Centre Method

icm is used to fit a linear regression model to symbolic interval-valued variables based on the centre method (Billard and Diday, 2000).

icm(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

Billard and Diday (2000) presented the first approach to fitting a linear regression model to symbolic interval data sets from a SDA of view. Their approach consists on fitting a linear regression model to the mid-points of the interval values assumed by the symbolic interval variables in the learning set and applies this model to the lower and upper bounds of the interval values of the independent symbolic interval variables to be predicted, respectively, the lower and upper bounds of the interval value of the dependent variable. The Centre Method is based on the minimization of the midpoint error. The lower and upper bounds of the dependent variable are predicted, respectively, from the lower and upper bounds of the independent variable using the same vector of parameters \(latex\).

Value

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

coefficients

a named vector of coefficients.

sigma

an estimate of standard deviation.

df

the residual degrees of freedom.

fitted.values.l

the fitted values for the lower interval bound.

fitted.valuues.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 .

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.

Note

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

See also

summary.icm, coef, fitted.icm, residuals.icm, formula

Examples

data("Cardiological.MinMax", package = "iRegression") ## see Billard and Diday (2000)
ex.icm <- icm(PulseMin~SystMin+DiastMin,PulseMax~SystMax+DiastMax,data=Cardiological.MinMax)
ex.icm
#> Call:
#> icm.default(formula1 = PulseMin ~ SystMin + DiastMin, formula2 = PulseMax ~ 
#>     SystMax + DiastMax, data = Cardiological.MinMax)
#> 
#> $coefficients
#> (Intercept)      beta_1      beta_2 
#>  21.1708061   0.3288879   0.1698512 
#> 
#> $sigma
#> [1] 9.516986
#> 
#> $df
#> [1] 8
#>