Description Usage Arguments Details Value NOTE Author(s) References See Also Examples

Constructs a functional principal component regression (Reiss and Ogden,
2007, 2010) term for inclusion in an `mgcv::gam`

-formula (or
`bam`

or `gamm`

or `gamm4:::gamm`

) as
constructed by `pfr`

. Currently only one-dimensional functions
are allowed.

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

`X` |
functional predictors, typically expressed as an |

`argvals` |
indices of evaluation of |

`method` |
the method used for finding principal components. The default
is an unconstrained SVD of the |

`ncomp` |
number of principal components. if |

`pve` |
proportion of variance explained; used to choose the number of principal components |

`penalize` |
if |

`bs` |
two letter character string indicating the |

`k` |
the dimension of the pre-smoothing basis |

`...` |
additional options to be passed to |

`fpc`

is a wrapper for `lf`

, which defines linear
functional predictors for any type of basis for inclusion in a `pfr`

formula. `fpc`

simply calls `lf`

with the appropriate options for
the `fpc`

basis and penalty construction.

This function implements both the FPCR-R and FPCR-C methods of Reiss and Ogden (2007). Both methods consist of the following steps:

project

*X*onto a spline basis*B*perform a principal components decomposition of

*XB*use those PC's as the basis in fitting a (generalized) functional linear model

This implementation provides options for each of these steps. The basis
for in step 1 can be specified using the arguments `bs`

and `k`

,
as well as other options via `...`

; see `s`

for
these options. The type of PC-decomposition is specified with `method`

.
And the FLM can be fit either penalized or unpenalized via `penalize`

.

The default is FPCR-R, which uses a b-spline basis, an unconstrained
principal components decomposition using `svd`

, and the FLM
fit with a second-order difference penalty. FPCR-C can be selected by
using a different option for `method`

, indicating a constrained
("functional") PC decomposition, and by default an unpenalized fit of the
FLM.

FPCR-R is also implemented in `fpcr`

; here we implement the
method for inclusion in a `pfr`

formula.

The result of a call to `lf`

.

Unlike `fpcr`

, `fpc`

within a `pfr`

formula does
not automatically decorrelate the functional predictors from additional
scalar covariates.

Jonathan Gellar JGellar@mathematica-mpr.com, Phil Reiss phil.reiss@nyumc.org, Lan Huo lan.huo@nyumc.org, and Lei Huang huangracer@gmail.com

Reiss, P. T. (2006). Regression with signals and images as predictors. Ph.D. dissertation, Department of Biostatistics, Columbia University. Available at http://works.bepress.com/phil_reiss/11/.

Reiss, P. T., and Ogden, R. T. (2007). Functional principal component
regression and functional partial least squares. *Journal of the
American Statistical Association*, 102, 984-996.

Reiss, P. T., and Ogden, R. T. (2010). Functional generalized linear models
with images as predictors. *Biometrics*, 66, 61-69.

`lf`

, `smooth.construct.fpc.smooth.spec`

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 | ```
data(gasoline)
par(mfrow=c(3,1))
# Fit PFCR_R
gasmod1 <- pfr(octane ~ fpc(NIR, ncomp=30), data=gasoline)
plot(gasmod1, rug=FALSE)
est1 <- coef(gasmod1)
# Fit FPCR_C with fpca.sc
gasmod2 <- pfr(octane ~ fpc(NIR, method="fpca.sc", ncomp=6), data=gasoline)
plot(gasmod2, se=FALSE)
est2 <- coef(gasmod2)
# Fit penalized model with fpca.face
gasmod3 <- pfr(octane ~ fpc(NIR, method="fpca.face", penalize=TRUE), data=gasoline)
plot(gasmod3, rug=FALSE)
est3 <- coef(gasmod3)
par(mfrow=c(1,1))
ylm <- range(est1$value)*1.35
plot(value ~ X.argvals, type="l", data=est1, ylim=ylm)
lines(value ~ X.argvals, col=2, data=est2)
lines(value ~ X.argvals, col=3, data=est3)
``` |

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