| Title: | Regression Methods for Interval-Valued Variables |
|---|---|
| Description: | Contains some important regression methods for interval-valued variables. For each method, it is available the fitted values, residuals and some goodness-of-fit measures. |
| Authors: | Eufrasio de A. Lima Neto / Claudio A. V. de Souza Filho / Pedro R. D. Marinho |
| Maintainer: | Eufrasio de A. Lima Neto <[email protected]> |
| License: | GPL (>= 2) |
| Version: | 1.2.1 |
| Built: | 2024-11-13 06:19:53 UTC |
| Source: | CRAN |
Contains some important regression methods for interval-valued variables. For each method, it is available the fitted values, residuals and some goodness-of-fit measures.
| Package: | iRegression |
| Type: | Package |
| Version: | 1.2.1 |
| Date: | 2016-07-16 |
| License: | GPL (>= 2) |
| LazyLoad: | yes |
Some available functions:
cm, MinMax, crm, ccrm, bivar
Eufrasio de A. Lima Neto [email protected] , Claudio A. V. de Souza Filho and Pedro R. D. Marinho
Maintainer: Eufrasio de A. Lima Neto [email protected]
Acknowledgments: The authors would like to thank CNPq (Brazilian Agency) for their financial support.
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.
Lima Neto, E.A. and De Carvalho, F.A.T. (2010). Constrained linear regression models for symbolic interval-valued variables. Computational Statistics and Data Analysis, 54, 333–347.
Lima Neto, E. A., Cordeiro, G. and De Carvalho, F.A.T. (2011). Bivariate symbolic regression models for interval-valued variables. Journal of Statistical Computation and Simulation (Print), 81, 1727–1744.
This function fits an bivariate regression model for interval-valued variables, based on bivariate exponential family of distributions, and return the fitted values, the residuals, rho, phi and the goodness-of-fit measure deviance
bivar(formula1, lig1, formula2, lig2, data, ...)bivar(formula1, lig1, formula2, lig2, data, ...)
formula1 |
an object of class " |
lig1 |
the link function to be considered in the first model: identity, inverse or log |
formula2 |
an object of class " |
lig2 |
the link function to be considered in the second model: identity, inverse or log |
data |
an optional data frame containing the variables in the model. |
... |
other arguments. |
This function fits an bivariate regression model for interval-valued variables considering the bivariate Gaussian distribution in the random component Y = [Y1, Y2]. It is possible consider any pair of interval features for the bivariate random vector Y. For example, the lower and upper interval bounds or the midpoint and the range of intervals, respectively. It also possible to choice different link functions (identity, inverse or log) to connect the random variables Y1 and Y2 with the respective linear predictors.
bivar returns an object of class "bivar" including at least the following elements:
coefficients1 |
a named vector of coefficients for the explanatory variables of the model "1". |
coefficients2 |
a named vector of coefficients for the explanatory variables of the model "2". |
fitted.values1 |
the fitted values for the response variable Y1 . |
fitted.values2 |
the fitted values for the response variable Y2. |
residuals1 |
the ordinary residual for the response variable Y1. |
residuals2 |
the ordinary residual for the response variable Y2. |
residual.deviance |
the global residual for the bivariate vector Y=[Y1, Y2]. |
Rho |
the estimative for the correlation coefficient between Y1 and Y2. |
Phi |
the estimative of the dispersion parameter. |
D |
the goodness-of-fit measure deviance for the current model. |
lig1 and lig2 must be "identity", "inverse" or "log" for identity, inverse or logarithmic link functions, respectively.
