Repeated categorical measures in a survey Last year, we did a survey that asked people a question about their belief in climate change. The respondents could select 1 from a list of 5 categorical responses.
In the fall, there was an event that we believe might affect respondents' climate change beliefs, so we're repeating the survey this year. I haven't done much in the way of longitudinal analysis: how can I compare the responses to see if the proportions have changed?
Thanks!
 A: Welcome to the site, @griseus.
The simplest comparison is just a two-way contingency table. It ignores the ordinal relations between your categories, and in a sense is the most conservative test. If you have a complex sample design (stratification, clustering, unequal probabilities of selection), you need to use Rao-Scott corrections to the $\chi^2$ independence test.
As the next step up the sophistication ladder, you can entertain an ordinal logistic regression model with a dummy variable for the second wave. Then significance of this variable is indicative of the change in population attitudes. Such a model implicitly assumes that the measurement properties of your instrument did not change, which is probably an OK assumption given a short time period between the two surveys. You can relax and test this assumption by specifying an interaction between the thresholds and the time period; if you specify all four interactions, then you have to omit the trend from the main regression. Of course, you can also add demographic variables to that regression, which will shed some light on the differences between men and women, political party affiliation, or different levels of education. Again, the logistic regression analysis needs to be conducted with appropriate complex sample design specifications, easily done in Stata or R.
