refund (version 0.1-37)

fgam: Functional Generalized Additive Models

Description

Implements functional generalized additive models for functional and scalar covariates and scalar responses. Additionally implements functional linear models. This function is a wrapper for mgcv's [mgcv]{gam} and its siblings to fit models of the general form $$g(E(Y_i)) = \beta_0 + \int_{T_1} F(X_{i1},t)dt+ \int_{T_2} \beta(t)X_{i2}dt + f(z_{i1}) + f(z_{i2}, z_{i3}) + \ldots$$ with a scalar (but not necessarily continuous) response Y, and link function g

Usage

fgam(formula, fitter = NA, tensortype = c("te", "t2"), ...)

Value

a fitted fgam-object, which is a {gam}-object with some additional information in a fgam-entry. If fitter is "gamm" or "gamm4", only the $gam part of the returned list is modified in this way.

Arguments

formula

a formula with special terms as for gam, with additional special terms {af}(), {lf}(), {re}().

fitter

the name of the function used to estimate the model. Defaults to [mgcv]{gam} if the matrix of functional responses has less than 2e5 data points and to [mgcv]{bam} if not. "gamm" (see [mgcv]{gamm}) and "gamm4" (see [gamm4]{gamm4}) are valid options as well.

tensortype

defaults to [mgcv]{te}, other valid option is [mgcv]{t2}

...

additional arguments that are valid for [mgcv]{gam} or [mgcv]{bam}; for example, specify a gamma > 1 to increase amount of smoothing when using GCV to choose smoothing parameters or method="REML" to change to REML for estimation of smoothing parameters (default is GCV).

Warning

Binomial responses should be specified as a numeric vector rather than as a matrix or a factor.

Author

Mathew W. McLean and Fabian Scheipl

References

McLean, M. W., Hooker, G., Staicu, A.-M., Scheipl, F., and Ruppert, D. (2014). Functional generalized additive models. Journal of Computational and Graphical Statistics, 23 (1), pp. 249-269.

See Also

{af}, {lf}, {predict.fgam}, {vis.fgam}

Examples

data(DTI)
## only consider first visit and cases (no PASAT scores for controls)
y <- DTI$pasat[DTI$visit==1 & DTI$case==1]
X <- DTI$cca[DTI$visit==1 & DTI$case==1, ]
X_2 <- DTI$rcst[DTI$visit==1 & DTI$case==1, ]

## remove samples containing missing data
ind <- rowSums(is.na(X)) > 0
ind2 <- rowSums(is.na(X_2)) > 0

y <- y[!(ind | ind2)]
X <- X[!(ind | ind2), ]
X_2 <- X_2[!(ind | ind2), ]

N <- length(y)

## fit fgam using FA measurements along corpus callosum
## as functional predictor with PASAT as response
## using 8 cubic B-splines for marginal bases with third
## order marginal difference penalties
## specifying gamma > 1 enforces more smoothing when using
## GCV to choose smoothing parameters
#fit <- fgam(y ~ af(X, k = c(8, 8), m = list(c(2, 3), c(2, 3))), gamma = 1.2)


## fgam term for the cca measurements plus an flm term for the rcst measurements
## leave out 10 samples for prediction
test <- sample(N, 10)
#fit <- fgam(y ~ af(X, k = c(7, 7), m = list(c(2, 2), c(2, 2))) +
 #      lf(X_2, k=7, m = c(2, 2)), subset=(1:N)[-test])
#plot(fit)
## predict the ten left outs samples
#pred <- predict(fit, newdata = list(X=X[test, ], X_2 = X_2[test, ]), type='response',
 #               PredOutOfRange = TRUE)
#sqrt(mean((y[test] - pred)^2))
## Try to predict the binary response disease status (case or control)
##   using the quantile transformed measurements from the rcst tract
##   with a smooth component for a scalar covariate that is pure noise
y <- DTI$case[DTI$visit==1]
X <- DTI$cca[DTI$visit==1, ]
X_2 <- DTI$rcst[DTI$visit==1, ]

ind <- rowSums(is.na(X)) > 0
ind2 <- rowSums(is.na(X_2)) > 0

y <- y[!(ind | ind2)]
X <- X[!(ind | ind2), ]
X_2 <- X_2[!(ind | ind2), ]
z1 <- rnorm(length(y))

## select=TRUE allows terms to be zeroed out of model completely
#fit <- fgam(y ~ s(z1, k = 10) + af(X_2, k=c(7,7), m = list(c(2, 1), c(2, 1)),
 #           Qtransform=TRUE), family=binomial(), select=TRUE)
#plot(fit)