Gradient Boosting for Generalized Additive Mixed Models.

mermboost

Installation Instructions

• Currently only available via github:

  devtools::install_github("larsknieper/mermboost")
  library("mermboost")
  

Tutorial

Simulations as well as data applications show that users can benefit from using mermboost as unbiased estimates as well as an enabled estimation of random effects variation is included.

Technically, it is calling a newly defined family (merMod), in which random components are treated as nuisance parameters and are repeatedly estimated by an glmer() object from lme4. Simultaneously, fixed effects are estimated in a common way by the established mboost package. Since a lme4 model is included mermboost is restricted to distributions of base-R-families with the negative binomial distribution in addition. From a user's perspective, four functions are provided, namely:

The function find_ccc() takes the arguments of a dataframe and a name of a cluster-defining variable. It gives logical values corresponding to all further variables, whether or not these are constant across each cluster as this is causing the described bias. Still, by providing an estimation of random effects' covariance $\boldsymbol{Q}$ mermboost is a good choice for boosting mixed models even when there are no cluster constant covariates in the data set.

The boosting functions are wrappers of the corresponding mboost functions. Hence, glmerboost() is a wrapper of glmboost() and mermboost() is a wrapper of mboost(). After initialising a lme4 object, both start the corresponding mboost model with the merMod family.

To call the boosting functions some modifications are needed in comparison to mboost. The random effects are not specified within the base-learner brandom() anymore but in the way they are specified in lme4 (and other mixed model packages) by "... + (random formula | id)". By this, the add-on package differs visually from the mboost package even though this leads to a mixed formula format. Thus, to estimate a specified model formulation of $\boldsymbol{\eta} = \beta_0 + \beta_1 \boldsymbol{x}_1 + \beta_2 \boldsymbol{x}_2 + \boldsymbol{\gamma}_0$ for a binomial distributed response variable $\boldsymbol{y}$ with a cluster specifying id the differences are as follows:

mboost

mboost(y ~ bols(x1) + bols(x2) + brandom(id),
        family = Binomial(type = "glm"),
        data = df)

mermboost

glmerboost(y ~ x1 + x2 + (1 | id),,
            family = binomial(),
            data = df)

To clarify this even further, assume a GAMM with an additional random slope defined as $\boldsymbol{\eta} = f_1 (\boldsymbol{x}_1) + f_2 (\boldsymbol{x}_2) + \boldsymbol{\gamma}_0 + \boldsymbol{\gamma}_1 \boldsymbol{z}_2$, where $\boldsymbol{x}_2 = \boldsymbol{z}_2$. The corresponding models are to be called as follows without consideration of possible adjustments within bbs():

mboost

mboost(y ~ bbs(x1) + bbs(x2) + brandom(id) + brandom(id, by = x2),
        family = Binomial(type = "glm"), data = df)

mermboost

mermboost(y ~ bbs(x1) + bbs(x2) + (1 + x2 | id), 
          family = binomial(), data = df)

Some methods of functions got adjusted to, where predict() is considering the nuisance estimations and therefore the random effects as well. With the argument RE it can be controlled whether to include random effects (TRUE) or not (FALSE).

To perform a cross-validation with a cluster-wise test-train split mer\_cvrisk() takes the mermboost object and the number of folds as an argument. The folds are then generated automatically within the function considering the cluster structure by its identifying variable, which is stored in the mermboost object. However, this might lead to unwanted splits. This is why alternatively pre-specified folds can be given as an argument as well by a matrix containing 0's and 1's indicating the folds. The cross-validation can can further be conducted by parallel computing, where the number of cores are to be specified by the core argument.