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Main Question

Can you include a dichotomous independent variable in a random slopes & intercepts model? Or does the dichotomous nature of the variable violate any assumptions of random slope GLM models?

Context

I am examining incident-level data of protests in Europe. I have a dichotomous variable that indicates whether a given incident was primarily concerned with immigration, and I am trying to estimate whether immigration leads to protesters to escalate their protests into riots. As such, I am estimating the correlation of a dichotomous DV (escalation) with a dichotomous IV (immigration). The data is structured at the incident-level, and I am including administrative districts and countries as levels.

When I run the models with just random intercepts, immigration is strongly correlated with escalation. But when I include random slopes, that significance drops away. I'm confused by this, and wondering whether I'm violating multilevel GLM assumptions by including random slopes with a dichotomous IV.

Thank you!

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  • $\begingroup$ Would you be able to describe more exactly what your model is? Is this a fixed effect binary predictor that isn't interacting with anything else, or are you interaction a random intercept with it or something like that? $\endgroup$
    – jld
    Commented May 1, 2018 at 20:14

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What assumption would you be violating by including a dichotomous variable as a random effect?

You have the mean level correlation between immigration and rioting across countries. Then you have the correlation between immigration and rioting within a country.

To explain your predicament. You have a few countries with no correlation between immigration and escalation and a few with a really high correlation between immigration and escalation. The average of those is a moderate correlation I imagine. When you included a random slope, it shows that there is no real across country (global) effect of immigration on escalation. Instead, there are a countries where this is the case.

To me, this seems to be the case where there is some hidden country level variable at play.

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Yes, you can have dichotomous predictors. Assuming that immigration is at Level 1, I think introducing random slopes and losing the significance means that the between-country variability is so great that immigration is no longer a significant predictor (i.e. it may be strongly related in some countries, but insignificant in others). So assuming your model looks like $$ln{\frac{p}{1-p}}=\beta_{0j}+\beta_{1j}immigration$$ $$\beta_{0j}=\gamma_{00}+\mu_{0j}$$ $$\beta_{1j}=\gamma_{10}+\mu_{1j}$$ you might consider looking at the level 2 residuals ($\mu_{1j}$) to get a sense of their distribution.

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  • $\begingroup$ If that were the case, I would strongly feel that there is some hidden country-level variable at play. $\endgroup$
    – JWH2006
    Commented May 15, 2018 at 18:02
  • $\begingroup$ Ah, good point! I'll leave my answer and mark yours as correct. $\endgroup$
    – dankernler
    Commented May 15, 2018 at 20:02

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