I'm working through a course on datacamp on mixed effects modeling. This particualr section is a refresher on glm and lme4::glmer wrt the binomial distribution.

We have a mixed effects model:

```
summary(model_out)
Generalized linear mixed model fit by maximum likelihood (Laplace
Approximation) [glmerMod]
Family: binomial ( logit )
Formula: cbind(Purchases, Pass) ~ friend + ranking + (1 | city)
Data: all_data
AIC BIC logLik deviance df.resid
977.4 989.9 -484.7 969.4 164
Scaled residuals:
Min 1Q Median 3Q Max
-4.2003 -0.7846 0.0941 0.8244 4.1520
Random effects:
Groups Name Variance Std.Dev.
city (Intercept) 0.04958 0.2227
Number of obs: 168, groups: city, 4
Fixed effects:
Estimate Std. Error z value Pr(>|z|)
(Intercept) -1.345085 0.130655 -10.295 <2e-16 ***
friendyes 0.495616 0.059344 8.352 <2e-16 ***
ranking 0.088401 0.005036 17.554 <2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Correlation of Fixed Effects:
(Intr) frndys
friendyes -0.256
ranking -0.411 0.060
```

We are then asked:

Extract the coefficients from

`model_out`

with`fixef()`

and then convert to an odds-ratio by taking exponential. Repeat with`confint()`

to get the confidence intervals.

```
exp(fixef(model_out))
(Intercept) friendyes ranking
0.2605175 1.6415091 1.0924257
```

and:

```
exp(confint(model_out))
Computing profile confidence intervals ...
2.5 % 97.5 %
.sig01 1.1240517 1.7542617
(Intercept) 0.1910566 0.3542918
friendyes 1.4614997 1.8443209
ranking 1.0817427 1.1033118
```

Apparently the two blocks above are converting the model output into odds ratios.

Why/how is this?