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",
...
)
```

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.

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") # }