imcmuni: MCM for Interval-Valued Data Regression Using Uniform...
In jjt7549/intervalreg: Regression for Interval-valued Data

Description Usage Arguments Details Value Note References See Also Examples

imcmuni() is used to fit a linear regression model based on the Monte Carlo Method using uniform distribution.

1	imcmuni(formula = formula, data = data, b = 100)

`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.
`b`	number of resampling (default : 100)

Ahn et al.(2012) propose a regression approach for interval-valued data based on resampling. So this method is to resample by randomly selecting a single-valued point within each observed intervals. Then, fit a classical linear regression model on each single-valued points, and calculate the average of regression coefficients over the models. The use of the resampling approach method, called Monte Carlo method (MCM), has the advantage of estimating on sample distribution approximately, and statistical inference is possible using this.

`resampling.coefficients`	B coefficient vectors obtained by resampling.
`coefficients`	Average of B coefficients obtained by resampling, standard error and p-value.
`fitted.values`	The fitted values for the lower and upper interval bound.
`residuals`	The residuals for the lower and upper interval bound.

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.

Ahn, J., Peng, M., Park, C., Jeon, Y.(2012), A Resampling Approach for Interval-Valued Data Regression. Statistical Analysis and Data Mining, 5, 336-348

RMSE symbolic.r

data(example3)
m1 <- imcmuni(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, b = 100)
m1
m1$coefficients