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Non‐nested linear models: A conditional confidence approach
Author(s) -
Fraser D. A. S.,
Gebotys R. J.
Publication year - 1987
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.2307/3315256
Subject(s) - mathematics , confidence interval , dimension (graph theory) , statistics , variance components , sign (mathematics) , humanities , combinatorics , mathematical analysis , philosophy
The comparison of nested linear models with normal error is well standardized in the common procedures of the analysis of variance. This article considers the comparison of two non‐nested linear models that have the same parameter dimension; the comparison is made on the assumption that the true mean lies somewhere in the linear span of the two models. The analysis leads to a precision‐based conditional confidence interval for the unsigned angular direction of the true mean, and this in turn provides a confidence assessment of the two directions that correspond to the two models being compared. The confidence interval is an approximate conditional interval (given the distance of the estimate from the intersection of the hypotheses), and its length as a fraction of π indicates the precision of the confidence procedure. The method provides a conditional‐inference alternative to a confidence interval available by Creasy‐Fieller analysis.