SMI model estimation

Fits a single nonparametric multiple index model to the data. This is a helper function designed to be called from user-facing wrapper functions, model_smimodel and greedy_smimodel.

Usage

smimodel.fit(
  data,
  yvar,
  neighbour = 0,
  family = gaussian(),
  index.vars,
  initialise = c("ppr", "additive", "linear", "multiple", "userInput"),
  num_ind = 5,
  num_models = 5,
  seed = 123,
  index.ind = NULL,
  index.coefs = NULL,
  s.vars = NULL,
  linear.vars = NULL,
  lambda0 = 1,
  lambda2 = 1,
  M = 10,
  max.iter = 50,
  tol = 0.001,
  tolCoefs = 0.001,
  TimeLimit = Inf,
  MIPGap = 1e-04,
  NonConvex = -1,
  verbose = list(solver = FALSE, progress = FALSE)
)

Arguments

data

Training data set on which models will be trained. Must be a data set of class tsibble.(Make sure there are no additional date or time related variables except for the index of the tsibble).

yvar

Name of the response variable as a character string.

neighbour

neighbour argument passed from the outer function.

family

A description of the error distribution and link function to be used in the model (see glm and family).

index.vars

A character vector of names of the predictor variables for which indices should be estimated.

initialise

The model structure with which the estimation process should be initialised. The default is "ppr", where the initial model is derived from projection pursuit regression. The other options are "additive" - nonparametric additive model, "linear" - linear regression model (i.e. a special case single-index model, where the initial values of the index coefficients are obtained through a linear regression), "multiple" - multiple models are fitted starting with different initial models (number of indices = num_ind; num_models random instances of the model (i.e. the predictor assignment to indices and initial index coefficients are generated randomly) are considered), and the final optimal model with the lowest loss is returned, and "userInput" - user specifies the initial model structure (i.e. the number of indices and the placement of index variables among indices) and the initial index coefficients through index.ind and index.coefs arguments respectively.

num_ind

If initialise = "ppr" or "multiple": an integer that specifies the number of indices to be used in the model(s). The default is num_ind = 5.

num_models

If initialise = "multiple": an integer that specifies the number of starting models to be checked. The default is num_models = 5.

seed

If initialise = "multiple": the seed to be set when generating random starting points.

index.ind

If initialise = "userInput": an integer vector that assigns group index for each predictor in index.vars.

index.coefs

If initialise = "userInput": a numeric vector of index coefficients.

s.vars

A character vector of names of the predictor variables for which splines should be fitted individually (rather than considering as part of an index).

linear.vars

A character vector of names of the predictor variables that should be included linearly into the model.

lambda0

Penalty parameter for L0 penalty.

lambda2

Penalty parameter for L2 penalty.

M

Big-M value to be used in MIP.

max.iter

Maximum number of MIP iterations performed to update index coefficients for a given model.

tol

Tolerance for the objective function value (loss) of MIP.

tolCoefs

Tolerance for coefficients.

TimeLimit

A limit for the total time (in seconds) expended in a single MIP iteration.

MIPGap

Relative MIP optimality gap.

NonConvex

The strategy for handling non-convex quadratic objectives or non-convex quadratic constraints in Gurobi solver.

verbose

A named list controlling verbosity options. Defaults to list(solver = FALSE, progress = FALSE).

solver

Logical. If TRUE, print detailed solver output.

progress

Logical. If TRUE, print optimisation algorithm progress messages.

Value

A list with two elements:

initial

A list of information of the model initialisation. (For descriptions of the list elements see make_smimodelFit).

best

A list of information of the final optimised model. (For descriptions of the list elements see make_smimodelFit).