# ROC Curve - Mixed Model [closed]

I would like if it was possible that the Lord would help me in a review, lest it incur in error.

If it were a simple logistic regression, I could use The Area Under an ROC Curve, but since I'm using a generalized linear mixed model with reply Binaria, can analyze the same way this output?

I'm using the GLMER function with two models. One with (1 / g) (Random intercept with fixed mean ) and the other with x + (x | g) (Correlated random intercept and slope )

If not, what would you suggest to check the adjustment of the model?

Thank you

## closed as unclear what you're asking by AdamO, Michael Chernick, kjetil b halvorsen, Peter Flom♦May 7 '18 at 12:20

Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.

The AUC is interpreted as a probability that a randomly selected case is assigned higher risk than a randomly selected control. A mixed model combines fixed and random effects. If we characterize participants only by their fixed effects, participant A might receive higher risk than participant B, but the added contribution of the random effects might give participant B a higher risk than A. That is to say, $c = E[\hat{Y}_1 > \hat{Y}_2 | Y_1 = 1, Y_2=0]$
The obviously solution is far, far too computationally difficult: essentially you would have to marginalize the logistic model and calculate the U-statistic directly, i.e. for each participant, treat their linear predictor as a latent normally distributed variable and, rather than flagging each pair-wise comparison as "yes: the case had higher risk" vs "no: the case had equal or lower risk", you would need to obtain something like a $p$-value representing the risk that that particular case had higher risk than the control.