gplsim {gplsim}

Function to fit generalized partially linear single-index models via penalized splines

Description

This function employs penalized spline (P-spline) to estimate generalized partially linear single index models, which extend the generalized linear models to include nonlinear effect for some predictors.

This function add formula interface to gplsim function

Usage

gplsim(...)

## Default S3 method:
gplsim(
  Y = Y,
  X = X,
  Z = Z,
  family = gaussian(),
  penalty = TRUE,
  profile = TRUE,
  user.init = NULL,
  bs = "ps",
  ...
)

## S3 method for class 'formula'
gplsim(
  formula,
  data,
  family = gaussian(),
  penalty = TRUE,
  profile = TRUE,
  user.init = NULL,
  bs = "ps",
  ...
)

Arguments

...

includes optional arguments user can pass to mgcv::gam or glm, such as k, which is the dimension of the basis of the smooth term and m, which is the order of the penalty for the smooth term. Others include: scale The optional argument scale is a numeric indicator with a default value set to -1. Any negative value including -1 indicates that the scale of response distribution is unknown, thus need to be estimated. Another option is 0 signaling scale of 1 for Poisson and binomial distribution and unknown for others. Any positive value will be taken as the known scale parameter. smooth_selection The optional argument smooth_selection is another character variable that specifies the criterion used in the selection of a smoothing parameter. The supported criteria include "GCV.Cp","GACV.Cp", "ML","P-ML", "P-REML" and "REML", while the default criterion is "GCV.Cp".

Y

Response variable, should be a vector.

X

Single index covariates.

Z

Partially linear covariates.

family

A family object: a list of functions and expressions for defining link and variance functions. Families supported are binomial, gaussian. The default family is gaussian.

penalty

Whether use penalized splines or un-penalized splines to fit the model. The default is TRUE.

profile

profile is a logical variable that indicates whether the algorithm with profile likelihood or algorithm with NLS procedure should be used. The default algorithm is set to algorithm with profile likelihood.

user.init

The user.init is a numeric vector of the same length as the dimensionality of single index predictors. The users can use this argument to pass in any appropriate user-defined initial single-index coefficients based on prior information or domain knowledge. The default value is NULL.

bs

bs is a character variable that specifies the spline basis in the estimation of unknown univariate function of single index. Default is P-splines.

formula

A model formula;

data

A data matrix containing the variables in the formula.

Details

For formula method, see ?gplsim.formula

Value

theta Estimation of Theta

coefficients the coefficients of the fitted model. Parametric coefficients are first, followed by coefficients for each spline term in turn.

... See GAM object

theta Estimation of Theta

coefficients the coefficients of the fitted model. Parametric coefficients are first, followed by coefficients for each spline term in turn.

... See GAM object

Examples

# parameter settings
n=200
true.theta = c(1, 1, 1)/sqrt(3)
# Gaussian case
# This function generate a plain sin bump model with gaussian response.
data <- generate_data(n,true.theta=true.theta,family="gaussian")
y=data$Y       # continous response
X=data$X       # single index term ;
Z=data$Z       # partially linear term ;

result <- gplsim(y,X,Z,family = gaussian)
result$theta
result$coefficients
summary(result)


#plot the estimated single index function curve
plot_si(result)