Linear Model Trees
Model-based recursive partitioning based on least squares regression.
lmtree(formula, data, subset, na.action, weights, offset, cluster, ...)
formula |
symbolic description of the model (of type
|
data, subset, na.action |
arguments controlling formula processing
via |
weights |
optional numeric vector of weights. By default these are
treated as case weights but the default can be changed in
|
offset |
optional numeric vector with an a priori known component to be
included in the model |
cluster |
optional vector (typically numeric or factor) with a cluster ID to be employed for clustered covariances in the parameter stability tests. |
... |
optional control parameters passed to
|
Convenience interface for fitting MOBs (model-based recursive partitions) via
the mob function. lmtree internally sets up a model
fit function for mob, using either lm.fit
or lm.wfit (depending on whether weights are used or not).
Then mob is called using the residual sum of squares as the objective
function.
Compared to calling mob by hand, the implementation tries to avoid
unnecessary computations while growing the tree. Also, it provides a more
elaborate plotting function.
An object of class lmtree inheriting from modelparty.
The info element of the overall party and the individual
nodes contain various informations about the models.
Zeileis A, Hothorn T, Hornik K (2008). Model-Based Recursive Partitioning. Journal of Computational and Graphical Statistics, 17(2), 492–514.
if(require("mlbench")) {
## Boston housing data
data("BostonHousing", package = "mlbench")
BostonHousing <- transform(BostonHousing,
chas = factor(chas, levels = 0:1, labels = c("no", "yes")),
rad = factor(rad, ordered = TRUE))
## linear model tree
bh_tree <- lmtree(medv ~ log(lstat) + I(rm^2) | zn +
indus + chas + nox + age + dis + rad + tax + crim + b + ptratio,
data = BostonHousing, minsize = 40)
## printing whole tree or individual nodes
print(bh_tree)
print(bh_tree, node = 7)
## plotting
plot(bh_tree)
plot(bh_tree, tp_args = list(which = "log(lstat)"))
plot(bh_tree, terminal_panel = NULL)
## estimated parameters
coef(bh_tree)
coef(bh_tree, node = 9)
summary(bh_tree, node = 9)
## various ways for computing the mean squared error (on the training data)
mean((BostonHousing$medv - fitted(bh_tree))^2)
mean(residuals(bh_tree)^2)
deviance(bh_tree)/sum(weights(bh_tree))
deviance(bh_tree)/nobs(bh_tree)
## log-likelihood and information criteria
logLik(bh_tree)
AIC(bh_tree)
BIC(bh_tree)
## (Note that this penalizes estimation of error variances, which
## were treated as nuisance parameters in the fitting process.)
## different types of predictions
bh <- BostonHousing[c(1, 10, 50), ]
predict(bh_tree, newdata = bh, type = "node")
predict(bh_tree, newdata = bh, type = "response")
predict(bh_tree, newdata = bh, type = function(object) summary(object)$r.squared)
}
if(require("AER")) {
## Demand for economics journals data
data("Journals", package = "AER")
Journals <- transform(Journals,
age = 2000 - foundingyear,
chars = charpp * pages)
## linear regression tree (OLS)
j_tree <- lmtree(log(subs) ~ log(price/citations) | price + citations +
age + chars + society, data = Journals, minsize = 10, verbose = TRUE)
## printing and plotting
j_tree
plot(j_tree)
## coefficients and summary
coef(j_tree, node = 1:3)
summary(j_tree, node = 1:3)
}
if(require("AER")) {
## Beauty and teaching ratings data
data("TeachingRatings", package = "AER")
## linear regression (WLS)
## null model
tr_null <- lm(eval ~ 1, data = TeachingRatings, weights = students,
subset = credits == "more")
## main effects
tr_lm <- lm(eval ~ beauty + gender + minority + native + tenure + division,
data = TeachingRatings, weights = students, subset = credits == "more")
## tree
tr_tree <- lmtree(eval ~ beauty | minority + age + gender + division + native + tenure,
data = TeachingRatings, weights = students, subset = credits == "more",
caseweights = FALSE)
## visualization
plot(tr_tree)
## beauty slope coefficient
coef(tr_lm)[2]
coef(tr_tree)[, 2]
## R-squared
1 - deviance(tr_lm)/deviance(tr_null)
1 - deviance(tr_tree)/deviance(tr_null)
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