crm {iRegression}

Centre and Range Method

Description

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

Usage

crm(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

In the Center Method, the estimate of the parameters beta is based only on the midpoint of the intervals. However, the Centre and Range Method proposed by Lima Neto and De Carvalho (2008) consider suitable to include both the information given by the center and by the range of an interval-valued variable on a linear regression model to improve the model prediction performance. The Centre and Range Method fits two independent linear regression models on the midpoint and range of the intervals, respectively, and minimizes the error of the midpoint plus the error of the range.

Value

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

coefficients.C

a named vector of coefficients for the Centre variables.

coefficients.R

a named vector of coefficients for the Range variables.

sigma.C

an estimate of standard deviation for the Centre response variable.

sigma.R

an estimate of standard deviation for the Range response variable.

df.C

the degrees of freedom for the centre residuals

df.R

the degrees of freedom for the range residuals

fitted.values.l

the fitted mean values for the lower interval bound.

fitted.values.u

the fitted mean values for the upper interval bound.

residuals.l

the residuals for the lower interval bound (that is response minus fitted values).

residuals.u

the residuals for the upper interval bound (that is response minus fitted values).

Note

formula1 must contain the midpoint of the symbolic interval-valued variables. formula2 contain the range (upper limit minus lower 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.crm, coef.crm, fitted.crm, residuals.crm, formula

Examples

data("Cardiological.CR", package = "iRegression")
ex.crm <- crm("PulseC~SystC+DiastC","PulseR~SystR+DiastR",data=Cardiological.CR)
ex.crm