Groupwise Additive Index Models (GAIM)

A wrapper for cgaim::cgaim() enabling multiple GAIM models based on a grouping variable. Currently does not support Constrained GAIM (CGAIM)s.

Usage

model_gaim(
  data,
  yvar,
  neighbour = 0,
  index.vars,
  index.ind,
  s.vars = NULL,
  linear.vars = NULL,
  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.
index.ind: An integer vector that assigns group index for each predictor in index.vars.
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.
verbose: Logical; controls whether progress messages (model indices) are printed during fitting. Defaults to FALSE.
...: Other arguments not currently used. (Note that the arguments in cgaim::cgaim() related to constrained GAIMs are currently not supported. Furthermore, the argument subset is also not supported due to a bug in cgaim::cgaim().)

Value

An object of class gaimFit. 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 cgaim. For details refer cgaim::cgaim().

Details

Group-wise Additive Index Model (GAIM) can be written in the form $$y_{i} = \sum_{j = 1}^{p} g_{j}(\boldsymbol{\alpha}_{j}^{T}\boldsymbol{x}_{ij}) + \varepsilon_{i}, \quad i = 1, \dots, n,$$ where $y_{i}$ is the univariate response, $\boldsymbol{x}_{ij} \in \mathbb{R}^{l{j}}$, $j = 1, \dots, p$ are pre-specified non-overlapping subsets of $\boldsymbol{x}_{i}$, and $\boldsymbol{\alpha}_j$ are the corresponding index coefficients, $g_{j}$ is an unknown (possibly nonlinear) component function, and $\varepsilon_{i}$ is the random error, which is independent of $\boldsymbol{x}_{i}$.

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)

# Predictors taken as index variables
index.vars <- colnames(sim_data)[3:7]

# Assign group indices for each predictor
index.ind = c(rep(1, 3), rep(2, 2))

# Predictors taken as non-linear variables not entering indices
s.vars = "x_lag_005"

# Model fitting
gaimModel <- model_gaim(data = sim_data,
                        yvar = "y",
                        index.vars = index.vars,
                        index.ind = index.ind,
                        s.vars = s.vars)
# Fitted model
gaimModel$fit[[1]]
#> Formula:
#> y ~ g(x_lag_000, x_lag_001, x_lag_002) + g(x_lag_003, x_lag_004) + 
#>     s(x_lag_005)
#> 
#> Coefficients:
#> (Intercept)   x_lag_000   x_lag_003   x_lag_005 
#>  1.23026577  0.99071595  0.41458553  0.03298014 
#> 
#> Indices weights:
#> x_lag_000 
#>   x_lag_000   x_lag_001   x_lag_002 
#> 0.604670638 0.392787126 0.002542237 
#> x_lag_003 
#>   x_lag_003   x_lag_004 
#>  0.98152724 -0.01847276 
#> 
#> Residual sum of squares: 0.06248322

Usage

Arguments

Value

Details

See also

Examples