[Clyde Schechter]

I'm not sure what to tell you. I may not fully understand the way your supervisor is using terminology, but to the extent that I do, I would disagree with the advice given regarding #1. Doing four separate analyses like that is OK, but still, none of those analyses will shed light on hypotheses H2 or H3; in fact you will still end up with separate conclusions for H2 depending on whether or not the successor is an outsider, and separate conclusions for H3 depending on whether the departure of the CEO is forced. So, to that extent, your supervisor is agreeing with me, though suggesting a different approach that may give somewhat different results. Fair enough. Either way, you still get no answers for H2 and H3.

Regarding #2,

Not exactly. Interaction alone here is not directly interpretable. Rather, FORCED+OUTSIDE+INTERACTION (sum of coefficients) shows the effect for the forced&outside turnover, relative to all the other.

That's just wrong. FORCED+OUTSIDE_INTERACTION shows the difference in expected outcome from forced & outside turnover relative to voluntary & inside turnover.

voluntary internal is the baseline about which you cannot say much in from this test.

You can't say anything about it directly from the regression output, but the expected outcome for this condition is shown in the -margins- output.

These tests give you an insight to differences among turnovers. You can do simple pre-post tests (maybe simply ttests) on subsamples for:
- voluntary inside
- voluntary outside
- forced inside
- forced outside
Then you would have insight not only about the differences between groups (current results), but also changes in groups."

The advice your supervisor gives here, as I understand it, is the same as in #1: do four separate analyses. My reaction to it is the same.

Regarding #3

"I am not sure why you want to do this at all."

I am not sure why your supervisor says this. The marginal effects are the differences in outcome associated with the different conditions. Why would one analyze data on forced/voluntary and outsider/insider turnovers and not ask questions like "what is the effect of having an insider successor after a forced turnover compared to an outsider successor after a forced turnover?" That is the kind of question that the marginal effects analysis answers. If that's not what they are interested in, why analyze this data at all? It seems to me that when a firm decides to do a forced turnover, they would also want to contemplate who might be the successor and make a decision about seeking an insider or outsider based on what they could expect in terms of impact of that decision on future firm performance. Look, I don't work in the business world; I'm an academic epidemiologist--but this just strikes me as common sense. I really having a hard time imagining why one would analyze this kind of data if not to ask this kind of question.

So it seems your supervisor and I are at odds here (or perhaps I am misinterpreting your supervisor). At the end of the day, you work for your supervisor, not for me. I have tried to explain my reasoning on several occasions in this thread. Evidently it has not convinced you, and if you have shown it to your supervisor, it has not convinced him or her either. I can't think of a better, more persuasive way to explain what I think about this. So, I think you should follow your supervisor's advice and move forward with your project accordingly. I hope that you have nonetheless learned something from what I have said, and perhaps in future situations, in a different environment, you will be able to apply some of that knowledge.

[Carl-Johan Andersson]

Many thanks for your insights - I really appreciate hearing your arguments and I have certainly learnt a lot from them. I'm sorry if you think I ask too many questions, I'm just trying to form my understanding of things.

I agree on many things you point out. I will not proceed with H2 and H3 but rather formulate a hypothesis on the conditional effect.
- What I'm struggling with right now is the distinction she does between "the difference in effect between the different turnover types" and "the level changes". Isn't the expected outcome we have been discussing from the marginal effects analysis the same thing as a "level change"?

- She adds this: "Marginal effects analysis is used to better evaluate the size of the effect. That is, if your method allows you to evaluate the differences, then the marginal effects analysis will do exactly the same, only the size of the effect will be easier to interpret (sort of)."

- On your remark that she is "suggesting a different approach that may give somewhat different results" - why would we expect the results to be different from a multivariate regression on the subsamples?

Thanks!

[Clyde Schechter]

I do not think you ask too many questions. It is clear to me that you are earnestly trying to get a clear and complete understanding of what you are doing, and I respect and honor that. If I thought you ask too many questions, I would stop answering them. (N.B. While I post on the Forum most days, there are sometimes days when I don't have the time--and my schedule is going to get busier for a while over the next few weeks. So if I don't respond to something you post for one or a few days, don't interpret that as dissatisfaction with your questions--first check and see if I am posting at all during that time.)

- What I'm struggling with right now is the distinction she does between "the difference in effect between the different turnover types" and "the level changes". Isn't the expected outcome we have been discussing from the marginal effects analysis the same thing as a "level change"?

Yes, it is, at least as I understand these terms. When I alluded to my possibly not understanding her use of terminology, I had precisely this in mind--she is using terminology in a way that implies that they are different, and, to me, they are not.

She adds this: "Marginal effects analysis is used to better evaluate the size of the effect. That is, if your method allows you to evaluate the differences, then the marginal effects analysis will do exactly the same, only the size of the effect will be easier to interpret (sort of).

Sizes of effects can sometimes be understood directly from regression output--particularly if the regression is linear and involves no interaction terms. Then the coefficients are the same as the marginal effects. In linear models containing interaction terms, the coefficients are no longer the same as the marginal effects--the "main effect" coefficients become conditional marginal effects, certain other conditional marginal effects do not appear directly as coefficients and need to be calculated from them, and the interaction term is a difference between marginal effects. So the use of -margins, dydx()- makes life simpler by calculating all the relevant marginal effects directly, and in an error-proof way. Finally, there is the situation with non-linear models in which the coefficients are much more distantly related to the marginal effects (and sometimes, for practical purposes, unrelated to them), and then only the -margins, dydx()- command (or, in effect, writing your own code that emulates that command) will get them for you. So, again, I have the sense that her use of terminology is a bit off, or at least is different from my own understanding of it.

On your remark that she is "suggesting a different approach that may give somewhat different results" - why would we expect the results to be different from a multivariate regression on the subsamples?

There are two separate issues, one of which can be papered over, and the other cannot.

The first reason is that in the interaction model we have been discussing up to now, any other variables in the model are inherently constrained to have the same effect regardless of the values of FORCED and OUTSIDE. When you do four subset analyses, the effects of any other variables will be estimated separately in each subset, and, in general, the results will be somewhat different, with some of the difference spilling over into the coefficients of FORCED and OUTSIDE as well. Now, to be honest, we haven't revisited the regression code recently, and I don't remember clearly what these other variables in the model are, or even if there are any at all. If there aren't any, then this issue does not bite. If there are some, then the interaction model coefficients can be brought into alignment with those of the four separate models by extending the interaction to cover the other variables. That is, one could write -regress i.FORCED##i.OUTSIDE##(list the other variables here using factor variable notation to distinguish i.discrete from c.continuous)-. With this extension of the interaction will result in an interaction regression whose marginal effects are the same (except perhaps tiny rounding errors) as the coefficients you get in the four separate models. That is how this difference is papered over.

But there is another difference that cannot be gotten around. The interaction model is run on the entire data sample, so its sample size is larger than the sample sizes of the four subset models. In fact, at least one of the subset models must be one-fourth or less the size of the interaction model. Consequently, the standard errors in the interaction model will generally be smaller (about half the size) than the corresponding standard errors in the subset models. This in turn means that the interaction model will have narrower confidence intervals, larger test statistics, and smaller p-values than the subset models. In most situations this is considered to be a reason to prefer the interaction model.

[Carl-Johan Andersson]

Once again, your help is greatly appreciated.

I just had a call with my supervisor and it was indeed a bit of a misunderstanding.
We agreed that many of your remarks were both correct and relevant for how the study should proceed.

Many thanks for taking the time to give me a clearer understanding.