AME or MEM for continuous and binary variables.

[Jakob Berggreen]

Hi

So I am writing a paper where I am supposed to use AME or MEM on a fixed effect logit model. But I have come to a conclusion where I am a bit confused whether to use AME or MEM on the variables.
As I understand it I should not be using a lot of mental resources as the differences are not big and the AME is often used as a default, but here my questions come anyway.
I'm researching a regression where I both have multiple continuous and binary variables.
But it seems like a lot of people is using AME on continuous variables but MEM on the binary variables? Is this the correct understanding?

Furthermore, isn't it weird to use 2 different approaches to analyse the same regression?

Lastly, should I be concerned whether I use AME or MEM besides there is different understanding of the numbers. Is there any warning signs when to use what or where?

Hope anybody can help me with this and thank you in advance.

[Clyde Schechter]

I would not use AME for some variables and MEM for others in the same regression unless the research question posed specifically requires you to do that.

Moreover, it sounds like you want to compute AME or MEM for every variable in your regression. But why are you doing that? In most situations, there are a few key variables whose effects you are trying to estimate, and the others are just covariates ("control variables") that are included only to reduce omitted variable bias (confounding). There is no reason to calculate any marginal effect for the latter group of variables--by definition, you don't care about them and you include them only because you must adjust for their nuisance effects.

As between AME and MEM, they are different things. The AME is an average marginal effect: it is the average value of the marginal effect, averaged over all the values of the variable, and with all other variables held at their observed values. As such it does not represent the actual marginal effect of the variable under any particular circumstance. (Indeed, very rarely, the AME might not even correspond to the actual ME at any real-world possible values.) Nevertheless, it is often a handy way to think about a variable's effect because it does not privilege any particular value of the variable. And, though this is not guaranteed, it is often fairly typical of the MEs of the variable at "typical" values of the variable. By contrast, the MEM privileges the mean value of the variable and calculates the marginal effect of the variable at that specific value. As you noted, typically the two are fairly close to each other. But that is not guaranteed, and if they differ, which you will prefer depends on how you wish to use your results. If the mean value of the variable looms large in real-world applications of your model, then the MEM would be the way to go. On the other hand, if real-world applications of your model have a great deal of variation in the values that that variable takes on, the AME is going to be more similar to the overall observed effect.

[Jakob Berggreen]

#2 Thank you a lot for that answer, it was really helpful.

The reason why we are not just doing it on a single variable, is due to limited space. We can only provide 1 table, which is why we find it more relevant to present all variables with the marginal effect, beside providing a table with some being slope coefficients and others being marginal effects. This is to not confuse the reader to much.

Another question i stumbled upon is regarding the constant term. Is it possible to calculate the marginal effects for a constant term? I see authors leaving it out reasoning that it is a nuance parameter. I just tried at bit with the "margins, dydx(*)" command, and it does not seem like I get any numbers. Is this due to it not being possible?

[Felix Bittmann]

This information might also be useful: https://www3.nd.edu/~rwilliam/stats/Margins01.pdf

Regarding the question about constant terms: no, there is no AME for this term. An AME is an effect, that is a difference between groups. In a regression, the constant is the predicted value when all other variables in the model are set to 0. Think about the most simple case, an OLS regression model where all independent variables are continuous and mean-centered. Here, the constant is the outcome for the "average" case, where all predictors are at their means. This is not an effect but an average.

[Jakob Berggreen]

#4 Thank you for that.

Cool, makes perfect sense.

Then I have a couple of more questions and these should be the last (I hope so). I want to present a table where the marginal effects are shown. So I have looked through different articles and seen that people present the marginal effect and then p-value in parentheses. What kind of p-value should be shown here? Since there is difference in what is being researched, it would intuitively makes sense to present the p-value that is related to the number. But these might not be significant, where as the slope coefficient is significant. Is this just unfortunate then? I can only present 1 table so i am restricted to only provide few data.

Furthermore, I have in the same table some simple regressions where I am not researching the marginal effect and instead the slope coefficients are shown. To make it as intuitively and correct as possible, should I then show the same numbers in parentheses instead (often std. error), or is it okay show different values as long as it has a descriptive text for the table.

Hope somebody has some experience with this, as it should be included in a paper.

Thanks in advance.

[Clyde Schechter]

I think it would be confusing to show p-values in parentheses for some parts of the table but standard errors in parentheses for others, even if you explain in the accompanying text or notes that this is what is done. It would be cruel to the readers of your paper to place that kind of obstacle to understanding in their path. I have a couple of suggestions:

1. I can't think of a good reason for using p-values in some places and standard errors in others in the first place. In fact, in my own work, I hardly ever use p-values at all--I use standard errors or confidence intervals. These are much more informative than p-values in any case. So why not do standard errors (or confidence intervals) throughout?
2. But assuming you feel compelled to use both p-values and standard errors, why not show both for everything?
3. Or if you think suggestion 2 will make the table too cluttered, why not use ordinary parentheses, (), for p-values and square brackets, [ ], for the standard errors (or the other way around)?

I'm guessing that this paper is some kind of brief report, not a full research paper. If it is a full research paper, I don't understand why you would be limited to just one table: I have never encountered that in my entire 35+ year research career. Nor have I ever seen a project so minimalist in scope that a full research paper could be written with just one table and make an adequate presentation of methods and results. In short, I wouldn't submit a full research paper to a journal that had such an unreasonable restriction.

[Jakob Berggreen]

#6 I do agree on your point with it being confusing. I have just seen some papers do it, and therefore I thought it would be realistic to do some with p-values and some without.

1. This is also a discussion we are having right now. As this is not my daily work, I choose to be inspired through articles I have read and learn from those. Normally I also see all articles with std. error, there has just been a few where they show p-values when they provide marginal effects. What is correct or wrong, I actually have no idea about. But I will take your point with me.
2. & 3. True, atm. I am not compelled to anything in this regard. But I actually don't think we have the space for it (I will explain below why). But the idea is good, and if I figure out a way to fit both, this might be the way to show it instead. First I think we need to discuss what to show in the parentheses, so we are sure it is the correct numbers.

So I just finished my master degree, and wanted to publish it with my supervisor, so he is the guy that knows about the different options. But as of what I know the reason why we are limited, is due to a restricted amount of words and pages that they use in their research paper. So this is actually a research paper but it is limited. So we are trying to fit everything in to a single table on 1 page. We do have other tables as well (I might have expressed it wrong earlier then), but for this part of the paper we only want 1 table on 1 page. Hopes it make sense and thank you a lot for your input.