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I am trying to model how salary increases across time for different categories of college professor, and to determine the nature of how the trajectory of these increases differ from each other. Was planning a multilevel regression using the first level as a time variable, and three categorical moderator variables in the second:

  • x1 = gender (M/F)
  • x2 = size of school (small,med,large)
  • x3 = rank of professor (1,2,3)

Unfortunately, the data I have to work with is pretty messy. Most is presented in aggregate (averaged) and am not sure if an analysis of this sort is appropriate. I have:

  • Average salary data for each category
  • Number of schools reporting per category (different for each category and for each year of reporting; n between 50-100)
  • The lowest/highest reported value for each category;
  • the 25%,50%,and 75% percentile ranks for each category.

In other words, I have

  • Male Full Professors at Large Universities (AY2002), 65 schools reporting
  • Average salary $50000 (Low=15000 25%ile=22000 50%ile=49800 75%ile=75000 High=100000)

Is there anything that can be done with data in this format or am I doomed? Can I say that male full professor salary has increased at a faster/slower rate than female assistant professor salary?

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Great question. Unfortunately I'm not an expert in this field, but the challenge of analyzing aggregate data seems to be a focal research topic these days. The general concern is that relationships found in regressions with aggregate data might not hold at the lower level, like you've hinted at.

All in all, it's never safe to trust a model with aggregate data, but that doesn't mean it can't be interpreted in some sense. Some people argue that modeling techniques that occur at the same level as the theorized process can be "trusted."

And in some cases, aggregate data can't be avoided. Just make sure you state your assumptions.

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