The following screenshots show how to fit an example model in the shinybrms app. For instructions on how to launch the shinybrms app, see the starting page.

## Home

After launching the shinybrms app, the following page is shown:

Fig. 1: Page “Home”.

## Data

We then switch to page “Data”. Usually, you will want to upload a custom dataset, but for the purpose of demonstration, we will choose the example dataset MASS::bacteria here:

Fig. 2: Page “Data” (top).

Further down on page “Data”, we may choose, for example, to show all rows of the dataset:

Fig. 3: Page “Data” (further down when showing all rows of the dataset).

## Likelihood

### Outcome

On page “Likelihood”, the first tab is called “Outcome”. Here, we define variable y (from our dataset MASS::bacteria) to be the outcome and since this is a binary outcome, we choose the distributional family “Bernoulli with logit link”:

Fig. 4: Page “Likelihood”, tab “Outcome”.

### Predictors

After selecting tab “Predictors”, we set up (pooled) main effects for variables week and trt and partially pooled main effects (i.e., partially pooled intercepts) for variable ID:

Fig. 5: Page “Likelihood”, tab “Predictors” (top).

After scrolling down, we set up a (pooled) interaction term for week and trt:

Fig. 6: Page “Likelihood”, tab “Predictors” (bottom; setting up the interaction effect).

After clicking on “Add interaction term”, we get:

Fig. 7: Page “Likelihood”, tab “Predictors” (bottom; after adding the interaction effect).

## Prior

### Default priors

At the top of page “Prior”, we obtain a table with the default priors for the model we have specified so far:

Fig. 8: Page “Prior” (top).

### Custom priors

At the bottom of page “Prior”, we can specify custom priors. Here, we will use a Student-t prior distribution with 3 degrees of freedom, a location parameter of 0, and a scale parameter of 4 for all regression coefficients (parameter class b):

Fig. 9: Page “Prior” (bottom; setting up a custom prior).

After clicking on “Add prior”, we see that our Student-t prior was added to the preview table on the right:

Fig. 10: Page “Prior” (bottom; after adding a custom prior).

## Posterior

### Run Stan

On page “Posterior”, the first tab is called “Run Stan”. At the top of this tab, we could get a preview of the Stan code and the Stan data (and download them):

Fig. 11: Page “Posterior”, tab “Run Stan” (top).

Here, we focus on panel “Advanced options” where we set a seed for reproducibility:

Fig. 12: Page “Posterior”, tab “Run Stan”, panel “Advanced options”.

Next, we head over to the fundamental part of our analysis, the inference of the posterior distribution of all parameters. Since we have everything prepared now, this is accomplished quite easily: Right below panel “Advanced options”, we find panel “Run Stan” where we simply click the button for running Stan:

Fig. 13: Page “Posterior”, tab “Run Stan”, panel “Run Stan”.

Now Stan starts compiling the C++ code for our model and after having finished the compilation, Stan automatically starts sampling. As we have not changed the default for advanced option “Open progress”, a file will automatically open up (in a new browser tab) after completion of the compilation. This file shows the sampling progress:

Fig. 14: Sampling progress (top).

Depending on your model and data, the sampling might take a while. For the example here, the sampling proceeds quite fast. Note that the progress file needs to be refreshed manually (by refreshing the corresponding browser tab). When Stan has finished sampling, the bottom of the progress file looks something like this:

Fig. 15: Sampling progress (bottom; after completion of sampling).

We can now switch back to the browser tab where shinybrms is running. Most importantly, we get the result of an “overall check” for the Markov chain Monte Carlo (MCMC) diagnostics which are given in detail on tab “MCMC diagnostics”. Here, all MCMC diagnostics are OK:

Fig. 16: Page “Posterior”, tab “Run Stan”, panel “Run Stan” (after completion of the Stan run).

### MCMC diagnostics (details)

Tab “MCMC diagnostics” first shows a description which MCMC diagnostics are checked here:

Fig. 17: Page “Posterior”, tab “MCMC diagnostics” (top).

Underneath this description, the diagnostic results for the given Stan run are shown; first the diagnostics specific to Hamiltonian Monte Carlo (HMC) and then the general MCMC diagnostics:

Fig. 18: Page “Posterior”, tab “MCMC diagnostics” (bottom).

For the general MCMC diagnostics (which are computed for each parameter as well as for the accumulated log-posterior density), it is also possible to show a detailed table:

Fig. 19: Page “Posterior”, tab “MCMC diagnostics”, top of the detailed table of the general MCMC diagnostics.

### Default summary

Since all MCMC diagnostics look good, we may start interpreting the posterior. On tab “Default summary”, we get a short summary of our Stan run, including the median (column Estimate), the median absolute deviation (column Est.Error), and the 2.5% and 97.5% quantiles (columns l-95% CI and u-95% CI, respectively) of the marginal posterior distribution of the most important parameters:

Fig. 20: Page “Posterior”, tab “Default summary”.

### Custom summary

The purpose of tab “Custom summary” is explained in the help text of that tab:

Fig. 21: Page “Posterior”, tab “Custom summary” (top).

Here, it makes sense to calculate posterior summary quantities for the trt-specific week effects which are given by the sum of the main effect of week and the interaction effect with the corresponding trt value (except for the reference level of trt where this interaction effect does not exist):

Fig. 22: Page “Posterior”, tab “Custom summary” (bottom; showing a custom summary for the week:trt effects).

### Conditional effects

The purpose of tab “Conditional effects” is explained in the help text of that tab:

Fig. 23: Page “Posterior”, tab “Conditional effects” (top).

Here, it makes sense to plot the conditional effects for the week:trt interaction:

Fig. 24: Page “Posterior”, tab “Conditional effects” (bottom; showing the plot for week:trt).

### Launch shinystan

Note that the output shown on tab “Default summary” is only intended for a quick inspection. A much more comprehensive analysis of the output is possible using the shiny app from shinystan which also offers posterior predictive checks as well as more details concerning the MCMC diagnostics. We launch the shinystan app by clicking the corresponding button on tab “Launch shinystan” (after having entered a seed for the reproducibility of the posterior predictive checks):

Fig. 21: Page “Posterior”, tab “Launch shinystan”.

At this point, the shinybrms workflow ends and passes over to shinystan.