Hi. With stata and margins you can do it if you fix your random effects at zero, their theoretical mean. Just add the option "predict(mu fixedonly)". For example, if you are interested in the marg. effect of X on Y and X is interacted with Z, a level-2 vble, and both vbles are continuous, you could write:

margins, dydx(X) at(X=(-1.5(.5)1.5) Z = (-1.5, 0, 1.5) (mean) _all) predict(mu fixedonly)

so you get the marg. effects for that combinations of values of X and Z (where 1.5, etc. are values of interest for my imaginary vbles). The option "(mean)_all" implies fixing all control variables at their sample mean. If you omit this option, you`ll get the average marg. effect.

I am afraid that this is not a Stata answer.

But .....................

1) RunMlwin allows you to run MLwiN from within Stata see http://www.bristol.ac.uk/cmm/software/runmlwin/

this has a number of benefits -including fast algorithms and less biased MCMC estimation of discrete (including logit) models and - good facilities for post estimation analysis

2) including a customized predictions facilities - so you can keep all the other predictors at their mean value and then choose  (say) quintile values for the level 2 predictor and then (by simulation) obtain predictions (and confidence intervals) on the logit, probability and odds scale for both the cluster specific and population average values (that is the median and mean predictions) This is documented here

https://www.researchgate.net/publication/234015221_Manual_supplement_for_MLwiN_Version_2.14

and you get a guide to all of MLwin's material here

 http://www.bristol.ac.uk/cmm/software/mlwin/mlwin-resources.html

Data Manual supplement for MLwiN Version 2.14

Hi. With stata and margins you can do it if you fix your random effects at zero, their theoretical mean. Just add the option "predict(mu fixedonly)". For example, if you are interested in the marg. effect of X on Y and X is interacted with Z, a level-2 vble, and both vbles are continuous, you could write:

margins, dydx(X) at(X=(-1.5(.5)1.5) Z = (-1.5, 0, 1.5) (mean) _all) predict(mu fixedonly)

so you get the marg. effects for that combinations of values of X and Z (where 1.5, etc. are values of interest for my imaginary vbles). The option "(mean)_all" implies fixing all control variables at their sample mean. If you omit this option, you`ll get the average marg. effect.

Diego gave a very elegant approach for using -margins-, keeping  the analysis within Stata! Please note that "Stata" is the correct spelling, since it is not an acronym.

Dear Diego,

thank you very much for your answer. I believe your solution should work properly for a general multilevel model, but unfortunately I am not sure it is suitable for my situation. In order to simplify things I failed to provide a complete description of my model - my apologies -, which makes things a little bit complicated and I am not sure your approach will work for my situation. 

In reality, keeping your description (I am interested in the marginal effect of X on Y and X is interacted with the level2 variable Z), my X variable is a categorical variable and the highest category of X has a varying random coefficient.

In order to be able to make only the highest category of X vary randomly across countries, I had to dummify X, thus making the model (in its simplified version) :

with gllamm:

gen cons = 1

gen inter = cons

gen slope = XC

gllamm Y XA XB XC XC#Z XA#Z XB#Z Z, i(country) link(logit) family(binomial) adapt nrf(2) eqs(inter slope)

or with meqrlogit:

meqrlogit Y i.XA i.XB i.XC i.XC#c.Z i.XA#c.Z i.XB#c.Z Z

|| country: XC , cov (unstructured) mle variance intpoints(10)

Now, here are the problems:

1.) By using the "predict(mu fixedonly)" I am not calculating the random effect for XC, which probably should be included.

2.) since the coefficient varies randomly only for one category of X, I have to dummify the variable and cannot use i.X, because otherwise I would have to let randomly vary all the categories. On the other hand, margins calculates the marginal effects wrong, because it does not know that XA XB XC and their interactions are related so that for example if XC = 1 then XA and XB and their interactions must be 0.

Do you think there is any option for my particular situation?

Hi Lenka. I'm afraid I don't have satisfactory answers to your questions. Anyway two comments: to your first question, although you do not estimate values for the random effects, you fix them at their theoretical mean (zero). If you think about it, you also fix the values of the control variables at their means (if you use the atmeans option described previously, and in this case you use sample means). So in my opinion it is not a bad idea to use the fixedonly option. Your marginal effects are for a typical cluster and the coefficients are still consistent (if all assumptions are met). Nevertheless, if you are interested in the mean marginal effect and not in the marginal effect at the mean, then I don't know how to do it in Stata.

