SCM: Symbolic Covariance Method

In jjt7549/intervalreg: Regression for Interval-valued Data

Description

SCM() is used to fit a linear regression model based on symbolic covariance matrix(Xu, 2010).

Usage

SCM(formula = formula, data = data)

Arguments

formula	an object of class formula, a symbolic description of the model to be fitted.
data	an data frame containing the variables in the model.

Details

The SCM proposed by Xu(2010) is a method of estimating a regression coefficient using a symbolic covariance matrix. In SCM, the centralized linear regression model is used(model with centered variables). The regression coefficient is estimated by least squares method, but it is used by symbolic covariance matrix. Because the process of calculating the symbolic sample covariance uses the lower and upper limits of each variable, the SCM reflects the variability of the interval.

Value

symbolic.covariance.Sxx	Symbolic sample variance-covariance matrix between response variable Y and predictor variables X.
symbolic.covariance.Sxy	Symbolic sample covariance vector between response variable Y and predictor variables X
coefficients	regression coefficients
fitted.values	The fitted values for the lower and upper interval bound.
residuals	The residuals for the lower and upper interval bound.

Note

In dataset, a pair of the interval variables should always be composed in order from lower to upper bound. In order to apply this function, the data should be composed as follows:

y_L	y_U	x1_L	x1_U	x2_L	x2_U
y_L1	y_U1	x_L11	x_U11	x_L12	x_U12
y_L2	y_U2	x_L21	x_U21	x_L22	x_U22
y_L3	y_U3	x_L31	x_U31	x_L32	x_U32
y_L4	y_U4	x_L41	x_U41	x_L42	x_U42
y_L5	y_U5	x_L51	x_U51	x_L52	x_U52

The upper limit value of the variable should be unconditionally greater than the lower limit value. Otherwise, it will be output as NA or NAN, and the value can not be generated.

References

Xu, W.(2010), Symbolic Data Analysis: Interval-Valued Data Regression

See Also

RMSE symbolic.r

Examples

data(example3)
m1 <- SCM(cbind(Sepal.Length_L, Sepal.Length_U) ~ Sepal.Width_L + Sepal.Width_U + Petal.Length_L + Petal.Length_U + Petal.Length_L + Petal.Length_U, data = example3)
m1
m1$coefficients

jjt7549/intervalreg documentation built on May 19, 2019, 11:40 a.m.