gmdh.mia {GMDHreg}

GMDH MIA

Description

Build a regression model performing GMDH MIA (Multilayered Iterative Algorithm).
For more information, please read the package's vignette.

Usage

gmdh.mia(
  X,
  y,
  prune = ncol(X),
  criteria = c("PRESS", "test", "ICOMP"),
  x.test = NULL,
  y.test = NULL
)

Arguments

X

matrix with N>3 columns and M rows, containing independent variables in the model.
The data must not contain NAs

y

vector or matrix containing dependent variable in the model.
The data must not contain NAs

prune

an integer whose recommended minimum value is the number of initial regressors.
The maximum value will depend on the available RAM.
Prune is the selected number of neurons from layer i to layer i+1. The resulting layer i+1 has prune(prune-1)/2 neurons; for example with prune=150, the resulting nerurons will be 11.175

criteria

GMDH external criteria. Values:

• PRESS: Predicted Residual Error Sum of Squares. It take into account all information in data sample and it is computed without recalculating of system for each test point.
  

• test: use x.test and y.test to estimate RMSE (Root Mean Squeare Errors).
  

• ICOMP: Index of Informational Complexity. Like PRESS, it is computed without recalculating of system.

x.test

matrix with a sample randomly drawn from the initial data.
It is used when criteria = test.
This sample should not be included in X.

y.test

vector or matrix with y values correspond with x.test values.

Value

An object of class mia.

References

Bozdogan, H. and Haughton, D.M.A. (1998): "Information complexity criteria for regression models", Computational Statistics & Data Analysis, 28, pp. 51-76 <doi: 10.1016/S0167-9473(98)00025-5>

Farlow, S.J. (1981): "The GMDH algorithm of Ivakhnenko", The American Statistician, 35(4), pp. 210-215. <doi: 10.2307/2683292>

Hild, Ch. R. and Bozdogan, H. (1995): "The use of information-based model selection criteria in the GMDH algorithm", Systems Analysis Modelling Simulation, 20(1-2), pp. 29-50

Ivakhnenko, A.G. (1968): "The Group Method of Data Handling - A Rival of the Method of Stochastic Approximation", Soviet Automatic Control, 13(3), pp. 43-55

Müller, J.-A., Ivachnenko, A.G. and Lemke, F. (1998): "GMDH Algorithms for Complex Systems Modelling", Mathematical and Computer Modelling of Dynamical Systems, 4(4), pp. 275-316 <doi: 10.1080/13873959808837083>

Examples

set.seed(123)
x <- matrix(data = c(rnorm(1000)), ncol = 5, nrow = 200)
colnames(x) <- c("a", "b", "c", "d", "e")
y <- matrix(data = c(10 + x[, "a"] * x[, "e"]^3), ncol = 1)
colnames(y) <- "y"
x.test <- x[1:10, ]
y.test <- y[1:10]
x <- x[-c(1:10), ]
y <- y[-c(1:10)]

mod <- gmdh.mia(X = x, y = y, criteria = "PRESS")
pred <- predict(mod, x.test)
summary(sqrt((pred - y.test)^2))