Mixed-effects conditional inference trees

Fits a tree that partitions observations on candidate split variables (for example which mutations each sample carries, from haplotypeMatrix()) while a random effect absorbs differences between clusters (for example macrohaplogroups, from macroHaplogroup()). Without the random effect, a tree also splits on variables that merely track the clusters, such as clade-defining markers; with it, those differences are removed before the tree looks for splits.

Usage

mecit(
  y,
  partition,
  cluster = NULL,
  method = c("ctree", "mob"),
  slope = NULL,
  alpha = 0.05,
  minbucket = 20L,
  maxdepth = Inf,
  ranefstart = TRUE,
  abstol = 0.001,
  maxit = 50L
)

Arguments

y: Numeric response, one value per observation.
partition: Matrix or data frame of candidate split variables, one row per observation, with column names (which may be non-syntactic, like "16311").
cluster: Cluster of each observation, or NULL for no random effect.
method: "ctree" or "mob".
slope: Optional names of partition columns to give random slopes within clusters, as in (1 + slope | cluster).
alpha: Significance level for splitting (Bonferroni-adjusted over the candidate variables).
minbucket: Smallest allowed terminal node.
maxdepth: Maximum tree depth.
ranefstart: If TRUE, start from random effects estimated without a tree.
abstol, maxit: Convergence tolerance and the maximum number of iterations. For "ctree" the tolerance is on the largest change in any observation's random-effect contribution; for "mob" it is passed to glmertree::lmertree(), where it applies to the change in log-likelihood.

Value

An object of class mecit: tree (a partykit tree), lmer (the final mixed model, or NULL), strata (data frame of node, mean and n; mean is the stratum level net of random effects), node (terminal node of each observation), ranef (random-effect contribution of each observation), method, iterations and converged.

Details

method = "ctree" (the default) is the RE-EM algorithm of Sela & Simonoff (2012) with conditional inference trees, as proposed by Fu & Simonoff (2015). It alternates between (1) a partykit::ctree() on the response minus the current random-effect contribution and (2) a linear mixed model (lme4::lmer()) with one fixed effect per terminal node plus the random effects, until the random effects stop changing. method = "mob" uses model-based partitioning through glmertree::lmertree() (Fokkema et al. 2018). In both, ranefstart = TRUE estimates the random effects from an intercept-only mixed model before the first tree, which keeps that tree from splitting on cluster-level variables.

With cluster = NULL the result is a plain conditional inference tree, the baseline a mixed-effects tree is compared with.

References

Sela RJ, Simonoff JS (2012). RE-EM trees: a data mining approach for longitudinal and clustered data. Machine Learning 86, 169-207. doi:10.1007/s10994-011-5258-3

Fu W, Simonoff JS (2015). Unbiased regression trees for longitudinal and clustered data. Computational Statistics & Data Analysis 88, 53-74. doi:10.1016/j.csda.2015.02.004

Fokkema M, Smits N, Zeileis A, Hothorn T, Kelderman H (2018). Detecting treatment-subgroup interactions in clustered data with generalized linear mixed-effects model trees. Behavior Research Methods 50, 2016-2034. doi:10.3758/s13428-017-0971-x

Examples

if (FALSE) { # \dontrun{
sim <- simulateExpression(n = 600, genes = 6)
fit <- mecit(sim$expr[, 1], sim$X, sim$samples$macro)
fit
exportWizard(keyFromMecit(fit), "mecit.html")
} # }