This is my first question here and I want to make sure I am giving as much relevant background as possible, so please bear with me!
I am analysing the factors influencing commute mode choice in several cities, for commuters to the CBD (central business district), mainly using census data. So far, I am essentially dis-aggregating the census output for the neighbourhood level to create individual-level observations, and then run a logit regression. For example, if the census output for neighbourhood A tells me that there are 100 males who work full time, are 35 years old and take public transport to work, then I create 100 observations with the outcome variable 'public transport', and the independent variables 'sex=1' (for male vs female) 'full-time=1' (for full-time vs part-time), and 'age=35'.
Beyond these individual-level specific independent variables, there are also some variables which the census provides in brackets, such as income, so I know I'm already 'losing' some variation because of these grouped observations.
However, I also want to include some neighbourhood-level variables, for example the distance and travel time on public transport from the neighbourhood in question to the CBD. This means that each individual within one neighbourhood gets the same distance attributed to them, I can't account for the variation within a neighbourhood because I don't have that data (I don't know where people live within their neighbourhood). So, the variance and standard errors for these variables are much lower than they should be, and hence I get highly significant coefficients from my logit model, but can't be sure of this significance because I 'lost' variation from disaggregating from the neighbourhood level.
So regarding this situation, I have a couple of questions:
- Does everything I've said so far seem sensible or have I misunderstood something?
- The variance/standard errors for the coefficients on the individual-level specific independent variables (e.g. age) should still be correct, right?
- I'm assuming the 'most proper' way to deal with this would be to use a multilevel regression model. However, I should say that this is for my undergraduate dissertation in Economics and accordingly my Econometrics level isn't advanced (I've taken a semester-long Statistics course, and am currently taking my second semester-long Econometrics course). So I was wondering whether I can avoid using a multilevel model. For example, could I just run two separate regressions, one for the neighbourhood-level (OLS, with proportion of commuters using a specific mode as the DV), one for the individual-level? I was thinking that maybe I could use the results from the first regression to see if the coefficients on the neighbourhood-level variables are statistically significant, and then still include the variables in the second regression for the odds-ratio and marginal effect.
- If the only way around this is indeed a multilevel model, any advice on where to learn more about it and how to implement this practically (I'm using R, btw)?
Any pointers in the right direction would be greatly appreciated!