# Visualising the predictive distribution of a log-transformed linear model

Theoretical distributions |

Today I will take a closer look at the log-transformed linear model and use Stan/rstan, not only to model the sales statistics, but also to generate samples from the posterior predictive distribution.

The posterior predictive distribution is what I am most interested in. From the simulations I can get the 95% prediction interval, which will be slightly wider than the theoretical 95% interval, as it takes into account the parameter uncertainty as well.

Ok, first I take my log-transformed linear model of my earlier post and turn it into a Stan model, including a section to generate output from the posterior predictive distribution.

After I have complied and run the model, I can extract the simulations and calculate various summary statistics. Furthermore, I use my parameters also to predict the median and mean, so that I can compare them against the sample statistics. Note again, that for the mean calculation of the log-normal distribution I have to take into account the variance as well.

Ok, that looks pretty reasonable, and also quite similar to my earlier output with `glm`

. Using my plotting function of last week I can also create a nice 3D plot again.

Posterior predictive distributions |

### Session Info

```
R version 3.2.2 (2015-08-14)
Platform: x86_64-apple-darwin13.4.0 (64-bit)
Running under: OS X 10.10.5 (Yosemite)
locale:
[1] en_GB.UTF-8/en_GB.UTF-8/en_GB.UTF-8/C/en_GB.UTF-8/en_GB.UTF-8
attached base packages:
[1] stats graphics grDevices utils datasets
[6] methods base
other attached packages:
[1] rstan_2.7.0-1 inline_0.3.14 Rcpp_0.12.0
loaded via a namespace (and not attached):
[1] tools_3.2.2 codetools_0.2-14 stats4_3.2.2
```

### Citation

For attribution, please cite this work as:Markus Gesmann (Aug 25, 2015) Visualising the predictive distribution of a log-transformed linear model. Retrieved from https://magesblog.com/post/2015-08-25-visualising-predictive-distribution-of/

@misc{ 2015-visualising-the-predictive-distribution-of-a-log-transformed-linear-model,

author = { Markus Gesmann },

title = { Visualising the predictive distribution of a log-transformed linear model },

url = { https://magesblog.com/post/2015-08-25-visualising-predictive-distribution-of/ },

year = { 2015 }

updated = { Aug 25, 2015 }

}