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In the output of a GLMM, using a binary variable as response variable and continuous variables as explanatory variables [family = binomial(link="logit")], I obtain, for each variable, an estimate value, standard error, a z-value and a Pr(>|z|).

1) Is the z-value simmilar to the effect size?

2) If not, how can I obtain the effect size for each variable?

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  • $\begingroup$ 1: No, it's a test statistic to test the null hypothesis that the estimate is zero. 2: don't you mean "how can I obtain the effect size" ? Since you don't say what kind of glmm you are running, this is very hard to say, $\endgroup$
    – Robert Long
    Commented Jul 31, 2016 at 14:09
  • $\begingroup$ @RobertLong Yes, I meant effect size, the question is updated! $\endgroup$
    – mto23
    Commented Jul 31, 2016 at 14:14

2 Answers 2

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1) Is the z-value similar to the effect size?

No, it is a Wald statistic to test the null hypothesis that the estimate is zero.

2) If not, how can I obtain the effect size for each variable?

Since this is a generalized linear mixed model, you can't calculate effect sizes such as cohen's d, but since it is a logistic model with a logit link you can report odds ratios as effect sizes. The raw coefficients are on the log-odds scale, so to calculate the odds ratios, these are just exponentiated.

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  • $\begingroup$ Thank you for your answer! Just didn't understand very well how to obtain the odds ratios; do I need to exponentiate each estimate value? $\endgroup$
    – mto23
    Commented Jul 31, 2016 at 14:33
  • $\begingroup$ @Teresa yes that is correct. $\endgroup$
    – Robert Long
    Commented Jul 31, 2016 at 15:02
  • $\begingroup$ Ok, thanks!! Do you know of any book/paper with that information that I can cite? And which one (effect size/ Wald statistics) do you suggest to report relative differences between variabes? $\endgroup$
    – mto23
    Commented Jul 31, 2016 at 15:09
  • $\begingroup$ @Teresa try Hosmer Jr, David W., and Stanley Lemeshow. Applied logistic regression. John Wiley & Sons, 2004. $\endgroup$
    – Robert Long
    Commented Jul 31, 2016 at 15:19
  • $\begingroup$ One other thing: I have my variables transformed (z-score),so does that change the interpretation of the odds ratio? Which, I assume, is: higher odds ratio, higher "importance" of a given variable. $\endgroup$
    – mto23
    Commented Jul 31, 2016 at 16:13
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Here is for your second question. A new function has recently been added to the package emmeans to calculate effect sizes (Cohen´s d). To use it, you will need the GLMM adjusted, the Sigma, and the df. But, you need a trick to calculate the Sigma from a Mixed Model. Let me copy here a part of the information you can find at: https://rdrr.io/cran/emmeans/man/eff_size.html

Oats.lme <- lme(yield ~ Variety + factor(nitro), 
                  random = ~ 1 | Block / Variety,
                  data = Oats)
                  
VarCorr(Oats.lme) 
# Combine variance estimates

totSD <- sqrt(214.4724 + 109.6931 + 162.5590);
emmV <- emmeans(Oats.lme, ~ Variety);
print(eff_size(emmV, sigma = totSD, edf = 5));
print(eff_size(emmV, sigma = totSD, edf = 51)
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