What is the necessary number of Iterations for the calculation of a segregation index based on a multilevel binomial model?

You probably need quite lot - while writing this I am waiting for one with 5k burnin and 500k simulation to finish. I suggest that you look at the effective degrees of freedom of each simulated chain and I think you need 500+ for each parameter after you have run sufficient burnin to get to a converged distribution - you need this to characterize the uncertainty of the estimates by looking at the tails of simulated distribution - the Bayesian credible intervals.

The time taken depends on how complex a model it is and how many units you have - as well as how sticky - auto-correlated - the chains are. You will need to examine the chains to come to a judgment - increase the burnin if the estimates are still trending - and increase the monitoring chain if the ESS is low. This has to be done for each parameter that is being estimated.

This gives an introduction to MCMC and using MCMC in binomial models -

https://www.researchgate.net/publication/260771330_Developing_multilevel_models_for_analysing_contextuality_heterogeneity_and_change_using_MLwiN_Volume_1_%28updated_June_2015%29_Volume_2_is_also_on_RGate

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

More specifically, Becky Pillinger has written this guide for analyzing segregation in MLwin

http://www.bristol.ac.uk/media-library/sites/cmm/migrated/documents/modelling-segregation-mlwin.pdf

If you look at my Rgate site you will see a lot of recent papers on modeling segregation including

https://www.researchgate.net/publication/270579850_Ethnic_Residential_Segregation_a_Multi-Level_Multi-Group_Multi-Scale_Approach__Exemplified_by_London_in_2011

where we use a Poisson model instead of a Binomial one - but the ideas are the same .

I usually find that Hierarchical Centering in MCMC options in MLwiN and choosing the orthogonal parameterization helps a lot in getting less sticky chains.

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

Article Ethnic Residential Segregation: a Multi-Level, Multi-Group, ...

Christoph Weber

Dear Kelvyn, thanks a lot for your comprehensive response. It helps a lot. Acutally, I'm a mplus-user, so I have to transfer the estimation details to mplus.

In my application of the method I am interested in the point estimates for several regions - so I fit a multi-Group 2 Level logit model in mplus. In the next step I used the simple simulation method (not the MCMC-approach). This will underestimate the sampling variation, but this shouldn't be a problem because I focus on DI as a simple - bias corrected - descriptive measure.

Christoph

Kelvyn Jones

Just to say that MPlus is limited to two levels - I do not know the precise estimation algorithm used but (especially) when are relatively few units are available both the estimates and their standard errors can be biased with Max likelihood estimation and that is why MCMC estimation is used

see Stegmueller D. (2013). How many countries do you need for multilevel modeling? A comparison of Bayesian and frequentist approaches. American Journal of Political Science, 57, 748–761.

Christoph Weber

Thanks for the reference, unfortunately Mplus doesn’t allow bayes estimates with multigroup-models. Further I’m using multiple imputed data and bayes estimation isn’t possible with MI-data.

I would argue that ML-estimation is “appropriate” because parameter bias is “acceptable” even for small L2-n. Stegmueller writes that ML leads to limited bias in estimates for intercept only models (best case scenario). He doesn’t present results for intercept only models but he refers to the results of models with a macro predictor – here the main problem is CI-coverage, not the bias of the point estimate. As I am focusing on L2-variance estimates in a model with only a random intercept, and not on CI-intervals, ML seems to be justified.

Is this a sound argumentation for you?

Kelvyn Jones

It depends - on how many areas and how big the denominators are and how extreme (close to 0 and 1) are the proportions - and I do not know the qualities of the (EM?) estimator you are using. I do know that the quasi-likelihood estimators in MLwiN can be quite poor and that is why I use MCMC.

Leckie, G. and Goldstein, H. (2015). A multilevel modelling approach to measuring changing patterns of ethnic composition and segregation among London secondary schools, 2001-2010. Journal of the Royal Statistical Society: Series A (Statistics in Society), 178, 405-424.

used MCMC with "All models are run for a burn-in of 50000 iterations followed by a monitoring chain of 500000 iterations. Minimally informative prior distributions are specified for all parameters.We use hierarchical centring parameterizations (Browne, 2012; Browne et al., 2009) to produce chains that exhibit better mixing".

The very large burn-in was to get away from, the initial quasi-likelihood estimates. Sorry not to be more helpful.

Christoph Weber

thanks again for your comments, I will have a look in the literature if there are simulation papers on the performance of the MLR-estimator in mplus for twolevel-logit models.

Finally, you made me curious about the possibilities of MLwin.

thanks

Christoph

Kelvyn Jones

There is a 30 day trial version at

http://www.bristol.ac.uk/cmm/software/mlwin/download/

Monies from sales are put back into development and maintenance.

You can use MLwin from within Stata and R and many people do so because of its fast estimation engine and range of models.

This site gives some ideas of cpabilities and our extensive support - all of this is freely available

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

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