Confidence Intervals for Ratios of Linear Functions of Mixed Models with Reference to Animal Breeding Data

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Abstract
Mixed linear models are widely used in animal breeding experiments from which estimates of ratios are desired. This paper presents methods for the development of exact confidence intervals for ratios of linear functions of fixed effects in mixed models. Approximate confidence intervals for ratios involving random effects can also be obtained by these methods. Additional problems considered include pooled ratio estimation from multiple data sets with constant variance and the case of unequal error variance with two sources of heterogeneity. Confidence intervals obtained here are expected to be larger than those based on approximations of the variance of a ratio through Taylor's series, since the latter underestimate the true variance under certain conditions. Copyright © 1980. American Society of Animal Science . Copyright 1980 by American Society of Animal Science

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