[Mostafa Harakeh]

Hi Clyde,

Thank you so much for explaining Joseph's code for me. Now things make much more sense. I was able to apply the code to the original dataset I have. The inferences are similar (not identical) to those obtained by Joseph. I think that the reason for this is that the variable (X) is normally distributed.

Kindly, I have a few more questions please:

1) Can we use your bootstrapping approach(post #6) by these 4 time-group sub-samples (i.e. i.group##i.time)? That is, can the re-sampling take place in each of these 4 sub-samples separately?

2) Is the "mixed" model a generally accepted approach in this setting? I mean is there any credible reference which I can cite in my PhD thesis?

3) If I got you correctly, you meant that the _b[whatever]'s are the estimates stored in memory after running the -mixed- command and I do not necessarily need to understand the meaning of these _b[whatever]'s?

4) Do you agree on the following as a description for Joseph's approach:
We test the statistical difference between the variance ratios before and after the treatment by fitting a mixed linear model to the final data sample. Specifically, the mixed linear regression runs a random effects regression of the dependent variable on the time dummy, the group dummy and the interaction term. In this way, the mixed linear model clusters the sample into 4 sub-samples: (group=0 & time=0), (group=1 & time=0), (group=0 & time=1) and (group=1 & time=1). Then, the mixed linear model estimates the variance of the dependent variable in each sub-sample and calculates the standard deviation for each variance. Next, we calculate the variance ratios (pre- and post-treatment) through utilising a non-linear combination of estimators that uses the delta method. Finally, we test the difference between both ratios using the Chi-squared statistic.

Thank you for your time and effort, Clyde. I truly appreciate it.

Mostafa

[Clyde Schechter]

1. Yes, the bootstrap command has a -strata()- option. You would need to first create a variable that indicates those four strata: -egen combination = group(group time)- and then specify -strata()- combination as an option to -bootstrap-.

2. I have not seen it used for this purpose before and I can't give you a reference. But I don't think anybody who understands how it works would have a problem with it.

3. Yes. What I really meant is that there is not much point to learning the actual names of these whatevers. What matters is to understand that they can be used to calculate the variances in the four groups.

4. Pretty much. I wouldn't use the word "clusters." I would say "partitions" or "disaggregates" or something like that. The word cluster has other meaning(s) in statistics.

[Mostafa Harakeh]

Dear Clyde,

I don't know how I can thank you.

You have always offered me a big helping hand whenever was needed.

I wish you all the best.

Mostafa