RE: st: level of measurement for instrumental variable

[Cameron McIntosh <cnm100@hotmail.com>]

Hi Ilana,

I don't think it's that elementary. :) You are correct in being concerned about this issue. I would say that the instrumenting probably needs to be done directly at level 2, but I don't think it's necessary for the instrument itself to be measured at level 2, and you may indeed find important potential instruments measured at level 1. If that is the case, you would need to bring them to level 2 and there are some methods for doing that, which also help correct for measurement error at the same time:

Croon, M.A., & van Veldhoven, M.J. (2007). Predicting group-level outcome variables from variables measured at the individual level: a latent variable multilevel model. Psychological Methods, 12(1), 45-57. 
Lüdtke, O., Marsh, H.W., Robitzsch, A., Trautwein, U., Asparouhov, T., & Muthén, B. (2008). The multilevel latent covariate model: a new, more reliable approach to group-level effects in contextual studies. Psychological Methods, 13(3), 203-229.http://gseis.ucla.edu/faculty/muthen/articles/Article_127.pdf
Lüdtke, O., Marsh, H.W., Robitzsch, A., Trautwein, U., Asparouhov, T., Muthén, B., & Nagengast, B. (2009). Doubly-Latent models of School Contextual Effects: Integrating Multilevel and Structural Equation Approaches to Control Measurement and Sampling Error. Multivariate Behavioral Research, 44, 764–802.http://www.statmodel.com/download/doublylatent.pdf

van Mierlo, H., Vermunt, J.K., & Rutte, C.G. (2009). Composing group-level constructs from individual-level survey data. Organizational Research Methods, 12(2), 368-392.http://spitswww.uvt.nl/~vermunt/mierlo2008.pdf ;

But I imagine it will be easiest if you just have a binary instrument measured at level 2. You should also see:
Spencer, N.H., & Fielding, A. (2000). An Instrumental variable consistent estimation procedure to overcome the problem of endogenous variables in multilevel models. Multilevel Modeling Newsletter, 12(1), 4-7.https://uhra.herts.ac.uk/dspace/bitstream/2299/752/1/900763.pdf ;
Ebbes, P., Bockenholt, U., & Wedel, M. (2004). Regressor and random-effects dependencies in multilevel models. Statistica Neerlandica, 58(2), 161–178.http://www.personal.psu.edu/pxe12/pdfs/Ebbes_Bockenholt_Wedel_04_Regressors%20and%20random%20effects%20dependencies.pdf

Rice, N., Jones, A., & Goldstein, H. (1997). Multilevel models where the random effects are correlated with the fixed predictors: a conditioned iterative generalized least squares estimator.  CHE Technical Paper Series 10. York, UK: University of York, Centre for Health Economics.http://www.york.ac.uk/media/che/documents/papers/technicalpapers/CHE%20Technical%20Paper%2010.pdf

Best,
Cam

> From: redstone@illinois.edu
> To: statalist@hsphsun2.harvard.edu
> Subject: st: level of measurement for instrumental variable
> Date: Sat, 10 Sep 2011 10:51:27 +0000
> 
> I saw on the Statalist website that statistics are an appropriate topic of discussion (in addition to direct questions on Stata). Thus, my questions:
> 
> I am specifying the following multi-level regression:
> 
> yhat = x1i  + x2i + z1j
> 
> where x1 and x2 vary at the individual level, i, (the unit of analysis in my regression) and z1 varies at the census tract level, j
> 
> [1] Since where someone lives (and therefore their census tract) is a choice variable and isn't random, I believe I need to instrument for z1. In that case, does my ideal instrument vary at the level j (the level of measurement of z) or at the level i (the level of the analysis)?
> 
> [2] If I add z2j to the analysis (where z2 also varies at the tract level), would I need a separate instrument for z2?
> 
> Thank you for your patience with this (probably very elementary) question.
> 
> ----------------------------
> Ilana Redstone Akresh
> Department of Sociology
> University of Illinois at Urbana-Champaign
> Website: https://netfiles.uiuc.edu/redstone/www
> Email: redstone@illinois.edu
> 
> 
> 
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