Projection Pursuit Regression (PPR) models

A wrapper for stats::ppr() enabling multiple PPR models based on a grouping variable.

Usage

model_ppr(
  data,
  yvar,
  neighbour = 0,
  index.vars,
  num_ind = 5,
  verbose = 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). If multiple models are fitted, the grouping variable should be the key of the tsibble. If a key is not specified, a dummy key with only one level will be created.
yvar: Name of the response variable as a character string.
neighbour: If multiple models are fitted: Number of neighbours of each key (i.e. grouping variable) to be considered in model fitting to handle smoothing over the key. Should be an integer. If neighbour = x, x number of keys before the key of interest and x number of keys after the key of interest are grouped together for model fitting. The default is neighbour = 0 (i.e. no neighbours are considered for model fitting).
index.vars: A character vector of names of the predictor variables for which indices should be estimated.
num_ind: An integer that specifies the number of indices to be used in the model(s). (Corresponds to nterms in stats::ppr().)
verbose: Logical; controls whether progress messages (model indices) are printed during fitting. Defaults to FALSE.
...: Other arguments not currently used. (For more information on other arguments that can be passed, refer stats::ppr().)

Value

An object of class pprFit. This is a tibble with two columns:

key: The level of the grouping variable (i.e. key of the training data set).
fit: Information of the fitted model corresponding to the key.

Each row of the column fit is an object of class c("ppr.form", "ppr"). For details refer stats::ppr().

Details

A Projection Pursuit Regression (PPR) model (Friedman & Stuetzle (1981)) is given by $$y_{i} = \sum_{j=1}^{p} {g_{j}(\boldsymbol{\alpha}_{j}^{T}\boldsymbol{x}_{i})} + \varepsilon_{i}, \quad i = 1, \dots, n,$$ where $y_{i}$ is the response, $\boldsymbol{x}_{i}$ is the $q$-dimensional predictor vector, $\boldsymbol{\alpha}_{j} = ( \alpha_{j1}, \dots, \alpha_{jp} )^{T}$, $j = 1, \dots, p$ are $q$-dimensional projection vectors (or vectors of "index coefficients"), $g_{j}$'s are unknown nonlinear functions, and $\varepsilon_{i}$ is the random error.

References

Friedman, J. H. & Stuetzle, W. (1981). Projection pursuit regression. Journal of the American Statistical Association, 76, 817–823. doi:10.2307/2287576 .

Examples

library(dplyr)
library(tibble)
library(tidyr)
library(tsibble)

# Simulate data
n = 1005
set.seed(123)
sim_data <- tibble(x_lag_000 = runif(n)) |>
  mutate(
    # Add x_lags
    x_lag = lag_matrix(x_lag_000, 5)) |>
  unpack(x_lag, names_sep = "_") |>
  mutate(
    # Response variable
    y = (0.9*x_lag_000 + 0.6*x_lag_001 + 0.45*x_lag_003)^3 + rnorm(n, sd = 0.1),
    # Add an index to the data set
    inddd = seq(1, n)) |>
  drop_na() |>
  select(inddd, y, starts_with("x_lag")) |>
  # Make the data set a `tsibble`
  as_tsibble(index = inddd)

# Index variables
index.vars <- colnames(sim_data)[3:8]

# Model fitting
pprModel <- model_ppr(data = sim_data,
                      yvar = "y",
                      index.vars = index.vars)

# Fitted model
pprModel$fit[[1]]
#> Call:
#> ppr(formula = as.formula(pre.formula), data = df_cat, nterms = num_ind)
#> 
#> Goodness of fit:
#>  5 terms 
#> 9.210028