Eufrasio de A. Lima Neto [email protected] , Claudio A. V. de Souza Filho and Pedro R. D. Marinho
Lima Neto, E. A., Cordeiro, G. and De Carvalho, F.A.T. (2011). Bivariate symbolic regression models for interval-valued variables. Journal of Statistical Computation and Simulation (Print), 81, 1727–1744.
summary.bivar, coef.bivar, fitted.bivar, residuals.bivar, formula
data("soccer.bivar", package = "iRegression") ex.bivar <- bivar("yMin~t1Min+t2Min", "identity", "yMax~t1Max+t2Max", "identity", data=soccer.bivar) ex.bivardata("soccer.bivar", package = "iRegression") ex.bivar <- bivar("yMin~t1Min+t2Min", "identity", "yMax~t1Max+t2Max", "identity", data=soccer.bivar) ex.bivar
A real interval-valued data set represented in terms of the centre and the range of the intervals.
data("Cardiological.CR")data("Cardiological.CR")
A data frame containing the following variables:.
The midpoint of the response interval-valued variable Pulse
The midpoint of the explanatory interval-valued variable Systolic Pressure
The midpoint of the explanatory interval-valued variable Diastolic Pressure
The range of the response interval-valued variable Pulse
The range of the explanatory interval-valued variable Systolic Pressure
The range of the explanatory interval-valued variable Diastolic Pressure
This data set concerns the record of the pulse rate (Y), systolic blood pressure (X1) and diastolic blood pressure (X2) from 11 patients.
Billard and Diday (2000)
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.
data("Cardiological.CR", package = "iRegression") crm1 <- crm("PulseC~SystC+DiastC","PulseR~SystR+DiastR",data=Cardiological.CR) summary(crm1)data("Cardiological.CR", package = "iRegression") crm1 <- crm("PulseC~SystC+DiastC","PulseR~SystR+DiastR",data=Cardiological.CR) summary(crm1)
A real interval-valued data set.
data("Cardiological.CR")data("Cardiological.CR")
A data frame containing following variables:
Lower bound of the response interval-valued variable Pulse
Lower bound of the explanatory interval-valued variable Systolic Pressure
Lower bound of the explanatory interval-valued variable Diastolic Pressure
Upper bound of the response interval-valued variable Pulse
Upper bound of the explanatory interval-valued variable Systolic Pressure
Upper bound of the explanatory interval-valued variable Diastolic Pressure
This data set concerns the record of the pulse rate (Y), systolic blood pressure (X1) and diastolic blood pressure (X2) from 11 patients.
Billard and Diday (2000)
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.
data("Cardiological.MinMax", package = "iRegression") cm1 <- cm(PulseMin~SystMin+DiastMin,PulseMax~SystMax+DiastMax,data=Cardiological.MinMax) summary(cm1) ## data("Cardiological.MinMax", package = "iRegression") MinMax1 <- MinMax(PulseMin~SystMin+DiastMin,PulseMax~SystMax+DiastMax,data=Cardiological.MinMax) summary(MinMax1)data("Cardiological.MinMax", package = "iRegression") cm1 <- cm(PulseMin~SystMin+DiastMin,PulseMax~SystMax+DiastMax,data=Cardiological.MinMax) summary(cm1) ## data("Cardiological.MinMax", package = "iRegression") MinMax1 <- MinMax(PulseMin~SystMin+DiastMin,PulseMax~SystMax+DiastMax,data=Cardiological.MinMax) summary(MinMax1)
ccrm is used to fit a linear regression model to symbolic interval-valued variables based on the inequality constraints over
the range variables (Lima Neto and De Carvalho, 2010).
ccrm(formula1, formula2, data, ...)ccrm(formula1, formula2, data, ...)
formula1 |
an object of class " |
formula2 |
an object of class " |
data |
an optional data frame containing the variables in the model. |
... |
other arguments. |
The Constrained Centre and Range method (CCRM) was proposed by Lima Neto and De Carvalho (2010) and fits two independent linear regression models on the midpoint and range of the intervals. In the Constrained Centre and Range Method, the estimative of the parameters of the range's model is based on inequality constraints. There is no constraints over the parameters estimates for the midpoint regression equation. The aim is to guarantee mathematical coherence between the predicted values of the lower and upper bounds of the response interval-valued variable Y, i.e., yL < yU.
ccrm returns an object of class "ccrm" including at least the following elements:
coefficients.C |
a named vector of coefficients for the Centre's explanatory variables. |
coefficients.R |
a named vector of coefficients for the Range's explanatory variables. |
sigma.C |
an estimative of the standard deviation for the Centre's response variable. |
sigma.R |
an estimative of the standard deviation for the Range's 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 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. |
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.
