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This is a follow-up question to the one I posted earlier: Unequal sample sizes in generalized linear modeling

I want to compare a number of outcomes (depression, anxiety, aggression, etc). The predictor variable is categorical, has 2 groups: Province (over 3000 cases) and City withing the Province (around 300 cases). I understand that Province and City may not be independent, as the city may be influenced by processes in the Province.

If I use GLM with robust estimation, will it help me to correct for non-independence?

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  • $\begingroup$ Could you provide a specific example of an hypothesis you propose to test with respect to Province versus City within the Province? From the wording of this and the linked question, it seems that you have information about particular cities for 300 of your cases (with known provinces) and lack information about the particular city in the other 3000 cases. It's not clear how or why you would use such a predictor in your model, rather than use the information about Province that you have for all 3300 cases. $\endgroup$ – EdM Jan 18 '17 at 19:55
  • $\begingroup$ My research question is: is there a difference in the level of depression between children who live in the City and those who live in the province? I should add that there is no case cross-classification- one case can belong only to the City or only to the province. $\endgroup$ – Natalie Jan 18 '17 at 20:27
  • $\begingroup$ I got confused by the fact that the City is in the Province. However, each case belongs only to one group (City or province). Can they be considered as independent or not (to meet the assumption of independence of observations)? $\endgroup$ – Natalie Jan 18 '17 at 20:33
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If city-dwelling versus non-city-dwelling is dichotomous, I see no problem with using that distinction as a categorical predictor. If you think that specific Provinces might differ in terms of baseline measures of your outcomes, or in terms of the relation of city/non-city-dwelling to differences in outcomes, you could include the Province as a random effect in your model. The Province for each individual could be included as a random effect for either or both of the intercept (baseline outcome values, say, for non-city) or the slope (difference between city and non-city-dwelling outcome values) in the model.

It's not clear, however, how you are dealing with locations like suburbs that contain some aspects of both city and non-city; I live in such a suburban town immediately next to a large city. Instead of a strict dichotomy, I wonder if you would be better off using something like a measure of local population density as a continuous predictor instead.


I'm assuming here that Provinces are somewhat equivalent to States in the US, and that each city dweller is also a resident of one particular Province.

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  • $\begingroup$ Thank you, EdM. To illustrate: the overall sample (N=3300) comes from the province of Manitoba 9which is like a State in the US). 300 cases are coded as "lives in Winnipeg" = 1, 3000 cases are coded as "lives outside of Winnipeg" =2. I have to compare how Winipeg (the City) is different from the cases from outside of Winnipeg (the Province) - if the differ in terms of, say, depression. $\endgroup$ – Natalie Jan 18 '17 at 21:01
  • $\begingroup$ If all are from Manitoba then you can ignore my suggestion to include Province as a random effect; I'll leave that in the answer in case someone working on multiple Provinces looks to this thread for guidance. With about half of Manitoba residents living in Winnipeg, however, I do wonder why so few cases come from the City and whether you really have a representative sample. $\endgroup$ – EdM Jan 18 '17 at 21:09
  • $\begingroup$ EdM, if they all come from Manitoba- can I compare sample 1 (Winnipeg) to sample 2 (Manitoba) can they be considered as independent of each other? If not, how can I correct for non-independence when I run generalized linear models? Thank you again! $\endgroup$ – Natalie Jan 19 '17 at 0:43
  • $\begingroup$ Independent for your GLM, yes, but I'm still worried about why the 2 groups are so different in proportion in your sample than they are in Manitoba as a whole. That's potentially a much bigger problem. $\endgroup$ – EdM Jan 19 '17 at 1:53

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