I have cross-tabulated some data from a survey. The core survey questions have been cross-tabulated with demographic variables. I am looking at these cross-tabulations to see if any interesting trends occur. So the process i am going through is fairly exploratory.
One of the cross-tabs is as follows: Which mode of transport do you use (tick all that apply)? X What is your postcode?
The cross-tabulated results look like this:
| mode of transport | postcode area 1 | postcode area 2 | postcode areas 3 |
|---|---|---|---|
| Car | 33 | 56 | 48 |
| Cycle | 12 | 10 | 30 |
| Walk | 45 | 40 | 65 |
A section of the raw data looks like this:
| respondent ID | car | cycle | walk | postcode area |
|---|---|---|---|---|
| 1 | 1 | 1 | area 1 | |
| 2 | 1 | 1 | area 2 | |
| 3 | 1 | 1 | area 3 |
I want to know if respondents from particular postcode areas are more likely to use certain modes of transport. If the observations were independent, I would do a chi-sq test and look at the standardised residuals. However, the observations are not independent, as a respondent can select multiple modes of transport. This means that I cannot do a chi-square test as the assumption of independent observations is violated.
I have been considering what alternative tests I can perform. I think one possibility would be multinomial logistic regression with mode of transport as the response variable, postcode area as an explanatory variable and respondent ID as a random effect.
Other tests I have considered are McNemar test or Cochran's Q test, but from the examples I have seen, i am not sure if my data is applicable to these methods.
Which tests would you recommend for this scenario? I'd rather do something that is analogous to chi-square if possible, as i have done chi-sqaure tests on other parts of this data set where observations are independent.
