makessa {bigsplines}

Makes Objects to Fit Smoothing Spline ANOVA Models

Description

This function creates a list containing the necessary information to fit a smoothing spline anova model (see bigssa).

Usage

makessa(formula,data=NULL,type=NULL,nknots=NULL,rparm=NA,
        lambdas=NULL,skip.iter=TRUE,se.fit=FALSE,rseed=1234,
        gcvopts=NULL,knotcheck=TRUE,gammas=NULL,weights=NULL,
        random=NULL,remlalg=c("FS","NR","EM","none"),remliter=500,
       remltol=10^-4,remltau=NULL)

Arguments

formula

An object of class "formula": a symbolic description of the model to be fitted (see Details and Examples for more information).

data

Optional data frame, list, or environment containing the variables in formula.

type

List of smoothing spline types for predictors in formula (see Details). Options include type="cub" for cubic, type="acub" for another cubic, type="per" for cubic periodic, type="tps" for cubic thin-plate, and type="nom" for nominal.

nknots

Two possible options: (a) scalar giving total number of random knots to sample, or (b) vector indexing which rows of data to use as knots.

rparm

List of rounding parameters for each predictor. See Details.

lambdas

Vector of global smoothing parameters to try. Default uses lambdas=10^-c(9:0)

skip.iter

Logical indicating whether to skip the iterative smoothing parameter update. Using skip.iter=FALSE should provide a more optimal solution, but the fitting time may be substantially longer. See Computational Details.

se.fit

Logical indicating if the standard errors of the fitted values should be estimated.

rseed

Random seed for knot sampling. Input is ignored if nknots is an input vector of knot indices. Set rseed=NULL to obtain a different knot sample each time, or set rseed to any positive integer to use a different seed than the default.

gcvopts

Control parameters for optimization. List with 3 elements: (a) maxit: maximum number of algorithm iterations, (b) gcvtol: covergence tolerance for iterative GCV update, and (c) alpha: tuning parameter for GCV minimization. Default: gcvopts=list(maxit=5,gcvtol=10^-5,alpha=1)

knotcheck

If TRUE, only unique knots are used (for stability).

gammas

List of initial smoothing parameters for each predictor. See Details.

weights

Vector of positive weights for fitting (default is vector of ones).

random

Adds random effects to model (see Random Effects section).

remlalg

REML algorithm for estimating variance components (see Random Effects section). Input is ignored if is.null(random).

remliter

Maximum number of iterations for REML estimation of variance components. Input is ignored if random=NULL.

remltol

Convergence tolerance for REML estimation of variance components. Input is ignored if random=NULL.

remltau

Initial estimate of variance parameters for REML estimation of variance components. Input is ignored if random=NULL.

Details

See bigssa and below example for more details.

Value

An object of class "makessa", which can be input to bigssa.

Warning

When inputting a "makessa" class object into bigssa, the formula input to bigssa must be a nested version of the original formula input to makessa. In other words, you cannot add any new effects after a "makessa" object has been created, but you can drop (remove) effects from the model.

Author(s)

Nathaniel E. Helwig <[e-mail]>

References

Gu, C. (2013). Smoothing spline ANOVA models, 2nd edition. New York: Springer.

Helwig, N. E. (2013). Fast and stable smoothing spline analysis of variance models for large samples with applications to electroencephalography data analysis. Unpublished doctoral dissertation. University of Illinois at Urbana-Champaign.

Helwig, N. E. (2016). Efficient estimation of variance components in nonparametric mixed-effects models with large samples. Statistics and Computing, 26, 1319-1336.

Helwig, N. E. (2017). Regression with ordered predictors via ordinal smoothing splines. Frontiers in Applied Mathematics and Statistics, 3(15), 1-13.

Helwig, N. E. and Ma, P. (2015). Fast and stable multiple smoothing parameter selection in smoothing spline analysis of variance models with large samples. Journal of Computational and Graphical Statistics, 24, 715-732.

Helwig, N. E. and Ma, P. (2016). Smoothing spline ANOVA for super-large samples: Scalable computation via rounding parameters. Statistics and Its Interface, 9, 433-444.

Examples

##########   EXAMPLE  ##########

# function with two continuous predictors
set.seed(773)
myfun <- function(x1v,x2v){
  sin(2*pi*x1v) + log(x2v+.1) + cos(pi*(x1v-x2v))
}
x1v <- runif(500)
x2v <- runif(500)
y <- myfun(x1v,x2v) + rnorm(500)

# fit 2 possible models (create information 2 separate times)
system.time({
  intmod <- bigssa(y~x1v*x2v,type=list(x1v="cub",x2v="cub"),nknots=50)
  addmod <- bigssa(y~x1v+x2v,type=list(x1v="cub",x2v="cub"),nknots=50)
})

# fit 2 possible models (create information 1 time)
system.time({
  makemod <- makessa(y~x1v*x2v,type=list(x1v="cub",x2v="cub"),nknots=50)
  int2mod <- bigssa(y~x1v*x2v,makemod)
  add2mod <- bigssa(y~x1v+x2v,makemod)
})

# check difference (no difference)
crossprod( intmod$fitted.values - int2mod$fitted.values )
crossprod( addmod$fitted.values - add2mod$fitted.values )