numeric significance level. A node is splitted when the (possibly Bonferroni-corrected) p value for any parameter stability test in that node falls below alpha (and the stopping criteria minsize and maxdepth are not fulfilled).

logical. Should p values be Bonferroni corrected?

integer. The minimum number of observations in a node. If NULL, the default is to use 10 times the number of parameters to be estimated (divided by the number of responses per observation if that is greater than 1). minsize is the recommended name and minsplit/minbucket are only included for backward compatibility with previous versions of mob and compatibility with ctree, respectively.

integer. The maximum depth of the tree.

integer. The number of partitioning variables randomly sampled as candidates in each node for forest-style algorithms. If mtry is greater than the number of partitioning variables, no random selection is performed. (Thus, by default all available partitioning variables are considered.)

numeric. This specifies the trimming in the parameter instability test for the numerical variables. If smaller than 1, it is interpreted as the fraction relative to the current node size.

logical. Should ties in numeric variables be broken randomly for computing the associated parameter instability test?

numeric or character. Number or name of model parameters included in the parameter instability tests (by default all parameters are included).

logical or numeric. as.integer(dfsplit) is the degrees of freedom per selected split employed when computing information criteria etc.

character, numeric, or function for specifying post-pruning rule. If prune is NULL (the default), no post-pruning is performed. For likelihood-based mob() trees, prune can be set to "AIC" or "BIC" for post-pruning based on the corresponding information criteria. More general rules (also in scenarios that are not likelihood-based), can be specified by function arguments to prune, for details see below.

logical. When determining the optimal split point in a numerical variable: Should model estimation be restarted with NULL starting values for each split? The default is TRUE. If FALSE, then the parameter estimates from the previous split point are used as starting values for the next split point (because in practice the difference are often not huge). (Note that in that case a for loop is used instead of the applyfun for fitting models across sample splits.)

logical. Should information about the fitting process of mob (such as test statistics, p values, selected splitting variables and split points) be printed to the screen?

logical. Should weights be interpreted as case weights? If TRUE, the number of observations is sum(weights), otherwise it is sum(weights > 0).

character. Specification of how mob should preprocess y and x variables. Possible choice are: "vector" (for y only), i.e., only one variable; "matrix", i.e., the model matrix of all variables; "data.frame", i.e., a data frame of all variables.

character. Specification of which additional information ("estfun", "object", or both) should be stored in each node. If NULL, no additional information is stored.

logical. Should the full model frame be stored in the resulting object?

character indicating how splits for numeric variables should be justified. Because any splitpoint in the interval between the last observation from the left child segment and the first observation from the right child segment leads to the same observed split, two options are available in mob_control: Either, the split is "left"-justified (the default for backward compatibility) or "center"-justified using the midpoint of the possible interval.

character indicating how (unordered) categorical variables should be splitted. By default the best "binary" split is searched (by minimizing the objective function). Alternatively, if set to "multiway", the node is simply splitted into all levels of the categorical variable.

character indicating which type of covariance matrix estimator should be employed in the parameter instability tests. The default is the outer product of gradients ("opg"). Alternatively, vcov = "info" employs the information matrix and vcov = "sandwich" the sandwich matrix (both of which are only sensible for maximum likelihood estimation).

character indicating which type of parameter instability test should be employed for ordinal partitioning variables (i.e., ordered factors). This can be "chisq", "max", or "L2". If "chisq" then the variable is treated as unordered and a chi-squared test is performed. If "L2", then a maxLM-type test as for numeric variables is carried out but correcting for ties. This requires simulation of p-values via catL2BB and requires some computation time. For "max" a weighted double maximum test is used that computes p-values via pmvnorm.

numeric. Number of replications in the simulation of p-values for the ordinal "L2" statistic (if used).

an optional lapply-style function with arguments function(X, FUN, ...). It is used for refitting the model across potential sample splits. The default is to use the basic lapply function unless the cores argument is specified (see below).

numeric. If set to an integer the applyfun is set to mclapply with the desired number of cores.