undom: Finding undominated parameters
In linLIR: linear Likelihood-based Imprecise Regression

Description Usage Arguments Details Value References See Also

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.

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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)

`dat`	An `n`x4 `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.

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).

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.

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.

s.linlir, gen.lms, kl.ku

linLIR documentation built on May 2, 2019, 4:47 p.m.