Models For Bivariate Data Research Articles

On estimating a transformation correlation coefficient

We consider a semiparametric and a parametric transformation-to-normality model for bivariate data. After an unstructured or structured monotone transformation of the measurement scales, the measurements are assumed to have a bivariate normal distribution with correlation coefficient 𝜌 , here termed the 'transformation correlation coefficient'. Under the semiparametric model with unstructured transformation, the principle of invariance leads to basing inference on the marginal ranks. The resulting rank-based likelihood function of 𝜌 is maximized via a Monte Carlo procedure. Under the parametric model, we consider Box-Cox type transformations and maximize the likelihood of 𝜌 along with the nuisance parameters. Efficiencies of competing methods are reported, both theoretically and by simulations. The methods are illustrated on a real-data example.

Linear Mixtures: A New Approach to Bivariate Trend Lines

Abstract This article describes a new, biologically motivated model for bivariate data containing a trend line. The model is characterized by a mixture in which the component means lie on a line. Consistent methods for estimating the parameters of the mixture line are derived, as are procedures for obtaining a confidence interval for the slope. The methods are proved valid within a large class of models for bivariate data, including an errors-invariables model, and are illustrated with data on Canadian herring. This work provides one possible objective resolution of a (sometimes heated) debate in allometry and elsewhere on how to define and estimate a linear trend through bivariate data from a natural population.