inference from complex random effects models.

The vanilla versions of asymptotic bias correction and the adjusted score functions in @efron:1975 and @firth:1993, respectively, require the computation of expectations of products of log-likelihood derivatives under the model. Those expectations are intractable or expensive to compute for models with intractable or cumbersome likelihoods, and can be hard to derive even for relatively simple models [see, for example @grun+kosmidis+zeileis:2012 for the required expectations in Beta regression models].

  ----------------------------------------- --------------------- -------------------- ---------- ------------- ----------------- -------------------- --
                                                                                                                                                       
  Method                                     Model specification   Bias approximation     Type     Expectation   Differentiation   Original estimator  
  Asymptotic bias correction                       partial             analytical       Explicit       yes             yes                yes          
  Adjusted score functions                          full               analytical       Implicit       yes             yes                 no          
  Bootstrap                                        partial          simulation-based    Explicit       no              no                 yes          
  Jackknife                                        partial          simulation-based    Explicit       no              no                 yes          
  Iterated bootstrap / Indirect inference           full            simulation-based    Implicit       no              no                 yes          
  RB$M$-estimation                                 partial             analytical       Implicit       no              yes                 no          
  ----------------------------------------- --------------------- -------------------- ---------- ------------- ----------------- -------------------- --

\[br\_characteristics\]

Finally, except of the adjusted scores approach in @firth:1993, all the bias-reduction methods reviewed in Table \[br\_characteristics\] require the original estimator $\hat{{}\theta}$ and they cannot operate without it. For this reason, they directly inherit any of the instabilities that $\hat{{}\theta}$ may have. For example, in multinomial logistic regression, there 