潇湘渌水 @ 2010-06-27 17:26
Hand and Taylor (1987) provide a good summary:
"In general, when one is presented with measurements taken at two time points there are several ways in which the analysis may be approached, the the most obvious are either to work with difference scores or to use the first occasion's measurements as covariates in analysing the second. These two approaches can yield different results -- a fact which has led to some confusion in the past (and has been given the name of Lord's paradox). The reason that the results can differ is simply that the two approaches are asking different questions. This is most easily illustrated in the simple two-group comparison case; that is, we have two groups of subjects, each measured at two time points, and we wish to compare the changes the two groups experience. Then the difference-score approach enquires whether there is a difference in average change of the two populations. The covariance approach asks whether a member of group 1 is expected to change more than a member of group 2, given that they have the same initial value. It is this final question that distinguishes the questions." [p. 166]
The critical issue is then to understand which 'statistical question' addresses which 'scientific question'? The answer often hinges on the causal position of the first measurement. If it is a potential 'confounder' or covariate not affected by group membership, then it is correct to use it as a covariate. If it is a 'mediator' or a partial mediator, then the question is more complex. Different models may answer different scientific questions.
residualized change model（covariance approach, ANCOVA，不适合observational study，因为一开始的起点可能因为其它没观测的变量 (unobserved variables) 而影响），如果是 residualized change model，那你问的问题是：当控制了一开始的经验之后，在第一组的人是否比第二组的人改变更多。
如果是随机分组并在干预前作了 pre-test，这时候用 residualized change score 比较合适。PS：读到这篇后，感受是实验干预的统计学和经济学中常用的计量方法有很大差别。最后感谢研究生2.0
