makessp: Makes Objects to Fit Smoothing Splines with Parametric...
In bigsplines: Smoothing Splines for Large Samples

Description Usage Arguments Details Value Warning Author(s) References Examples

This function creates a list containing the necessary information to fit a smoothing spline with parametric effects (see bigssp).

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

`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. Use `type="prm"` for parametric effect.
`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).
`thetas`	List of initial smoothing parameters for each predictor subspace. 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`.

See bigssp and below example for more details.

An object of class "makessp", which can be input to bigssp.

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

Nathaniel E. Helwig <helwig@umn.edu>

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.

##########   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 <- bigssp(y~x1v*x2v,type=list(x1v="cub",x2v="cub"),nknots=50)
  addmod <- bigssp(y~x1v+x2v,type=list(x1v="cub",x2v="cub"),nknots=50)
})

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

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