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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.

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  • $\begingroup$ Old question, but if anyone stumble upon this question, it may be helpful to consider that we're not dealing with 2 variables here ("postal code" and "mode of transportation"), but with 4 variables, as each mode of transport is in fact a binary variable (car: yes/no, cycle: yes/no, wolk: yes/no). So the contingengy table showed in the question may be a bit misleading, as it leaves out information about people who did not tick the options. One way to analyze the data may be to consider each mode of transportation separately, and ask questions like "Where are cars more predominant?". $\endgroup$
    – J-J-J
    Commented Nov 8 at 20:34
  • $\begingroup$ Using methods like multiple correspondance analysis may be informative too, as well as visualizing the data with some maps. $\endgroup$
    – J-J-J
    Commented Nov 8 at 20:37

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