Should "City" be a fixed or a random effect variable? I am analyzing data on "BloodSugar" level (dependent variable) and trying to find its relation with "age", "gender" and "weight" (independent variables) of subjects. I have data collected from subjects sampled in four "city".
Should I use "city" variable as fixed effect or a random effect?
So which is correct:
lm(bloodsugar ~ age + gender + weight + city, mydata)

or:
lmer(bloodsugar ~ age + gender + weight + (1|city), mydata)

Thanks for your help.
Edit: In response to comment by @Dave , I would like to add following: Currently there is no data on relation between my real dependent variable and City. So, relation could be there. Relation with City is not my primary objective but it will be nice to determine that relation also, if it is feasible by proper statistical methods.
 A: Robert Long already gave a nice answer, but let me add my three cents. As already noticed by Dave in the comment, when fitting fixed effects models you are asking the question what are the differences between those particular cities, while with random effects model you ask what is the variability between cities. Those are quite different questions to ask.
If you are interested in more in-depth discussion of differences between both types of models, you can check my answer in the Fixed effect vs random effect when all possibilities are included in a mixed effects model thread. It's a different question, but the answer discusses the kind of issues that are closely related to questions as yours.
A: One further remark: If you assume that the city variable might be correlated with the other independent variables (and the blood sugar level), you need to model cities as fixed-effects because it would violate the assumption of independence of the random effects.
An example might be if one city is in Florida where older people with higher blood sugar levels tend to cluster due to the milder winter.
A: I would advise fitting both. Hopefully they will tell you the same thing. If not, that would be very interesting!
Conceptually, city should be random. You are not specifically interested in estimates for each city for you research question and your sample of cities can be thought of as coming from a wider population of cities. These are good reasons to treat it as random.
The problem is you only have 4 of them so you are asking the software to estimate a variance for a normally distributed variable with only 4 samples so that may not be very reliable.
It is perfectly valid to fit fixed effects and this will control for the non independence within each city.  In that case you are treating it a bit like a confounder. The reason for using random intercepts is that with many cities this becomes inconvenient and loses statistical power.
So with only 4, I would do both.
