gamsel: Fit Regularization Path for Gaussian or Binomial Generalized...
In gamsel: Fit Regularization Path for Generalized Additive Models

Description Usage Arguments Details Value Author(s) References See Also Examples

Using overlap grouped lasso penalties, gamsel selects whether a term in a gam is nonzero, linear, or a non-linear spline (up to a specified max df per variable). It fits the entire regularization path on a grid of values for the overall penalty lambda, both for gaussian and binomial families.

gamsel(
  x,
  y,
  num_lambda = 50,
  lambda = NULL,
  family = c("gaussian", "binomial"),
  degrees = rep(10, p),
  gamma = 0.4,
  dfs = rep(5, p),
  bases = pseudo.bases(x, degrees, dfs, parallel = parallel, ...),
  tol = 1e-04,
  max_iter = 2000,
  traceit = FALSE,
  parallel = FALSE,
  ...
)

`x`	Input (predictor) matrix of dimension `nobs` x `nvars`. Each observation is a row.
`y`	Response variable. Quantitative for `family="gaussian"` and with values in `{0,1}` for `family="binomial"`
`num_lambda`	Number of `lambda` values to use. (Length of `lambda` sequence.)
`lambda`	User-supplied `lambda` sequence. For best performance, leave as `NULL` and allow the routine to automatically select `lambda`. Otherwise, supply a (preferably gradually) decreasing sequence.
`family`	Response type. `"gaussian"` for linear model (default). `"binomial"` for logistic model.
`degrees`	An integer vector of length `nvars` specifying the maximum number of spline basis functions to use for each variable.
`gamma`	Penalty mixing parameter 0 ≤γ≤ 1. Values γ < 0.5 penalize linear fit less than non-linear fit. The default is γ = 0.4, which encourages a linear term over a nonlinear term.
`dfs`	Numeric vector of length `nvars` specifying the maximum (end-of-path) degrees of freedom for each variable.
`bases`	A list of orthonormal bases for the non-linear terms for each variable. The function `pseudo.bases` generates these, using the parameters `dfs` and `degrees`. See the documentation for `pseudo.bases`.
`tol`	Convergence threshold for coordinate descent. The coordinate descent loop continues until the total change in objective after a pass over all variables is less than `tol`. Default is `1e-4`.
`max_iter`	Maximum number of coordinate descent iterations over all the variables for each `lambda` value. Default is 2000.
`traceit`	If `TRUE`, various information is printed during the fitting process.
`parallel`	passed on to the `pseudo.bases()` function. Uses multiple process if available.
`...`	additional arguments passed on to `pseudo.bases()`

The sequence of models along the lambda path is fit by (block) cordinate descent. In the case of logistic regression the fitting routine may terminate before all num_lambda values of lambda have been used. This occurs when the fraction of null deviance explained by the model gets too close to 1, at which point the fit becomes numerically unstable. Each of the smooth terms is computed using an approximation to the Demmler-Reinsch smoothing spline basis for that variable, and the accompanying diagonal pernalty matrix.

An object with S3 class gamsel. %% If it is a LIST, use

`intercept`	Intercept sequence of length `num_lambda`
`alphas`	`nvars` x `num_lambda` matrix of linear coefficient estimates
`betas`	`sum(degrees)` x `num_lambda` matrix of non-linear coefficient estimates
`lambdas`	The sequence of lambda values used
`degrees`	Number of basis functions used for each variable
`parms`	A set of parameters that capture the bases used. This allows for efficient generation of the bases elements for `predict.gamsel`

, the predict method for this class.

`family`	`"gaussian"` or `"binomial"`
`nulldev`	Null deviance (deviance of the intercept model)
`dev.ratio`	Vector of length `num_lambda` giving fraction of (null) deviance explained by each model along the `lambda` sequence
`call`	The call that produced this object

%% ...

Alexandra Chouldechova and Trevor Hastie
Maintainer: Trevor Hastie hastie@stanford.edu

Chouldechova, A. and Hastie, T. (2015) Generalized Additive Model Selection, https://arxiv.org/abs/1506.03850

predict.gamsel, cv.gamsel, plot.gamsel, summary.gamsel, basis.gen,

##data=gamsel:::gendata(n=500,p=12,k.lin=3,k.nonlin=3,deg=8,sigma=0.5)
data = readRDS(system.file("extdata/gamsel_example.RDS", package = "gamsel"))
attach(data)
bases=pseudo.bases(X,degree=10,df=6)
# Gaussian gam
gamsel.out=gamsel(X,y,bases=bases)
par(mfrow=c(1,2),mar=c(5,4,3,1))
summary(gamsel.out)
gamsel.cv=cv.gamsel(X,y,bases=bases)
par(mfrow=c(1,1))
plot(gamsel.cv)
par(mfrow=c(3,4))
plot(gamsel.out,newx=X,index=20)
# Binomial model
gamsel.out=gamsel(X,yb,family="binomial")
par(mfrow=c(1,2),mar=c(5,4,3,1))
summary(gamsel.out)
par(mfrow=c(3,4))
plot(gamsel.out,newx=X,index=30)