Effect size of linear and quadratic variables

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, I am considering a variable with a linear (a) and quadratic form(a^2). Here is an example of a model:

model <- x ~ a + I(a^2) + (1|b)

In this case (linear and quadratic forms), 1) is the effect size estimated in the same way (odds ratio), and 2) with the same interpretation?

I can't seem to find information about this topic; do you know of any good literature?

• The odds ratio is the effect size so perhaps you need to explain what you are trying to do. – mdewey Mar 6 '17 at 14:25
• @mdewey I was looking for a way to estimate the effect size (which, in this case, should be done using odds ratio) for both terms of a variable, at the same time – mtao Mar 6 '17 at 14:27

• Well, but one could define an "effect size function" one could plot, maybe even with a confidence band. Or, if the population disteibution of $x$ is k own, integrate to find a population average effect size ... – kjetil b halvorsen Mar 25 '17 at 21:50