linLIR (version 1.1)

undom: Finding undominated parameters

Description

Functions within the s.linlir-function that determine the parameter combinations corresponding to undominated regression lines. The undom.a-function finds the set of undominated intercept values associated with a given slope and the undom.para-function finds the set of undominated intercept values associated with a given vector of slope values.

Usage

undom.a(dat, b, q.lrm, p = 0.5, bet, epsilon = 0)
undom.para(dat, b.range, a.grid = 100, q.lrm, p = 0.5, bet, epsilon = 0)

Arguments

dat

An nx4 data.frame containing the imprecise data of the analyzed variables. Columns 1 and 2 correspond to the interval-valued observations of the regressor variable, columns 3 and 4 to those of the dependent variable.

b

A given value for the slope of a regression line.

q.lrm

Value of the p-quantile of the absolute residuals associated with the LRM line(s).

p

Quantile of the abolute residuals' distribution to be used as loss function in the LIR analysis. (0.5 corresponds to the median.)

bet

Cutoff-point for the normalized profile likelihood function.

epsilon

Fraction of coarsening errors considered.

b.range

Vector of slope values handed over to the function undom.para.

a.grid

Particular parameter of the function undom.para indicating how fine the set of undominated parameter combinations is approximated with respect to the intercept values.

Value

The undom.a-function returns a list of 2 components:

result1

A 2-column matrix of possibly degenerate intervals for the undominated intercept values associated with the given slope b.

result2

The information of result1 reduced to the fewest intervals possible.

The undom.para-function returns a list of 3 components:

a.undom

Range of intercept values of the undominated regression lines.

b.undom

Range of slope values of the undominated regression lines.

undom.para

A matrix of undominated parameter combinations approximating the entire set of parameters corresponding to the set of undominated regression lines.

Details

The undom.para-function together with some preparational steps in the s.linlir-function implement the second part of the exact algorithm for the simple linear LIR analysis with interval data developed in M. Cattaneo, A. Wiencierz (2012c).

References

M. Cattaneo, A. Wiencierz (2012c). On the implementation of LIR: the case of simple linear regression with interval data. Technical Report No. 127. Department of Statistics. LMU Munich.

A. Wiencierz, M. Cattaneo (2012b). An exact algorithm for Likelihood-based Imprecise Regression in the case of simple linear regression with interval data. In: R. Kruse et al. (Eds.). Advances in Intelligent Systems and Computing. Vol. 190. Springer. pp. 293-301.

M. Cattaneo, A. Wiencierz (2012a). Likelihood-based Imprecise Regression. International Journal of Approximate Reasoning. Vol. 53. pp. 1137-1154.

See Also

s.linlir, gen.lms, kl.ku