refund: lf – R documentation

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lf

Construct an FLM regression term

Description

Defines a term \int_{T}β(t)X_i(t)dt for inclusion in an mgcv::gam-formula (or bam or gamm or gamm4:::gamm) as constructed by pfr, where β(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 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 `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 `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 mathew.w.mclean@gmail.com, 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.

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

Regression with Functional Data

v0.1-23

GPL (>= 2)

Authors

Jeff Goldsmith [aut], Fabian Scheipl [aut], Lei Huang [aut], Julia Wrobel [aut, cre], Chongzhi Di [aut], Jonathan Gellar [aut], Jaroslaw Harezlak [aut], Mathew W. McLean [aut], Bruce Swihart [aut], Luo Xiao [aut], Ciprian Crainiceanu [aut], Philip T. Reiss [aut], Yakuan Chen [ctb], Sonja Greven [ctb], Lan Huo [ctb], Madan Gopal Kundu [ctb], So Young Park [ctb], David L. Miller [ctb], Ana-Maria Staicu [ctb]

Initial release

2020-12-03

lf