statisticalrethinkin..

5.3. WHEN ADDING VARIABLES HURTS 155sigma ~ dunif( 0 , 10 )) ,data=d,start=list(a=10,bl=0,sigma=1) )precis(m5.9)Mean StdDev 2.5% 97.5%a 0.87 0.28 0.32 1.42bl 2.04 0.06 1.92 2.16sigma 0.57 0.04 0.49 0.65at 2.04 is almost identical to the mean value of sum_blbr.You’ll get slightly different results in your own simulation, due to random variationacross simulations. But the basic lesson remains intact across different simulations: Whentwo predictor variables are very strongly correlated, including both in a model may lead to confusion.e posterior distribution isn’t wrong, in such cases. It’s just giving the right answerto a badly-formed question.5.3.2. Multicollinear milk. In the leg length example, it’s easy to see that including both legsin the model is a little silly. But the problem that arises in real data sets is that we may notanticipate a clash between highly correlated predictors. And therefore we may mistakenlyread the posterior distribution to say that neither predictor is important. In this section, welook at an example of this issue with real data.Let’s return to the primate milk data from earlier in the chapter. Let’s get back the originaldata again:library(rethinking)data(milk)d