gmdh.combi {GMDHreg}

GMDH Combinatorial

Description

Build a regression model performing GMDH Combinatorial.
This is the basic GMDH algorithm. For more information, please read the package's vignette.

Usage

gmdh.combi(
  X,
  y,
  G = 2,
  criteria = c("PRESS", "test", "ICOMP"),
  x.test = NULL,
  y.test = NULL
)

Arguments

X

matrix with N>1 columns and M rows, containing independent variables in the model.
Be careful, N>4 and G=2, could be computationally very expensive and time consuming.
The data must not contain NAs

y

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

G

polynomial degree.
0: linear regression without quadratic and interactrion terms.
1: linear regression with interaction terms.
2: original Ivakhnenko quadratic polynomial.

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. This sample should not be included in X.
It is used when criteria = test.

y.test

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

Value

An object of class 'combi'. This is a list with two elements: results and G.
Results is a list with two elements:

• coef: coeficients of final selected GMDH Combinatorial model.

• CV: external criteria value for selected model.

G the grade of polynomial used in GMDH Combinatorial model.

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>

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(1050)), ncol = 3, nrow = 350)
colnames(x) <- c("a", "b", "c")
y <- matrix(data = c(10 + x[, "a"] + x[, "b"]^2 + x[, "c"]^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.combi(X = x, y = y, criteria = "PRESS")
pred <- predict(mod, x.test)
summary(sqrt((pred - y.test)^2))