MinMax: MinMax Method

In iRegression: Regression Methods for Interval-Valued Variables

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.

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.

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.

Note

formula1 must contain the lower limit of the symbolic interval-valued variables. formula2 contain the upper limit of the symbolic interval-valued variables.

Author(s)

Eufrasio de A. Lima Neto [e-mail] , Claudio A. V. de Souza Filho and Pedro R. D. Marinho

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

Example output

Attaching package: 'iRegression'

The following object is masked from 'package:grDevices':

    cm

Call:
MinMax.formula(formula1 = PulseMin ~ SystMin + DiastMin, formula2 = PulseMax ~ 
    SystMax + DiastMax, data = Cardiological.MinMax)

$coefficients.l
(Intercept)     SystMin    DiastMin 
 22.5765996   0.2654480   0.1952525 

$coefficients.u
(Intercept)     SystMax    DiastMax 
 34.0809692   0.3061762   0.1089141 

$sigma.l
[1] 12.18673

$sigma.u
[1] 11.3557

$df.l
[1] 8

$df.u
[1] 8

iRegression documentation built on May 2, 2019, 8:24 a.m.