Description Usage Arguments Details Value Author(s) References Examples

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

1 2 3 4 5 6 7 8 9 10 11 12 |

`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 |

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.

`fit ` |
result of the call to |

```
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 |

Jeff Goldsmith <jeff.goldsmith@columbia.edu>

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.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 | ```
## 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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