Suppose I have a model below (in R):

glmer(Y~X + (1|subject), family="binomial", data=dat)

Where Y is the binary outcome variable and X is the sole predictor variable with 6 levels.

The results of the regression test is below. The intercept is the log odds of success for the reference level (level 1 of X), and the slopes indicate the log odds ratio of the other levels to the reference level.

Estimate Std. Error z value Pr(>|z|)

(Intercept) 2.1745 0.3517 6.183 6.3e-10 ***

X2 -0.5559 0.3276 -1.697 0.0897 .

X3 0.2309 0.3634 0.635 0.5252

X4 -4.8587 0.4155 -11.693 < 2e-16 ***

X5 -2.8946 0.3200 -9.045 < 2e-16 ***

X6 -3.6111 0.3387 -10.663 < 2e-16 ***

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Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

This is all fine. However, what kinds of statistical tests can I use if I would also like to check whether each level (including the reference level)'s odds of success are significantly higher than 0? Thank you!