Selection bias: Suppose the normal linear model ????i = ????0 + ????1xi holds with ????1 > 0,
Question:
Selection bias: Suppose the normal linear model ????i = ????0 + ????1xi holds with
????1 > 0, but the responses are truncated and we observe yi only when yi > L
(or perhaps only when yi < L) for some threshold L.
a. Describe a practical scenario for which this could happen. How would you expect the truncation to affect ????̂
1 and s? Illustrate by sketching a graph.
(You could check this with data, such as by fitting the model in Section 3.4.1 only to house sales having yi > 150.)
b. Construct a likelihood function with the conditional distribution of y, to enable consistent estimation of ????. (See Amemiya (1984) for a survey of modeling with truncated or censored data. In R, see the truncreg package.)
Step by Step Answer:
Foundations Of Linear And Generalized Linear Models
ISBN: 9781118730034
1st Edition
Authors: Alan Agresti