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Yibi Huang

2008-08-26
13:30:00 - 15:00:00

Potential sampling bias of regression models and evolving population models

308 , Mathematics Research Center Building (ori. New Math. Bldg.)

In a regression model, the joint distributionfor each finite sample of units is determined by a function f_x(y) depending only on the list of covariate values x = (x(u_1), x(u_2),...,x(u_n)) on the sampled units (u_1,u_2,...,u_n). Often it is implicitly assumed that the population is fixed. However, in biological work, random population is usually unavoidable, in which case the joint distribution p(y,x) depends on the sampling scheme. The conditional distribution p(y|x) might not agree with p_x(y), the distribution of y in a fixed sample with a non-random configuration x. A model that avoids the concept of a fixed populaon of units is proposed. In this model, the sampling distribution of (x, y)will very with the sampling plan. For some specific sampling scheme, the sampling distribution agrees with the standard logistic model with correlated components. For others the conditional distribution p(y|x) is not the sample as the regression distribution unless p_x(y) has independent components.