An increase by x in odds for an unlikely event is much more impactful than the same increase for a likely event. E.g. odds going from 0 to 1 -> prob goes from 0 to 0.5 odds going from 1 to 2 -> prob goes from 0.5 to 0.67

--- # Adding covariates <div class=gridded style="grid-template: auto 1fr / 1.3fr 1fr"> <div style="margin-top:10px"> $$ \begin{aligned} C_i &\sim\mathrm{Norm}(\mu_i,\sigma)\\ \mu_i &= \alpha + \beta_G G_i + \beta_D D_i + \beta_W W_i\\ \\ \alpha &\sim\mathrm{Norm}(0,1.7)\\ \beta_G,\beta_D,\beta_W &\sim \mathrm{Norm}(0,0.4) \end{aligned} $$ </div> <div class=regtable style="font-size:70%;margin:auto;margin-top:10px"> <table style="margin:auto"> <tr> <th></th> <th>Mean</th> <th>95% C.I.</th> </tr> <tr> <td> $\alpha$</td> <td>-4.48</td> <td>(-4.81, -4.16)</td> </tr> <tr> <td> $\beta_G$</td> <td>0.22</td> <td>(0.13, 0.32)</td> </tr> <tr> <td> $\beta_D$</td> <td>0.89</td> <td>(0.78, 1.00)</td> </tr> <tr> <td> $\beta_W$</td> <td>0.62</td> <td>(0.32, 0.94)</td> </tr> </table> </div> <div style="grid-area:2/1/3/3; display:grid; grid-template: repeat(3, max-content) / 30% 1fr 1fr"> <div style="grid-area:1/1/4/2; border-right:5px solid var(--dark);padding:0;padding-right:10px;margin-right:10px;text-align:right; font-size:80%"> ## Interpreting results using _odds ratios_ Each coefficient has an easy-to-calculate (but hard-to-interpret) meaning </div> <div> **exp(_α_)** = </div> </div>