Marginal effects and standardized coefficients after xtgee

[Robbie Dembo]

Hi there,

I am new to the forum. Hopefully I am posting correctly!

I am running a model with xtgee. It includes an interaction, and I'd like to use margins to interpret the results. However, because one of the variables in the interaction does not have a natural unit (it is a scale), I would also like to standardize that predictor. (Incidentally, it appears that the listcoef, help command does not work after an xtgee model). My question is: can I run the margins command to compute marginal effects if I use a standardized version of the variable (using egen std). In other words, does it make any sense to have a marginal effect of a standardized variable? I anticipate an interpretation along the lines of "the marginal effect of a unit increase in x", for which x has been standardized. But I don't know if that makes substantive sense.

Code:
xtgee y i.x1##c.zx2 x3...xn, i(id) corr(exch) robust

mtable, dydx(zx2) at(x1=(0 1))

where "zx2" is the standardized version of x2.

Many thanks,
Robbie Dembo

[Clyde Schechter]

Yes, you can do this. The interpretation would be that you have the rate of change in y per 1 standard deviation change in x2, and I would say it that way.

Now, this is really only meaningful to do if the original units of x2 are truly meaningless. Remember that nobody will know what 1 standard deviation of x2 means. So this is harmful and obfuscatory unless nobody would know what a 1 unit change of x2 is either.

It is not really true that a scale lacks a natural unit. The natural unit of a scale is the number of endorsed responses (or perhaps some weighted count of endorsed responses). When a scale has achieved wide-spread use, everybody has a sense of what 1 unit in the scale means. For example, everybody understands that a 1 point increase in score on the PHQ-8 is a moderate increase, but that a 1 point increase in score the PCL is pretty small, if only because of the number of items in each scale. People usually don't standardize these variables when using them or reporting analyses. If your scale is new, at least relatively speaking, then people won't have much sense of that, so whether you use the natural units or the standardized units won't make much difference in understandability: both will be unfamiliar. But it is hard to argue that the standardized version is actually better. If nothing else, the standardized scores are calculated relative to the standard deviation in your sample, so they are not really replicable.

[Robbie Dembo]

Thank you Clyde. I certainly don't want to do something that is harmful or obfuscatory.

Just as a follow-up, and perhaps to provide more context: would using standardized variables be more appropriate if one is running several models, each considering the effects of different scales, and thus allowing for a consistent interpretation across models (e.g. a standard deviation change in scale 1 is associated with..., a standard deviation in scale 2 is associated with.., a standard deviation in scale 3 is associated with...). In this case, I have a model with a scale for emotion-focused coping, a model with a scale for problem-focused coping, and a model with a scale for perceived control. While a change in the natural unit could be used to interpret the effects of each scale, it seems like if the scales are composed of different questions and have different ranges, then perhaps it makes sense to standardize?

Thank you in advance for your insights.

[Clyde Schechter]

would using standardized variables be more appropriate if one is running several models, each considering the effects of different scales, and thus allowing for a consistent interpretation across models (e.g. a standard deviation change in scale 1 is associated with..., a standard deviation in scale 2 is associated with.., a standard deviation in scale 3 is associated with...)

Well, this is the context in which standardization is most frequently used, I think. You will certainly see a lot of this in the mental health literature, and to some extent in other disciplines as well. The idea is that the measurements are all on the same scale so that comparisons of their coefficients can be consistently interpreted.

In my opinion, however, this notion is illusory. If all of these measures strictly followed normal distributions, you could make this case for standardizing. But real life is typically not that clean. If one scale is, say, normal, and another is skew left, and another skew right, and maybe another has a sharp ceiling or floor effect, then these comparisons, despite standardization to mean zero and standard deviation 1 are by no means sensible; they are not apples to apples. The notion that a 1 sd change means the same thing from one measure to the next is only coherent if the shapes of the distributions are identical, which, in real life, they seldom are.

Of course, the inverse notion, that unit increases in different scales are not comparable is quite true. The problem is that, standardization creates only the illusion, not the reality, of solving the problem. Indeed, in my considered opinion, this is a problem that simply has no solution, and the quest for one is futile.

Evidently you are working in the mental health field, and I don't want to push you to try to swim upstream here. You will get resistance, and I would almost bet that if you don't standardize the variables, some editor or reviewer or advisor will say you should. But, in my opinion, that is just testimony to the extent of misunderstanding and misinformation that prevails out there.

This issue is probably not the hill you would choose to die on, and you have to present your findings in ways that your audience thinks they understand. If you do proceed with standardized analysis of variables with different shaped distributions, I hope you will just tuck away in a corner of your mind the observation that it sweeps the problem of incomparability under the rug, rather than acknowledging it. And perhaps some day when you are in a secure enough position to insist on doing things correctly, rather than conventionally, you will remember it.

[Robbie Dembo]

Thanks again, Clyde. Your argument makes intuitive sense, especially when considering the likely differences in the distributions of the scales. And yes, your career advice is well taken too. My experience is that, unfortauntely, graduate school does not lend itself to pushing the boundaries of convention too much.