# Is it possible to fit a quantile regression fixed effects model on a repeated measures, panel data, with a nested structure?

In the package manual it is demonstrated how to fit a fixed effects model on a repeated measures data structure. I am looking for ways to extend this to a repeated measures nested structure, i.e. not only repeated measures, but nested and repeated, e.g. children nested in classes repeated over time.

I'm currently using plm() from the package to estimate a repeated measures fixed effects model with a nested structure cf. SO question and answer here (a nice reproducible nested data example is also available that that question).

How do I use , or some other package, to fit a panel data quantile regression fixed effects model on a nested structure? Thanks.

• You should write out a mathematical equation for your model May 27, 2018 at 11:30
• I wouldn't be surprised if a Bayesian model is required. Bayesian models tend to handle hierarchies quite well. E.g. math.uci.edu/~xli/Bayesian_Quantile_Regression_Yu.pdf May 27, 2018 at 11:38
• Hierarchical or multilevel are synonyms for the OPs use of nested panel data structures. The literature on that class of models is large particularly in econometrics. While quantile regression (Bayesian or not) is amenable to multilevel panel data structures Keming Yu's article does not specifically address them. One useful reference which does discuss multilevel Bayesian panel data models is Gelman and Hill's Data Analysis Using Regression and Multilevel/Hierarchical Models. M. Hashem Pesaran's more recent book Time Series and Panel Data Econometrics is massive and definitive. May 27, 2018 at 12:09
• Thank you for the comments. I'm familiar with the Gelman and Hill book, but to my knowledge it does not cover quantile regression as such. Regarding the Yu and Moyeed paper, I believe they cover similar material to what is covered in the rqpd package manual, but does not bento questions regarding a nested structure. Which is my specific issue. Unless I have overlooked something. May 27, 2018 at 13:41
• You are correct that Gelman and Hill do not discuss QR per se but is that a barrier to leveraging their insights into Bayesian approaches to panel data models? My view is that the similarities between GLM and QR, whether Bayesian or not, are of much greater relevance when it comes to dealing with the idiosyncrasies of hierarchical panel data structures and models. To me it sounds like a good intro to HLMs would be useful. Judith Singer's paper Using SAS PROC MIXED to Fit Multilevel Models is one example ida.liu.se/~732G34/info/singer.pdf. Forget the SAS part, it's a great intro May 27, 2018 at 14:37