Eufrasio de A. Lima Neto [email protected] , Claudio A. V. de Souza Filho and Pedro R. D. Marinho
Lima Neto, E.A. and De Carvalho, F.A.T. (2010). Constrained linear regression models for symbolic interval-valued variables. Computational Statistics and Data Analysis, 54, 333–347.
summary.ccrm, coef.ccrm, fitted.ccrm, residuals.ccrm, formula
data("Cardiological.CR", package = "iRegression") ex.ccrm <- ccrm("PulseC~SystC+DiastC","PulseR~SystR+DiastR",data=Cardiological.CR) ex.ccrmdata("Cardiological.CR", package = "iRegression") ex.ccrm <- ccrm("PulseC~SystC+DiastC","PulseR~SystR+DiastR",data=Cardiological.CR) ex.ccrm
cm is used to fit a linear regression model to symbolic interval-valued variables based on the centre method (Billard and Diday, 2000).
cm(formula1, formula2, data, ...)cm(formula1, formula2, data, ...)
formula1 |
an object of class |
formula2 |
an object of class |
data |
an optional data frame containing the variables in the model. |
... |
other arguments. |
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 beta.
cm returns an object of class "cm" 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 . |
formula1 must contain the lower limit of the symbolic interval-valued variables. formula2 contain the upper limit
of the symbolic interval-valued variables.
Eufrasio de A. Lima Neto [email protected], Claudio A. V. de Souza Filho and Pedro R. D. Marinho
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.
summary.cm, coef, fitted.cm, residuals.cm, formula
data("Cardiological.MinMax", package = "iRegression") ## see Billard and Diday (2000) ex.cm <- cm(PulseMin~SystMin+DiastMin,PulseMax~SystMax+DiastMax,data=Cardiological.MinMax) ex.cmdata("Cardiological.MinMax", package = "iRegression") ## see Billard and Diday (2000) ex.cm <- cm(PulseMin~SystMin+DiastMin,PulseMax~SystMax+DiastMax,data=Cardiological.MinMax) ex.cm
Returns the coefficients from an object class bivar.
## S3 method for class 'bivar' coef(object, ...)## S3 method for class 'bivar' coef(object, ...)
object |
an object class |
... |
other arguments. |
Coefficients extracted from an object class bivar.
Returns the coefficients from an object class ccrm.
## S3 method for class 'ccrm' coef(object, ...)## S3 method for class 'ccrm' coef(object, ...)
object |
an object class |
... |
other arguments. |
Coefficients extracted from an object class object.
Returns the coefficients from an object class crm.
## S3 method for class 'crm' coef(object, ...)## S3 method for class 'crm' coef(object, ...)
object |
an object class |
... |
other arguments. |
Coefficients extracted from an object class object.
Returns the coefficients from an object class MinMax.
## S3 method for class 'MinMax' coef(object, ...)## S3 method for class 'MinMax' coef(object, ...)
object |
an object class |
... |
other arguments. |
Coefficients extracted from an object class MinMax.
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).
crm(formula1, formula2, data, ...)crm(formula1, formula2, data, ...)
formula1 |
an object of class " |
formula2 |
an object of class " |
data |
an optional data frame containing the variables in the model. |
... |
other arguments. |
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.
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). |
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.
Eufrasio de A. Lima Neto [email protected] , Claudio A. V. de Souza Filho and Pedro R. D. Marinho
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.
summary.crm, coef.crm, fitted.crm, residuals.crm, formula
data("Cardiological.CR", package = "iRegression") ex.crm <- crm("PulseC~SystC+DiastC","PulseR~SystR+DiastR",data=Cardiological.CR) ex.crmdata("Cardiological.CR", package = "iRegression") ex.crm <- crm("PulseC~SystC+DiastC","PulseR~SystR+DiastR",data=Cardiological.CR) ex.crm
Returns the fitted values from an object class bivar.
