I am trying to perform a multilevel regression analysis with SAS and I found a lot of information on how to do this if your dependent variable is at the lowest level (in my case, this would be the individual level). The problem is that I am trying to find out how individual and school variables influence a school level dependent variable (e.g., a perception of school safety or school climate). Is it possible? What kind of analysis would be the most appropriate? Thank you very much in advance!
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$\begingroup$ Is the dependent variable really measured at the school level, or is it an aggregate of data from the individual level? $\endgroup$– hplieningerCommented Jul 26, 2017 at 8:37
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$\begingroup$ Thank you for your answer! It is an aggregate of data. Students give their opinon on their school climate (e.g., In my school, students have good relationships with teachers). There are 3 questions which we summed up, calculated means in each classroom and then assigned this score to all the students in the classroom. This is our dependent variable. Independent variables are such as self-reported level of empathy, self-esteem, etc. at the individual level. $\endgroup$– IzabelaCommented Jul 26, 2017 at 9:02
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$\begingroup$ Check out Judith Singer's paper Using SAS PROC MIXED to Fit Multilevel Models, Hierarchical Models, and Individual Growth Models (ungated copy here ... ida.liu.se/~732G34/info/singer.pdf). It's almost 20 years old but her discussion remains quite topical and relevant, not to mention that she fits all of her models in SAS, your software of choice. $\endgroup$– user78229Commented Jul 26, 2017 at 13:16
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1 Answer
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If you are really interested just in the relationship at level 2 (the schools), then you might just use the level-2 data and run a standard linear model. However, your results may be biased, for example because your measurement of that level-2 variable (school climate) is unreliable---you can think of it as something like a latent variable measured by x indicators, where x are the students. Lüdtke et al. (2008) developed models that take that into account (but I fear this relates only to independent variables). And Croon and van Veldhoven (2007) have a nicer paper where the dependent variable is an aggregated level-1 variable.
References
- 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, 45-57.
- Lüdtke, O., Marsh, H. W., Robitzsch, A., Trautwein, U., Asparouhov, T., & Muthén, B. O. (2008). The multilevel latent covariate model: A new, more reliable approach to group-level effects in contextual studies. Psychological Methods, 13, 203–229. doi:10.1037/a0012869
answered Jul 26, 2017 at 9:34
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$\begingroup$ Level 2 is individual, not schools. $\endgroup$ Commented Jul 26, 2017 at 9:58
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$\begingroup$ Thank you so much for helping me. HPlieninger - I will definitely read through these papers and check what can be done. SmallChess - what are the implications of this? I´m sorry but I don´t understand... $\endgroup$– IzabelaCommented Jul 26, 2017 at 10:02
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$\begingroup$ @SmallChess: From my understanding, the OP has students nested within schools (or classes), so level 1 are individuals. $\endgroup$ Commented Jul 26, 2017 at 10:07
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$\begingroup$ @Izabela you can also aggregate the student level variables to make them useful for the higher level regression. However a proper analysis will then take the variance in that estimate into account, for example using a Bayesian analysis and/or Monte Carlo methods $\endgroup$– tomkaCommented Jul 26, 2017 at 11:25
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$\begingroup$ Great! Thank you so much for your help. This also sounds like a good option. The paper recommended by hplieninger also seems to answer my question. It seems that a regression analysis can be performed with these data and then the results can be easily corrected with a formula. The paper is: 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, 45-57. $\endgroup$– IzabelaCommented Jul 26, 2017 at 11:59