smooth.cov=FALSE)
fit.rcst = lpfr(Y=DTI$pasat, subj=DTI$ID, funcs = rcst, smooth.cov=FALSE)
par(mfrow = c(1,2))
matplot(cbind(fit.cca$BetaHat[[1]], fit.cca$Bounds[[1]]),
type = 'l', lty = c(1,2,2), col = c(1,2,2), ylab = "BetaHat",
main = "CCA")
matplot(cbind(fit.rcst$BetaHat[[1]], fit.rcst$Bounds[[1]]),
type = 'l', lty = c(1,2,2), col = c(1,2,2), ylab = "BetaHat",
main = "RCST")
# fit a model with two functional predictors and plot the results
fit.cca.rcst = lpfr(Y=DTI$pasat, subj=DTI$ID, funcs = list(cca,rcst),
smooth.cov=FALSE)
par(mfrow = c(1,2))
matplot(cbind(fit.cca.rcst$BetaHat[[1]], fit.cca.rcst$Bounds[[1]]),
type = 'l', lty = c(1,2,2), col = c(1,2,2), ylab = "BetaHat",
main = "CCA")
matplot(cbind(fit.cca.rcst$BetaHat[[2]], fit.cca.rcst$Bounds[[2]]),
type = 'l', lty = c(1,2,2), col = c(1,2,2), ylab = "BetaHat",
main = "RCST")
# }