## S3 method for class 'bivar' fitted(object, ...)## S3 method for class 'bivar' fitted(object, ...)
object |
an object class |
... |
other arguments. |
Fitted values extracted from the object class bivar.
Returns the fitted values from an object class ccrm.
## S3 method for class 'ccrm' fitted(object, ...)## S3 method for class 'ccrm' fitted(object, ...)
object |
an object class |
... |
other arguments. |
Fitted values extracted from the object class object.
Returns the fitted values from an object class cm.
## S3 method for class 'cm' fitted(object, ...)## S3 method for class 'cm' fitted(object, ...)
object |
an object class |
... |
other arguments. |
Fitted values extracted from an object class cm.
Returns the fitted values from an object class crm.
## S3 method for class 'crm' fitted(object, ...)## S3 method for class 'crm' fitted(object, ...)
object |
an object class |
... |
other arguments. |
Fitted values extracted from the object class object.
Returns the fitted values from an object class MinMax.
## S3 method for class 'MinMax' fitted(object, ...)## S3 method for class 'MinMax' fitted(object, ...)
object |
an object class |
... |
other arguments. |
Fitted values extracted from the object class MinMax.
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).
MinMax(formula1, formula2, data, ...)MinMax(formula1, formula2, data, ...)
formula1 |
an object of class " |
formula2 |
an object of class " |
data |
an optional data frame containing the variables in the model. |
... |
other arguments. |
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.
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. |
formula1 must contain the lower limit of the symbolic interval-valued variables. formula2 contain the upper limit of the symbolic interval-valued variables.
Eufrasio de A. Lima Neto [email protected] , Claudio A. V. de Souza Filho and Pedro R. D. Marinho
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.
summary.MinMax, coef.MinMax, fitted.MinMax, residuals.MinMax, formula
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.MinMaxdata("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
print prints its argument.
## S3 method for class 'cm' print(x, ...) ## S3 method for class 'crm' print(x, ...) ## S3 method for class 'ccrm' print(x, ...) ## S3 method for class 'MinMax' print(x, ...) ## S3 method for class 'bivar' print(x, ...) ## S3 method for class 'summary.cm' print(x, ...) ## S3 method for class 'summary.crm' print(x, ...) ## S3 method for class 'summary.ccrm' print(x, ...) ## S3 method for class 'summary.MinMax' print(x, ...) ## S3 method for class 'summary.bivar' print(x, ...) ## S3 method for class 'coef.crm' print(x, ...) ## S3 method for class 'coef.ccrm' print(x, ...) ## S3 method for class 'coef.MinMax' print(x, ...) ## S3 method for class 'coef.bivar' print(x, ...)## S3 method for class 'cm' print(x, ...) ## S3 method for class 'crm' print(x, ...) ## S3 method for class 'ccrm' print(x, ...) ## S3 method for class 'MinMax' print(x, ...) ## S3 method for class 'bivar' print(x, ...) ## S3 method for class 'summary.cm' print(x, ...) ## S3 method for class 'summary.crm' print(x, ...) ## S3 method for class 'summary.ccrm' print(x, ...) ## S3 method for class 'summary.MinMax' print(x, ...) ## S3 method for class 'summary.bivar' print(x, ...) ## S3 method for class 'coef.crm' print(x, ...) ## S3 method for class 'coef.ccrm' print(x, ...) ## S3 method for class 'coef.MinMax' print(x, ...) ## S3 method for class 'coef.bivar' print(x, ...)
x |
an object used to select a method.. |
... |
further arguments passed to or from other methods. |
Returns the residuals from an object class bivar.
## S3 method for class 'bivar' residuals(object, ...)## S3 method for class 'bivar' residuals(object, ...)
object |
an object class |
... |
other arguments. |
Residuals extracted from the object class bivar.
Returns the residuals from an object class ccrm.
