`library(lme4) out <- glmer(cbind(incidence, size - incidence) ~ period + (1 | herd), data = cbpp, family = binomial, contrasts = list(period = "contr.sum")) summary(out) Fixed effects: Estimate Std. Error z value Pr(>|z|) (Intercept) -2.32337 0.22129 -10.499 < 2e-16 *** period1 0.92498 0.18330 5.046 4.51e-07 *** period2 -0.06698 0.22845 -0.293 0.769 period3 -0.20326 0.24193 -0.840 0.401`

I was never in a situation where I needed to fit a generalised linear model with effect coding (

`contr.sum`

for`R`

users). Can I apply the same interpretation as in the linear model case? In a normal linear model the intercept would be the grand mean and the $\beta$s (parameters for`period1`

,`period2`

,`period3`

and`period4 = (Intercept) - period1 - period2 - period3`

the effects i.e. how the factor levels deviate from the grand mean.Here is how I think the analogous interpretation for generalised linear models goes. (I will exponentiate all parameters and hence transform the log-odds(-ratios) to odds(-ratios).) The intercept $\exp((\text{Intercept}))$ would then be the overall

oddsof success vs. failure (sticking here to classical binomial terminology) and the $\beta$s thelog-odds-ratios. And we get theoddsfor e.g.`period1`

by adding $\text{(Intercept)}+\text{period1}$ and then exponentiating: $\exp(\text{(Intercept)}+\text{period1})$. Is the $\text{(Intercept)}$ really the overall/mediumoddsand the $\beta$sodds-ratios?

**Answer**

Under effect coding, the intercept in the summary table summary(out) is the average logit (log-odds or the log of odds ratio) across all the four periods in your case, and each of the other effects is the logit difference of the corresponding period relative to the average logit.

You can easily verify your interpretation by comparing your current results to a different coding method such as dummy coding on your data:

```
out2 <- glmer(cbind(incidence, size - incidence)
~ period
+ (1 | herd),
data = cbpp,
family = binomial,
contrasts = list(period = "contr.treatment"))
summary(out2)
```

**Attribution***Source : Link , Question Author : lord.garbage , Answer Author : bluepole*