

Type twolevel random with binary outcome 

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I am running multilevel regressions with random slopes and binary outcome (type=twolevel random). I am mainly interested in the extent to which the relationship x>y varies across clusters. Due to my limited statistics knowledge I have difficulties interpreting the random slope coefficient. When I estimate the same model with Stata (gllamm) or R (lme4) the output provides odds ratios for the "fixed part" in addition to acrosscluster variances. Is the mean slope on logit scale or is it a linear regression coefficient? How can I interpret it? 


The mean slope is on a logit scale so you can consider odds ratios. Note that interpreting this model requires some study  see for example the reference that we give when teaching: Larsen & Merlo (2005). Appropriate assessment of neighborhood effects on individual health: Integrating random and fixed effects in multilevel logistic regression. American Journal of Epidemiology, 161, 8188. 

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