lf: Construct an FLM regression term

In refund: Regression with Functional Data

Construct an FLM regression term

Description

Defines a term \int_{T}\beta(t)X_i(t)dt for inclusion in an mgcv::gam-formula (or {bam} or {gamm} or gamm4:::gamm) as constructed by {pfr}, where \beta(t) is an unknown coefficient function and X_i(t) is a functional predictor on the closed interval T. See {smooth.terms} for a list of basis and penalty options; the default is thin-plate regression splines, as this is the default option for [mgcv]{s}.

Usage

lf(
  X,
  argvals = NULL,
  xind = NULL,
  integration = c("simpson", "trapezoidal", "riemann"),
  L = NULL,
  presmooth = NULL,
  presmooth.opts = NULL,
  ...
)

Arguments

X	functional predictors, typically expressed as an N by J matrix, where N is the number of columns and J is the number of evaluation points. May include missing/sparse functions, which are indicated by NA values. Alternatively, can be an object of class "fd"; see [fda]{fd}.
argvals	indices of evaluation of X, i.e. (t_{i1},.,t_{iJ}) for subject i. May be entered as either a length-J vector, or as an N by J matrix. Indices may be unequally spaced. Entering as a matrix allows for different observations times for each subject. If NULL, defaults to an equally-spaced grid between 0 or 1 (or within X$basis$rangeval if X is a fd object.)
xind	same as argvals. It will not be supported in the next version of refund.
integration	method used for numerical integration. Defaults to "simpson"'s rule for calculating entries in L. Alternatively and for non-equidistant grids, "trapezoidal" or "riemann".
L	an optional N by ncol(argvals) matrix giving the weights for the numerical integration over t. If present, overrides integration.
presmooth	string indicating the method to be used for preprocessing functional predictor prior to fitting. Options are fpca.sc, fpca.face, fpca.ssvd, fpca.bspline, and fpca.interpolate. Defaults to NULL indicating no preprocessing. See {create.prep.func}.
presmooth.opts	list including options passed to preprocessing method {create.prep.func}.
...	optional arguments for basis and penalization to be passed to mgcv::s. These could include, for example, "bs", "k", "m", etc. See [mgcv]{s} for details.

Value

a list with the following entries

call	a call to te (or s, t2) using the appropriately constructed covariate and weight matrices
argvals	the argvals argument supplied to lf
L	the matrix of weights used for the integration
xindname	the name used for the functional predictor variable in the formula used by mgcv
tindname	the name used for argvals variable in the formula used by mgcv
LXname	the name used for the L variable in the formula used by mgcv
presmooth	the presmooth argument supplied to lf
prep.func	a function that preprocesses data based on the preprocessing method specified in presmooth. See {create.prep.func}

Author(s)

Mathew W. McLean [e-mail], Fabian Scheipl, and Jonathan Gellar

References

Goldsmith, J., Bobb, J., Crainiceanu, C., Caffo, B., and Reich, D. (2011). Penalized functional regression. Journal of Computational and Graphical Statistics, 20(4), 830-851.

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.

See Also

{pfr}, {af}, mgcv's {smooth.terms} and {linear.functional.terms}; {pfr} for additional examples

Examples

data(DTI)
DTI1 <- DTI[DTI$visit==1 & complete.cases(DTI),]

# We can apply various preprocessing options to the DTI data
fit1 <- pfr(pasat ~ lf(cca, k=30), data=DTI1)
fit2 <- pfr(pasat ~ lf(cca, k=30, presmooth="fpca.sc",
                       presmooth.opts=list(nbasis=8, pve=.975)), data=DTI1)
fit3 <- pfr(pasat ~ lf(cca, k=30, presmooth="fpca.face",
                       presmooth.opts=list(m=3, npc=9)), data=DTI1)
fit4 <- pfr(pasat ~ lf(cca, k=30, presmooth="fpca.ssvd"), data=DTI1)
fit5 <- pfr(pasat ~ lf(cca, k=30, presmooth="bspline",
                       presmooth.opts=list(nbasis=8)), data=DTI1)
fit6 <- pfr(pasat ~ lf(cca, k=30, presmooth="interpolate"), data=DTI1)

# All models should result in similar fits
fits <- as.data.frame(lapply(1:6, function(i)
  get(paste0("fit",i))$fitted.values))
names(fits) <- c("none", "fpca.sc", "fpca.face", "fpca.ssvd", "bspline", "interpolate")
pairs(fits)

refund documentation built on Sept. 21, 2024, 1:07 a.m.