An empirical evaluation of coefficients used in residual and allometric adjustment of size covariation

Univariate computation of residuals or allometric variates should be used to estimate the shape of body parts of ectothermic vertebrates. For studies involving more than one group, three types of relationships may be used to calculate the slopes or allometric coefficients necessary for computing the shape variate: pooled group, common-within groups, and individual-within groups. For both residuals and allometric variates, the pooled and common-within groups coefficients resulted in similar estimates of shape when there was no between-group heterogeneity in relationships. Within-group coefficients resulted in quite different estimates of shape. Heterogeneity of slopes or allometric coefficients resulted in different estimates of shape for the same individual for pooled common-within and within-groups data. Such differences in the shape variates were cumulative in subsequent analyses such that considerably different biological interpretations of group interrelationships resulted. Thus, if any between-group heterogeneity exists in regression or allometric relationships, it is imperative that shape be estimated from the common-within groups relationship.