Linear Mixtures: A New Approach to Bivariate Trend Lines
提出一种受生物学启发的双变量数据趋势线模型，通过混合分布中成分均值位于一条直线来刻画，并给出参数估计和斜率置信区间方法，适用于含测量误差的模型，以加拿大鲱鱼数据为例。
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.