To your second point, I don't have an answer but I find it quite odd to include a random slope for only one category of a categorical variable. If it would have only 2 categories, ok, but this is not the case. I have never seen that and I find it strange. Actually I have never seen a mulilevel model with random slopes for categorical variables with more than 2 categories, so I plead ignorance here.

One more thing to what you write in point 2, the margins command does understand that your variables are interacted and takes this into account when estimating marginal effects.

A final comment, if your X is categorical, your stata command should look as follow:

margins X, dydx(Z) at(Z=(-1.5(.5)1.5)) predict(mu fixedonly) atmeans

this is taking the example a gave previously.

This is a comment on allowing complex variances for referenced-coded dummy variables.as Diego comments that he has not seen this in use with multiple categories and Lenkha has chosen to drop the random effects for one category of a dummy variable set .The punch line is that you need to take into account the covariances as well as the variances in evaluating/ understanding the size of effects.

Imagine you have a categorical variable with 3 categories eg Class1, Class2 and Class3 and you choose Class 1 as the base or reference category – the mean effect of this omitted category will then be captured by the intercept term Beta0. Consequently, Beta1 and Beta2 will then give the differential effect so to get the mean fixed effect for class 2 you have to add Beta1 to Beta0; similarly to get the mean effect for Class 3 you have to add Beta2 to Beta0. Very clearly you are not modelling the effect directly but as a difference from a base category. This is well known; but no so well-known is what happens in the random part.

With the reference category specification and 2 categories contrasted against a base, the full random effects variance-covariance matrix is (excuse my clumsy setup without mathematical symbolism ):

VarBase

CovarBase&Class2     VarClass2

CovarBase&Class3     CovarClass2&Class3 VarClass3

The variance for Class2 is not given directly (as VarClass2) because this is the variance of the differentials from the base category; you instead have to do this calculation:

Varbase + 2*CovarBase&Class2 +VarClass2

That is variance of the base plus 2 * the covariance plus the variance of the contrasted category. So the Variance for Class 3 is not simply VarClass3 but

VarBase + 2*CovarBase&Class3 +VarClass3

It is quite clearly possible to have insignificant/ unsubstantial variances but non-trivial covariances. I would therefore not reduce the var-cov matrix down to 2 categories unless the covariances are unimportant. I have seen several presentations where people are interpreting variances without taking covariances into account – you have to do this with dummy coded variables as the underlying variances are not given directly.

This is all discussed and demonstrated in

https://www.researchgate.net/publication/260771330_Developing_multilevel_models_for_analysing_contextuality_heterogeneity_and_change_using_MLwiN_Volume_1_%28updated_June_2014%29_Volume_2_is_also_on_RGate

as MLwin has facilities for calculating such variance functions and their standard errors.

And in case it got lost – MLwiN fits the random effects model but can make predictions for both cluster-specific and population average effects for specified characteristic values of the predictor variables. It can also do coverage intervals taking account of the size of the random effects.

The differences between cluster-specific and population average predictions can be quite large when the random effects are large such as when dealing with panel data. This is discussed here

http://www.bristol.ac.uk/cmm/software/mlwin/mlwin-resources.html#discrete

And the procedures are used here in logit and Poisson models

https://www.researchgate.net/publication/260772180_Developing_multilevel_models_for_analysing_contextuality_heterogeneity_and_change_using_MLwiN_Volume_2

And finally there is extensive support for using MLwiN from within Stata so here a some do and log files of many analyses

http://www.bristol.ac.uk/cmm/software/runmlwin/examples/

Apologies for going on at such length.

Book Developing multilevel models for analysing contextuality, he...

Book Developing multilevel models for analysing contextuality, he...

Thank you both, Diego and Kelvyn for your answers! I really appreciate it.

I will definitely have a look at  the references Kelvyn posted, maybe after all using MLwiN will be the answer to my problem.

Hello Lenka,

late to the scene, but maybe the link below will be helpful in the future. I was searching for a similar problem and my web search found this thread as well as the link below. 

http://www.ats.ucla.edu/stat/stata/faq/xtmelogit_prob.htm

Hello

In stata you have to use additional command : "predict(mu fixedonly)"