Description Usage Arguments Details Value Author(s) References See Also Examples
The tvcolmm
function implements the
treebased longitudinal varying coefficient regression algorithm
proposed in Buergin and Ritschard (2015). 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.
1 2 3 4 5 6 7 8 9  tvcolmm(formula, data, family = cumulative(),
weights, subset, offset, na.action = na.omit,
control = tvcolmm_control(), ...)
tvcolmm_control(sctest = TRUE, 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, maxstep = 1e3, verbose = FALSE, ...)

formula 
a symbolic description of the model to fit, e.g.,
where 
family 
the model family. An object of class

data 
a data frame containing the variables in the model. 
weights 
an optional numeric vector of weights to be used in the fitting process. 
subset 
an optional logical or integer vector specifying a
subset of 
offset 
this can be used to specify an a priori known component to be included in the linear predictor during fitting. 
na.action 
a function that indicates what should happen if data
contain 
control 
a list with control parameters as returned by

sctest 
logical scalar. Defines whether coefficient constancy tests should be used for the variable and node selection in each iteration. 
alpha 
numeric significance threshold between 0 and 1. A node is
splitted when the smallest (possibly Bonferronicorrected) p
value for any coefficient constancy test in the current step falls
below 
bonferroni 
logical. Indicates if and how pvalues of coefficient constancy tests must be Bonferroni corrected. See details. 
minsize 
numeric scalar. The minimum sum of weights in terminal nodes. 
maxnomsplit, maxordsplit, maxnumsplit 
integer scalars for split
candidate reduction. See 
fast 
logical scalar. Whether the approximative model should be
used to search for the next split. See

trim 
numeric between 0 and 1. Specifies the trimming parameter
in coefficient constancy tests for continuous partitioning
variables. See also the argument 
estfun.args 
list of arguments to be passed to

nimpute 
a positive integer scalar. The number of times coefficient constancy tests should be repeated in each iteration. See details. 
seed 
an integer specifying which seed should be set at the beginning. 
maxstep 
integer. The maximum number of iterations i.e. number of splits to be processed. 
verbose 
logical. Should information about the fitting process be printed to the screen? 
... 
additional arguments passed to the fitting function

The tvcolmm
function iterates the following steps:
Fit the current mixed model
y ~ Node:x1 + ... + Node:xP + re(1 + w1 + ... id)
with olmm
, where Node
is a categorical
variable with terminal node labels 1
, ..., M
.
Test the constancy of the fixed effects Node:x1,
...
, separately for each moderator z1
, ..., zL
in each node 1
, ..., M
. This yields L
times
M
(possibly Bonferroni corrected) pvalues for
rejecting coefficient constancy.
If the minimum pvalue is smaller than alpha
,
then select the node and the variable corresponding to the minimum
pvalue. Search and incorporate the optimal
among the candidate splits in the selected node and variable by
exhaustive likelihood search.
Else if minimum pvalue is larger than 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 Mfluctuation 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 intraindividual correlations
between such observation scores, the estfun.olmm
function decorrelates the observation scores. In cases of unbalanced
data, the predecorrelation method requires imputation. nimpute
gives the number of times the coefficient constancy tests are repeated
in each iteration. The final pvalues 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
(2017). 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.
An object of class tvcm
Reto Buergin
Zeileis, A., T. Hothorn, and K. Hornik (2008). ModelBased Recursive Partitioning. Journal of Computational and Graphical Statistics, 17(2), 492–514.
Zeileis A., Hornik K. (2007), Generalized MFluctuation Tests for Parameter Instability, Statistica Neerlandica, 61(4), 488–508.
Buergin R. and Ritschard G. (2015), TreeBased Varying Coefficient Regression for Longitudinal Ordinal Responses. Computational Statistics & Data Analysis, 86, 65–80.
Buergin, R. and G. Ritschard (2017), CoefficientWise TreeBased Varying Coefficient Regression with vcrpart. Journal of Statistical Software, 80(6), 1–33.
Sela R. and J. S. Simonoff (2012). REEM 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
, tvcmmethods
,
tvcmplot
, fvcolmm
,
olmm
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23  ##  #
## Example: 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 (2015)
##  #
data(unemp)
## fit the model
model.UE <
tvcolmm(GHQL ~ 1 +
vc(AGE, FISIT, GENDER, UEREGION, by = UNEMP, intercept = TRUE) +
re(1PID), data = unemp)
## diagnosis
plot(model.UE, "coef")
summary(model.UE)
splitpath(model.UE, steps = 1, details = TRUE)

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