# Component-wise Gradient Boosting for Generalised Mixed Models Gradient boosting for optimizing negative log-likelihoods as loss functions where component-wise linear models are utilized as base-learners and an estimation of random components is guaranteed via a maximum likelihood approach. ```r glmermboost(formula, data = list(), weights = NULL, offset = NULL, family = gaussian, na.action = na.omit, contrasts.arg = NULL, center = TRUE, control = boost_control(), oobweights = NULL, ...) ``` ## Arguments - `formula`: a symbolic description of the model to be fit in the lme4-format including random effects. - `data`: a data frame containing the variables in the model. - `weights`: an optional vector of weights to be used in the fitting process. - `offset`: a numeric vector to be used as offset (optional). - `family`: !! This is in contrast to usual mboost - "only" a `family` object is possible - except for `NBinomial()`. - `na.action`: a function which indicates what should happen when the data contain `NA`s. - `contrasts.arg`: a list, whose entries are contrasts suitable for input to the `contrasts` replacement function and whose names are the names of columns of `data` containing factors. See `model.matrix.default`. - `center`: logical indicating of the predictor variables are centered before fitting. - `control`: a list of parameters controlling the algorithm. For more details see `boost_control`. - `oobweights`: an additional vector of out-of-bag weights, which is used for the out-of-bag risk (i.e., if `boost_control(risk = "oobag")`). - ``...``: additional arguments passed to `mboost_fit`; currently none. ## Details The warning "model with centered covariates does not contain intercept" is correctly given - the intercept is estimated via the mixed model. A (generalized) linear mixed model is fitted using a boosting algorithm based on component-wise univariate linear models. Additionally, a mixed model gets estimated in every iteration and added to the current fit. The fit, i.e., the regression coefficients and random effects, can be interpreted in the usual way. This particular methodology is described in Knieper et al. (2025). ## Returns The description of `glmboost` holds while some methods are newly implemented like `predict.mermboost`, `plot.mer_cv` and `mstop.mer_cv`. Only the former one requires a further argument. Additionally, methods `VarCorr.mermboost` and `ranef.mermboost`are implemented specifically. ## See Also See `mermboost` for the same approach using additive models. See `mer_cvrisk` for a cluster-sensitive cross-validation. ## Examples ```r data(Orthodont) # are there cluster-constant covariates? find_ccc(Orthodont, "Subject") # fit initial model mod <- glmermboost(distance ~ age + Sex + (1 |Subject), data = Orthodont, family = gaussian, control = boost_control(mstop = 100)) # let mermboost do the cluster-sensitive cross-validation for you norm_cv <- mer_cvrisk(mod, no_of_folds = 10) opt_m <- mstop(norm_cv) # fit model with optimal stopping iteration mod_opt <- glmermboost(distance ~ age + Sex + (1 |Subject), data = Orthodont, family = gaussian, control = boost_control(mstop = opt_m)) # use the model as known from mboost # in additional, there are some methods knwon from lme4 ranef(mod_opt) VarCorr(mod_opt) ####################### set.seed(123) # Parameters n_groups <- 10 # Number of groups n_per_group <- 50 # Number of observations per group beta_fixed <- c(0.5, -0.3, 0.7) # Fixed effects for intercept, covariate1, covariate2 sigma_random <- 1 # Random effect standard deviation # Simulate random effects (group-specific) group_effects <- rnorm(n_groups, mean = 0, sd = sigma_random) # Simulate covariates covariate1 <- rnorm(n_groups * n_per_group) covariate2 <- rnorm(n_groups * n_per_group) # Simulate data group <- rep(1:n_groups, each = n_per_group) random_effect <- group_effects[group] # Linear predictor including fixed effects and random effects linear_predictor <- beta_fixed[1] + beta_fixed[2] * covariate1 + beta_fixed[3] * covariate2 + random_effect prob <- plogis(linear_predictor) # Convert to probabilities # Simulate binomial outcomes y <- rbinom(n_groups * n_per_group, size = 1, prob = prob) # Combine into a data frame sim_data <- data.frame(group = group, y = y, covariate1 = covariate1, covariate2 = covariate2) sim_data$group <- as.factor(sim_data$group) mod3 <- glmermboost(y ~ covariate1 + covariate2 + (1 | group), data = sim_data, family = binomial()) bin_cv <- mer_cvrisk(mod3, no_of_folds = 10) mstop(bin_cv) ```

glmermboost function