I have two types of departments (Dept_typ) and 5 departments per Dept_typ for a total of 10 departments. I have 3 years of data measured per month (at the department level) of the dependent variable (DV) - 360 total observations. I have between 10 -20 people in each department for a total of 196 people. My independent variable (IV) of interests was measured at the individual level. I averaged the individual (IV) measure for each department. I want to perform a regression showing that the IV (measured at the individual level and averaged) is associated with the department measure captured over 36 periods. My hypothesis suggests that more of the IV leads to greater level of the DV. Is it okay to repeat/replicate the same value of the IV, i.e., have the IV constant for each of the 36 observations per department? Thus, there is no variation within the department of the IV only across the 10 departments.
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Averaging lower level variables to get estimate for higher level grouping variable is generally a bad idea - it gives biased results. We call this atomistic fallacy and it is connected to Stein's paradox. For this kind of, hierarchical, data multilevel (or mixed) model is method you should consider. In linear mixed model you estimate both effects for individual-level observations and group level effects, so no information is lost and both levels are included in the model. In LMM you could also include time as a variable in a model.
See more:
- Snijders, T.A.B. and Bosker, R.J. (2012). Multilevel Analysis: An Introduction to Basic and Advanced Multilevel Modeling. London: Sage Publishers.
- Hox, J. (2010). Multilevel Analysis: Techniques and Applications. New York: Routledge.
- Gelman, A. and Hill, J. (2006). Data Analysis Using Regression and Multilevel/Hierarchical Models. Cambridge: Cambridge University Press.
- Pinheiro, J.C. and Bates, D.M. (2000). Mixed-Effects Models in S and S-PLUS. New York: Springer.
