tvcolmm function implements the
tree-based longitudinal varying coefficient regression algorithm
proposed in Buergin and Ritschard (2015a). The algorithm approximates
varying fixed coefficients in the cumulative logit mixed model by a
(multivariate) piecewise constant function using recursive
partitioning, i.e., it estimates the fixed effect component of the
model separately for strata of the value space of partitioning
variables.
tvcolmm(formula, data, family = cumulative(), weights, subset, offset, na.action = na.omit, control = tvcolmm_control(), ...)
tvcolmm_control(alpha = 0.05, bonferroni = TRUE, minsize = 50, maxnomsplit = 5, maxordsplit = 9, maxnumsplit = 9, fast = TRUE, trim = 0.1, estfun.args = list(), nimpute = 5, seed = NULL, ...)y ~ -1 + vc(z1, ..., zL, by = x1 + ... + xP, intercept = TRUE) + re(1|id)
where vc term specifies the varying fixed coefficients. Only
one such vc term is allowed with
tvcolmm (in contrast to commandtvcglm
where multiple vc terms can be specified). The above example
formula removes the global intercepts and adds locally varying
intercepts, by adding a -1 term and specfiying intercept
= TRUE in the vc term. If varying intercepts are desired, we
recommend to always remove the global intercepts. For more details on
the formula specification, see olmm and
vcrpart-formula.family.olmm.'data' to be used in the fitting process.NAs. The default na.action = na.omit is
listwise deletion, i.e., observations with missings on any variable
are dropped. See na.action.tvcolmm_control.alpha.tvcm_control.tvcm_control.from of function
supLM in package strucchange.gefp.olmm. See details.fit or to tvcm_control.tvcolmm function iterates the following steps:
y ~ Node:x1 + ... + Node:xP + re(1 + w1 + ... |id)
with olmm, where Node is a categorical
variable with terminal node labels 1, ..., M.
Node:x1,
..., separately for each moderator z1, ..., zL
in each node 1, ..., M. This yields L times
M (possibly Bonferroni corrected) $p$-values for
rejecting coefficient constancy.
alpha,
then select the node and the variable corresponding to the minimum
$p$-value. Search and incorporate the optimal
among the candidate splits in the selected node and variable by
exhaustive likelihood search.
alpha,
stop the algorithm and return the current model.
The implemented coefficient constancy tests used for node and variable
selection (step 2) are based on the M-fluctuation tests of Zeileis and
Hornik (2007), using the observation scores of the fitted mixed
model. The observation scores can be extracted by
estfun.olmm for models fitted with
olmm. To deal with intra-individual correlations
between such observation scores, the estfun.olmm
function decorrelates the observation scores. In cases of unbalanced
data, the pre-decorrelation method requires imputation. nimpute
gives the number of times the coefficient constancy tests are repeated
in each iteration. The final $p$-values are then the averages of
the repetations.
The algorithm combines the splitting technique of Zeileis (2008) with the technique of Hajjem et. al (2011) and Sela and Simonoff (2012) to incorporate regression trees into mixed models.
For the exhaustive search, the algorithm implements a number of split
point reduction methods to decrease the computational complexity. See
the arguments maxnomsplit, maxordsplit and
maxnumsplit. By default, the algorithm also uses the
approximative search model approach proposed in Buergin and Ritschard
(2014c). To disable this option to use the original algorithm, set
fast = FALSE in tvcolmm_control.
Special attention is given to varying intercepts, i.e. the terms that account for the direct effects of the moderators. A common specification is
y ~ -1 + vc(z1, ..., zL, by = x1 + ... + xP, intercept = TRUE) + re(1 + w1 + ... |id)
Doing so replaces the globale intercept by local intercepts. As mentioned, if a varying intercepts are desired, we recommend to always remove the global intercept.
Zeileis A., Hornik K. (2007), Generalized M-Fluctuation Tests for Parameter Instability, Statistica Neerlandica, 61(4), 488--508. Buergin R. and Ritschard G. (2015a), Tree-Based Varying Coefficient Regression for Longitudinal Ordinal Responses. Computational Statistics & Data Analysis. Forthcoming. Sela R. and J. S. Simonoff (2012). RE-EM trees: A Data Mining Approach for Longitudinal and Clustered data, Machine Learning 86(2), 169--207. A. Hajjem, F. Bellavance and D. Larocque (2011), Mixed Effects Regression Trees for Clustered Data, Statistics & Probability Letters 81(4), 451--459.
tvcm_control, tvcm-methods,
tvcm-plot, fvcolmm,
olmm## ------------------------------------------------------------------- #
## Example 1: Moderated effect effect of unemployment
##
## Here we fit a varying coefficient ordinal linear mixed on the
## synthetic ordinal longitudinal data 'unemp'. The interest is whether
## the effect of unemployment 'UNEMP' on happiness 'GHQL' is moderated
## by 'AGE', 'FISIT', 'GENDER' and 'UEREGION'. 'FISIT' is the only true
## moderator. For the the partitioning we coefficient constancy tests,
## as described in Buergin and Ritschard (2014a)
## ------------------------------------------------------------------- #
data(unemp)
## fit the model
model.UE <-
tvcolmm(GHQL ~ -1 +
vc(AGE, FISIT, GENDER, UEREGION, by = UNEMP, intercept = TRUE) +
re(1|PID), data = unemp)
## diagnosis
plot(model.UE, "coef")
summary(model.UE)
splitpath(model.UE, steps = 1, details = TRUE)
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