## S3 method for class 'ccrm' residuals(object, ...)## S3 method for class 'ccrm' residuals(object, ...)
object |
an object class |
... |
other arguments. |
Residuals extracted from the object class ccrm.
Returns the residuals from an object class cm.
## S3 method for class 'cm' residuals(object, ...)## S3 method for class 'cm' residuals(object, ...)
object |
an object class |
... |
other arguments. |
Residuals extracted from the object class cm.
Returns the residuals from an object class crm.
## S3 method for class 'crm' residuals(object, ...)## S3 method for class 'crm' residuals(object, ...)
object |
an object class |
... |
other arguments. |
Residuals extracted from the object class crm.
Returns the residuals from an object class MinMax.
## S3 method for class 'MinMax' residuals(object, ...)## S3 method for class 'MinMax' residuals(object, ...)
object |
an object class |
... |
other arguments. |
Residuals extracted from the object class MinMax.
A real interval-valued data set.
data("soccer.bivar")data("soccer.bivar")
A data frame containing following variables:
Minimum of the response variable Y (weight)
Minimum of the explanatory variable T1 (height)
Minimum of the explanatory variable T2 (age)
Maximum of the response variable Y (weight)
Maximum of the explanatory variable T1 (height)
Maximum of the explanatory variable T2 (age)
This data set concerns the record of the Weight (Y), Height (T1) and Age (T2) from 20 soccer teams of the premiere French championship.
Lima Neto et. al. (2011)
Lima Neto, E. A., Cordeiro, G. and De Carvalho, F.A.T. (2011). Bivariate symbolic regression models for interval-valued variables. Journal of Statistical Computation and Simulation (Print), 81, 1727–1744.
data("soccer.bivar", package = "iRegression") bivar1 <- bivar(yMin~t1Min+t2Min, "identity", yMax~t1Max+t2Max, "identity", data=soccer.bivar) summary(bivar1)data("soccer.bivar", package = "iRegression") bivar1 <- bivar(yMin~t1Min+t2Min, "identity", yMax~t1Max+t2Max, "identity", data=soccer.bivar) summary(bivar1)
summary method for class bivar.
## S3 method for class 'bivar' summary(object, ...)## S3 method for class 'bivar' summary(object, ...)
object |
an object of class " |
.
... |
other arguments. |
The function summary.bivar returns the following elements, given an object of the class "bivar",
Coefficients1 |
a named vector of coefficients for the explanatory variables of the model "1". |
Coefficients2 |
a named vector of coefficients for the explanatory variables of the model "2". |
RMSE1 |
root mean square error for the model "1". |
RMSE2 |
root mean square error for the model "2". |
Rho |
the estimative for the correlation coefficient between Y1 and Y2. |
Phi |
the estimative of the dispersion parameter. |
D |
the goodness-of-fit measure deviance for the current model. |
Lima Neto, E. A., Cordeiro, G. and De Carvalho, F.A.T. (2011). Bivariate symbolic regression models for interval-valued variables. Journal of Statistical Computation and Simulation (Print), 81, 1727–1744.
##-- Continuing the bivar() example: data("soccer.bivar", package = "iRegression") ex.bivar <- bivar(yMin~t1Min+t2Min, "identity", yMax~t1Max+t2Max, "identity", data=soccer.bivar) ex.sum <- summary(ex.bivar) ex.sum##-- Continuing the bivar() example: data("soccer.bivar", package = "iRegression") ex.bivar <- bivar(yMin~t1Min+t2Min, "identity", yMax~t1Max+t2Max, "identity", data=soccer.bivar) ex.sum <- summary(ex.bivar) ex.sum
summary method for class ccrm.
## S3 method for class 'ccrm' summary(object, ...)## S3 method for class 'ccrm' summary(object, ...)
object |
an object of class " |
... |
other arguments. |
The function summary.ccrm returns the following elements, given an object of the class "ccrm",
Coef.C |
a named vector of coefficients for the Centre explanatory variables. |
Coef.R |
a named vector of coefficients for the Range explanatory variables. |
RMSE.l |
root mean square error for the lower bound. |
RMSE.u |
root mean square error for the upper bound. |
Lima Neto, E.A. and De Carvalho, F.A.T. (2010). Constrained linear regression models for symbolic interval-valued variables. Computational Statistics and Data Analysis, 54, 333–347.
