iRegression (version 1.2.1)

MinMax: MinMax Method

Description

MinMax is used to fit a linear regression model to symbolic interval-valued variables based on the MinMax method (Lima Neto and De Carvalho, 2008).

Usage

MinMax(formula1, formula2, data, ...)

Arguments

formula1

an object of class "formula": a symbolic description of the model to be fitted.

formula2

an object of class "formula": a symbolic description of the model to be fitted.

data

an optional data frame containing the variables in the model.

...

other arguments.

Value

MinMax returns an object of class "MinMax" including at least the following elements:

coefficients.l

a named vector of coefficients for the Minimum explanatory variables.

coefficients.u

a named vector of coefficients for the Maximum explanatory variables.

sigma.l

an estimate of standard deviation for the Minimum response variable

sigma.u

an estimate of standard deviation for the Maximum response variable

df.l

the degrees of freedom for the lower residuals

df.u

the degrees of freedom for the upper residuals

fitted.values.l

the fitted values for the lower interval bound.

fitted.values.u

the fitted values for the upper interval bound.

residuals.l

the ordinary residuals for the lower interval bound.

residuals.u

the ordinary residuals for the upper interval bound.

Details

The Min-Max Method suggests to estimate the lower and upper bounds of the intervals using different vectors of parameters. This is equivalent to supposing independence between the values of lower and upper bounds of the intervals. The MinMax Method fits two independent linear regression models on the lower and upper bounds of the intervals, respectively, and minimizes the error of the lower bounds plus the error of the upper bounds.

References

Billard, L. and Diday, E. (2000) Regression analysis for interval-valued data. Data Analysis, Classification and Related Methods: Proceedings of the Seventh Conference of the International Federation of Classification Societies, Springer-Verlag, pp. 369-374.

Lima Neto, E.A. and De Carvalho, F.A.T. (2008). Centre and range method to fitting a linear regression model on symbolic interval data. Computational Statistics and Data Analysis, 52, 1500--1515.

See Also

summary.MinMax, coef.MinMax, fitted.MinMax, residuals.MinMax, formula

Examples

data("Cardiological.MinMax", package = "iRegression") ## see Billard, L. and Diday, E. (2000)
ex.MinMax <- MinMax(PulseMin~SystMin+DiastMin,PulseMax~SystMax+DiastMax,data=Cardiological.MinMax)
ex.MinMax