Learn R Programming

linLIR (version 1.0-1)

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 all slope values in a given range.

Usage

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

undom.para(dat, b.range, b.extra = 0, b.grid = 1000, 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 errors considered.
b.range
Considered interval of slope values.
b.extra
If it is likely that the set of undominated regression parameters is unbounded, one can consider very small or large values in addition to the b.range.
b.grid
1/b.grid is the width between two points of the considered grid of slope values within b.range.

Value

  • The undom.a-function returns a list of 2 components:
  • result1A 2-column matrix of possibly degenerate intervals for the undominated intercept values associated with the given slope b.
  • result2The information of result1 reduced to the fewest intervals possible.
  • The undom.para-function returns a list of 3 components:
  • a.undomRange of intercept values of the undominated regression lines.
  • b.undomRange of slope values of the undominated regression lines.
  • undom.paraA matrix of undominated parameter combinations approximating the entire set of parameters corresponding to the set of undominated regression lines.

References

A. Wiencierz, M. Cattaneo (2012). An exact algorithm for Likelihood-based Imprecise Regression in the case of simple linear regression with interval data. (Accepted for the 6th International Conference on Soft Methods in Probability and Statistics (SMPS 2012). Publication in the series Advances in Intelligent and Soft Computing. Springer-Verlag.) M. Cattaneo, A. Wiencierz (2012). Likelihood-based Imprecise Regression. (Accepted for publication in the International Journal of Approximate Reasoning. A preliminary version of the paper is available as a research report at: http://epub.ub.uni-muenchen.de/12450/.)

See Also

s.linlir, gen.lms, kl.ku