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I am fitting GLMM's (using a binary variable as response variable and continuous variables as explanatory variables [family = binomial(link="logit")]), and I am interested in obtaining the effect sizes for each explanatory variable.

I obtain the effect size value by calculating odds ratios:(Effect size in GLMM).

However, my variables are standardized, so how do I interpret the odds ratios ?

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    $\begingroup$ @Tereas I have edited the question substantially. Feel free to roll back if you disagree with my edits. $\endgroup$ – Robert Long Jul 31 '16 at 16:48
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    $\begingroup$ Odds ratio is computed from a 2x2 contingency table. Even if you standardized your binary variables, you would still have a 2x2 contingency table and odds ratio interpretation wouldn't change. $\endgroup$ – Pere Jul 31 '16 at 17:11
  • $\begingroup$ @Pere they are continuous variables; does it change anything or the interpretation is still de same (with any kind of variables, standardized or not)? $\endgroup$ – mtao Jul 31 '16 at 17:20
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The odds ratios you get are for a unit change in the explanatory variable. If you have standardised the variables the unit is now the standard deviation (presumably, you did not say how you standardised them) so the odds ratio is for an increase of one standard deviation in the explanatory variable. The problem with doing this as compared to using the original units is that your odds ratio cannot easily be compared with someone else's odds ratio if s/he had different standard deviations in their sample.

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