##-- Continuing the ccrm() example: data("Cardiological.CR", package = "iRegression") ex.ccrm <- ccrm(PulseC~SystC+DiastC,PulseR~SystR+DiastR,data=Cardiological.CR) ex.sum <- summary(ex.ccrm) ex.sum##-- Continuing the ccrm() example: data("Cardiological.CR", package = "iRegression") ex.ccrm <- ccrm(PulseC~SystC+DiastC,PulseR~SystR+DiastR,data=Cardiological.CR) ex.sum <- summary(ex.ccrm) ex.sum
summary method for class cm.
## S3 method for class 'cm' summary(object, ...)## S3 method for class 'cm' summary(object, ...)
object |
an object of class " |
... |
other arguments. |
The function summary.cm returns the following elements, given an object of the class "cm",
coefficients |
a named vector of coefficients. |
RMSE.l |
root mean square error for the lower interval bound. |
RMSE.u |
root mean square error for the upper interval bound. |
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.
##-- Continuing the cm() example: data("Cardiological.MinMax", package = "iRegression") ex.cm <- cm(PulseMin~SystMin+DiastMin,PulseMax~SystMax+DiastMax,data=Cardiological.MinMax) ex.sum <- summary(ex.cm) ex.sum##-- Continuing the cm() example: data("Cardiological.MinMax", package = "iRegression") ex.cm <- cm(PulseMin~SystMin+DiastMin,PulseMax~SystMax+DiastMax,data=Cardiological.MinMax) ex.sum <- summary(ex.cm) ex.sum
summary method for class crm.
## S3 method for class 'crm' summary(object, ...)## S3 method for class 'crm' summary(object, ...)
object |
an object of class " |
... |
other arguments. |
The function summary.crm returns the following elements, given an object of the class "crm",
Coef.C |
a named vector of coefficients for the Centre explanatory variables. |
Coef.R |
a named vector of coefficients for the Range explanatory variables. |
RMSE.l |
root mean square error for the lower bound. |
RMSE.u |
root mean square error for the upper bound. |
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.
##-- Continuing the crm() example: data("Cardiological.CR", package = "iRegression") ex.crm <- crm(PulseC~SystC+DiastC,PulseR~SystR+DiastR,data=Cardiological.CR) ex.sum <- summary(ex.crm) ex.sum##-- Continuing the crm() example: data("Cardiological.CR", package = "iRegression") ex.crm <- crm(PulseC~SystC+DiastC,PulseR~SystR+DiastR,data=Cardiological.CR) ex.sum <- summary(ex.crm) ex.sum
summary method for class MinMax.
## S3 method for class 'MinMax' summary(object, ...)## S3 method for class 'MinMax' summary(object, ...)
object |
an object of class " |
.
... |
other arguments. |
The function summary.MinMax returns the following elements, given an object of the class "MinMax",
Coef.L |
a named vector of coefficients for the Min explanatory variables. |
Coef.U |
a named vector of coefficients for the Max explanatory variables. |
RMSE.l |
root mean square error for the lower bound. |
RMSE.u |
root mean square error for the upper bound. |
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.
##-- Continuing the MinMax() example: data("Cardiological.MinMax", package = "iRegression") ex.MinMax <- MinMax(PulseMin~SystMin+DiastMin,PulseMax~SystMax+DiastMax,data=Cardiological.MinMax) ex.sum <- summary(ex.MinMax) ex.sum##-- Continuing the MinMax() example: data("Cardiological.MinMax", package = "iRegression") ex.MinMax <- MinMax(PulseMin~SystMin+DiastMin,PulseMax~SystMax+DiastMax,data=Cardiological.MinMax) ex.sum <- summary(ex.MinMax) ex.sum