statisticalrethinkin..

142 5. MULTIVARIATE LINEAR MODELS5.1.3.3. Posterior prediction plots. In addition to understanding the estimates, it’s importantto check the model fit against the observed data. is is what you did in Chapter 3,when you simulated globe tosses, averaging over the posterior, and compared the simulatedresults to the observed. ese kind of checks are useful in many ways. For now, we’ll focuson two uses for them.(1) Did the model fit correctly? Golems do make mistakes, as do golem engineers.Many common soware and user errors can be more easily diagnosed by comparingimplied predictions to the raw data. Some caution is required, because not allmodels try to exactly match the sample. But even then, you’ll know what to expectfrom a successful fit. You’ll see some examples later.(2) How does the model fail? All models are useful fictions, so they always fail in someway. Sometimes, the model fits correctly but is still so poor for our purposes that itmust be discarded. More oen, a model predicts well in some respects, but not inothers. By inspecting the individual cases where the model makes poor predictions,you might get an idea of how to improve the model.Let’s begin by simulating predictions, averaging over the posterior.R code5.10# call link without specifying new data# so it uses original datamu