lpfr: Longitudinal penalized functional regression

In refund: Regression with Functional Data

Longitudinal penalized functional regression

Description

Implements longitudinal penalized functional regression (Goldsmith et al., 2012) for generalized linear functional models with scalar outcomes and subject-specific random intercepts.

Usage

lpfr(
  Y,
  subj,
  covariates = NULL,
  funcs,
  kz = 30,
  kb = 30,
  smooth.cov = FALSE,
  family = "gaussian",
  method = "REML",
  ...
)

Arguments

Y	vector of all outcomes over all visits
subj	vector containing the subject number for each observation
covariates	matrix of scalar covariates
funcs	matrix or list of matrices containing observed functional predictors as rows. NA values are allowed.
kz	dimension of principal components basis for the observed functional predictors
kb	dimension of the truncated power series spline basis for the coefficient function
smooth.cov	logical; do you wish to smooth the covariance matrix of observed functions? Increases computation time, but results in smooth principal components
family	generalized linear model family
method	method for estimating the smoothing parameters; defaults to REML
...	additional arguments passed to gam to fit the regression model.

Details

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.

Value

fit	result of the call to gam
fitted.vals	predicted outcomes
betaHat	list of estimated coefficient functions
beta.covariates	parameter estimates for scalar covariates
ranef	vector of subject-specific random intercepts
X	design matrix used in the model fit
phi	list of truncated power series spline bases for the coefficient functions
psi	list of principal components basis for the functional predictors
varBetaHat	list containing covariance matrices for the estimated coefficient functions
Bounds	list of bounds of a 95% confidence interval for the estimated coefficient functions

Author(s)

Jeff Goldsmith <[e-mail]>

References

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.

Examples

## 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")

## End(Not run)

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