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Likelihood ratio tests are derived for bivariate normal structural relationships in the presence of group structure. These tests may also be applied to less restrictive models where only errors are assumed to be normally distributed. Tests for a common slope amongst those from several datasets are derived for three different cases – when the assumed ratio of error variances is the same across datasets and either known or unknown, and when the standardised major axis model is used. Estimation of the slope in the case where the ratio of error variances is unknown could be considered as a maximum likelihood grouping method. The derivations are accompanied by some small sample simulations, and the tests are applied to data arising from work on seed allometry.
Warton et al. (Fri,) studied this question.