Problem with interaction terms in logit model

[Elena Baro]

Hi everyone,
I am working on a logistic regression model with five independent, continuous key variables: authoritarianism, nationalism, social conservatism, religiosity and anti-immigrants attitudes + controls, which are used to predict the preference for authoritarian populist parties. These variables are indexes made of items combined with

rowmean

.
I am having troubles with fitting a model for robustness test with interaction terms among these variables. For instance, when using the code

logit c.nationalism##c.anti-immigrants socialconservatism religiosity authoritarianism

I obtain negative coefficients for the interaction terms. This might not seem to be a problem, however all the results are highly counter-intuitive and I obtain negative coefficients for the interaction terms for any variable combination, across the four countries that I am analysing. However, if for instance I use the code

logit c.nationalism#c.anti-immigrants socialconservatism religiosity authoritarianism

the results are more in line with the theory and also with the correlation matrix of the variables. I already tried to centre the variables and to rescale them, but with no success. As I need to include both the variables and the interaction terms in the model as in the code

logit c.nationalism##c.anti-immigrants socialconservatism religiosity authoritarianism

I was wondering if you have any suggestions on how I could solve this or why this is happening.
Thank you very much

[Maarten Buis]

You did not give us the code you used to estimate your model, as you left out the dependent variable.

An interaction effect without main effects is a very bad idea. As always, there are exceptions, but you need to know what you are doing if you want to go down that road. So forget about the singly #.

Theoretically I would expect positive correlations between these variables, but not necessarily positive interaction terms. A positive correlation means that if someone is more nationalistic than one is also more likely to be anti-immigrant. A positive interaction effect means that if someone is more nationalistic then the effect of anti-immigrant attitudes on voting for populist parties increases. I can imagine a person who mainly identifies along the nationalism axis, so all other variables become less important, while another person mainly identifies along the social conservatism axis, thus making the other axes less important. If we assume that the most important axis for a person will also have the most extreme score (a big if), then we would expect negative interaction effects. I don't say that this is true, but it is at least possible.

But before theorizing, first check your variables. In particular, what did you do with missing values?

[Elena Baro]

Dear Maarten, thank you for your reply. The complete code I used to estimate my model is the following

logit authoritarianpop_vote anti_immigrants nationalism authoritarianism socialconservatism trust_supranational trust_stateinstitution religiosity income socialsecurity unemployment EduLevel age Gender, nolog

I am using the European Values Study dataset. As I said the dependent variable is a dichotomous variable for expressing preference for authoritarian populist parties. Anti_immigrants, nationalism, authoritarianism, social conservatism, trust_supranational, trust_stateinstitution and religiosity are continuous variables made of items combined with rowmean, after controlling for Cronbach's alpha. Socialsecurity and unemployment are dichotomous variables asking if the respondents experienced unemployment or benefitted from social security in the previous years.

I treated the missing values coding them as . - but I did not have many missing values either, with the exception of the income variable. Here I recoded them assigning the average income value, however the results don’t change too much with or without this recode.

[Maarten Buis]

Sounds ok (except that you don't control for Chronbach's alpha, but check Chronbach's alpha. However, that is just a matter of language not your analysis).

Does the distinction I made between correlation and interaction in #2 resolve your problem, or do you still need help?

[Elena Baro]

The distinction you made is very helpful, thanks for that. I just find a bit suspicious that every single interaction is negative. However I don't know what the source of an eventual problem with the model might be, so I will just stick to your distinction. Thank you again