update recommendations for responding to convergence warnings

Author: jgabry

vignettes/rstanarm.Rmd

@@ -334,15 +334,16 @@ the relevant issues.
 
 ### Markov chains did not converge
 
-__Recommendation:__ run the chains for more iterations. <br>
+__Recommendation:__ run the chains for more iterations (in certain cases, see qualification below). <br>
 
 By default, all __rstanarm__ modeling functions will run four randomly 
 initialized Markov chains, each for 2000 iterations (including a warmup period 
 of 1000 iterations that is discarded). All chains must converge to the target 
 distribution for inferences to be valid. For most models, the default settings 
 are sufficient, but if you see a warning message about Markov chains not 
 converging, the first thing to try is increasing the number of iterations. This 
-can be done by specifying the `iter` argument (e.g. `iter = 3000`).
+can be done by specifying the `iter` argument (e.g. `iter = 3000`). However, if all parameters have proper priors (no priors were set to `NULL`), and you used the default values
+for iterations (2000) and chains (4), and Rhats (explained below) are greater than 2, then increasing the number of iterations alone is unlikely to solve to the problem.
 
 One way to monitor whether a chain has converged to the equilibrium distribution
 is to compare its behavior to other randomly initialized chains. This is the 
@@ -388,6 +389,7 @@ any(summary(good_rhat)[, "Rhat"] > 1.1)
 Details on the computation of Rhat and some of its limitations can be found in
 [Stan Modeling Language User's Guide and Reference Manual](https://mc-stan.org/users/documentation/).
 
+
 ### Divergent transitions
 
 __Recommendation:__ increase the target acceptance rate `adapt_delta`. <br>
@@ -418,7 +420,8 @@ the slower sampling is a minor cost.
 
 ### Maximum treedepth exceeded
 
-__Recommendation:__ increase the maximum allowed treedepth `max_treedepth`. <br>
+__Recommendation:__ increase the maximum allowed treedepth `max_treedepth` unless
+all other convergence diagnostics are ok. <br>
 
 Configuring the No-U-Turn-Sampler (the variant of HMC used by Stan) involves 
 putting a cap on the depth of the trees that it evaluates during each iteration.
@@ -427,11 +430,17 @@ maximum allowed tree depth is reached it indicates that NUTS is terminating
 prematurely to avoid excessively long execution time. If __rstanarm__ prints a
 warning about transitions exceeding the maximum treedepth you should try 
 increasing the `max_treedepth` parameter using the optional `control` argument. 
-For example, to increase `max_treedepth` to 20 (the default used __rstanarm__ is
-15) you can provide the argument `control = list(max_treedepth = 20)` to any of 
+For example, to increase `max_treedepth` to 16 (the default used __rstanarm__ is
+15) you can provide the argument `control = list(max_treedepth = 16)` to any of 
 the __rstanarm__ modeling functions. If you do not see a warning about hitting 
 the maximum treedepth (which is rare), then you do not need to worry.
 
+With the models __rstanarm__ is capable of fitting, when you get a warning about 
+max treedepth you will typically also get warnings about other diagnostics. However,
+if you see a max treedepth warning but all other convergence diagnostics
+are fine, you can typically ignore the warning. In that case the warning
+likely indicates efficiency issues but not that the results are invalid to analyze.
+
 # Conclusion
 
 In this vignette, we have gone through the four steps of a Bayesian analysis.