Package 'longitree'

Construction of a Decision Tree for Longitudinal Data

Description

Constructs a single decision tree for longitudinal data. The method evaluates both the main effect of a covariate and its interaction with time, incorporating a weighting mechanism to balance the two effects. Three single-tree construction procedures (ST1, ST2, ST3) are available; see Details. For the underlying methodology, refer to Obata and Sugimoto (2026).

Usage

longitree(
  formula,
  time,
  random,
  weight = "w",
  data,
  alpha = "no",
  gamma = "no",
  cv = "no",
  maxdepth = 5,
  minbucket = 5,
  minsplit = 20,
  xval = 10
)

## S3 method for class 'longitree'
summary(object, ...)

## S3 method for class 'longitree'
print(x, ...)

## S3 method for class 'longitree'
predict(object, ...)

## S3 method for class 'longitree'
plot(x, ...)

Arguments

formula	A formula specifying the model. The response variable should be on the left side and covariates on the right side. Use response ~ . to include all covariates except the time variable and the random effect, or select specific covariates such as response ~ x1 + x2. Time-invariant (baseline) covariates are assumed.
time	Character string giving the column name of the time variable. All individuals are assumed to be observed at the same time points.
random	Character string giving the column name of the random effect (subject identifier).
weight	Weight for balancing the main effect of a covariate and its interaction with time. A value in $\{0.0, 0.1, \ldots, 1.0\}$: 1.0 evaluates only the mean difference in the response variable between the two groups and 0.0 evaluates only the difference in change over time of the response variable between the two groups. Set weight = "w" (the default) to select the optimal weight from the same grid at each node.
data	A data frame containing the variables in formula together with the time and random-effect variables.
alpha	Significance level used as the stopping rule for tree growth. A smaller value produces a more conservative (smaller) tree. Specify a numeric value or "no" (default) if not used. Corresponds to ST2.
gamma	Complexity parameter for pruning. A larger value prunes more aggressively, yielding a smaller and simpler tree; a smaller value retains more branches. Specify a numeric value or "no" (default) if not used. Corresponds to ST3.
cv	Set "yes" to construct the decision tree using cross-validation, or "no" (default) otherwise. Corresponds to ST1.
maxdepth	Maximum depth of the tree (default 5).
minbucket	Minimum number of subjects in a terminal node (default 5).
minsplit	Minimum number of subjects required to attempt a split (default 20).
xval	Number of cross-validation folds (default 10). Used to compute the cross-validated coefficient of determination ($R^2_{\mathrm{CV}}$); when cv = "yes", also used for final tree selection.
object	A longitree object.
...	Additional arguments passed to treeplot.
x	A longitree object.

Details

Exactly one of alpha, gamma, or cv must be specified. Specifying more than one will result in an error. These correspond to the three single-tree construction procedures:

ST1 (cv = "yes")

Tree growth, pruning, and final tree selection via cross-validation.

ST2 (alpha)

Tree growth with a significance threshold. No pruning or final tree selection via cross-validation.

ST3 (gamma)

Tree growth followed by pruning with a pre-specified complexity parameter. No final tree selection via cross-validation.

Since the time variable is not used as a splitting variable, each terminal node (leaf) contains the full longitudinal responses for every subject assigned to it, allowing direct evaluation of longitudinal trajectories within each leaf.

Value

An object of class "longitree". Use summary.longitree, predict.longitree, or plot.longitree to inspect the results.

Methods (by generic)

• summary(longitree): Print a brief summary of a longitree object.

• print(longitree): Print method (calls summary).

• predict(longitree): Extract predicted values and terminal node assignments from a longitree object. Returns a data frame with columns predict (predicted values) and terminalnode (terminal node assignments).

• plot(longitree): Plot a longitree object. A convenience wrapper around treeplot.

References

Obata, R. and Sugimoto, T. (2026). A decision tree analysis for longitudinal measurement data and its applications. Advances in Data Analysis and Classification. doi:10.1007/s11634-025-00665-2

See Also

treeplot, longitrees

Examples

data(ltreedata)
# ST1: tree construction via cross-validation
result_st1 <- longitree(y ~ ., time = "time", random = "subject",
                           weight = 0.7, data = ltreedata, cv = "yes")
summary(result_st1)
predict(result_st1)
plot(result_st1)

# ST2: tree growth with a significance threshold
result_st2 <- longitree(y ~ ., time = "time", random = "subject",
                           weight = 0.1, data = ltreedata, alpha = 0.05)
summary(result_st2)
predict(result_st2)
plot(result_st2)

# ST3: pruning with a complexity parameter
result_st3 <- longitree(y ~ ., time = "time", random = "subject",
                           weight = "w", data = ltreedata, gamma = 3)
summary(result_st3)
predict(result_st3)
plot(result_st3)

---

Construction of Multiple Decision Trees for Longitudinal Data

Description

Generates multiple trees from bootstrap samples and evaluates all three-tree combinations based on two criteria: cross-validated prediction error and tree diversification measured by the adjusted Rand index (ARI). Bootstrap sampling is performed at the subject level to preserve longitudinal structure.

Usage

longitrees(
  formula,
  time,
  random,
  weight = "w",
  data,
  alpha = "no",
  gamma = "no",
  cv = "no",
  maxdepth = 5,
  minbucket = 5,
  minsplit = 20,
  xval = 10,
  bootsize,
  trees = 100,
  mins = 40
)

Arguments

formula	A formula specifying the model. The response variable should be on the left side and covariates on the right side. Use response ~ . to include all covariates except the time variable and the random effect, or select specific covariates such as response ~ x1 + x2. Time-invariant (baseline) covariates are assumed.
time	Character string giving the column name of the time variable. All individuals are assumed to be observed at the same time points.
random	Character string giving the column name of the random effect (subject identifier).
weight	Weight for balancing the main effect of a covariate and its interaction with time. A value in $\{0.0, 0.1, \ldots, 1.0\}$: 1.0 evaluates only the mean difference in the response variable between the two groups and 0.0 evaluates only the difference in change over time of the response variable between the two groups. Set weight = "w" (the default) to select the optimal weight from the same grid at each node.
data	A data frame containing the variables in formula together with the time and random-effect variables.
alpha	Significance level used as the stopping rule for tree growth. A smaller value produces a more conservative (smaller) tree. Specify a numeric value or "no" (default) if not used. Corresponds to ST2.
gamma	Complexity parameter for pruning. A larger value prunes more aggressively, yielding a smaller and simpler tree; a smaller value retains more branches. Specify a numeric value or "no" (default) if not used. Corresponds to ST3.
cv	Set "yes" to construct the decision tree using cross-validation, or "no" (default) otherwise. Corresponds to ST1.
maxdepth	Maximum depth of the tree (default 5).
minbucket	Minimum number of subjects in a terminal node (default 5).
minsplit	Minimum number of subjects required to attempt a split (default 20).
xval	Number of cross-validation folds (default 10). Used to compute the cross-validated coefficient of determination ($R^2_{\mathrm{CV}}$); when cv = "yes", also used for final tree selection.
bootsize	Number of subjects in each bootstrap sample.
trees	Number of bootstrap trees to grow (default 100).
mins	Number of top-ranking candidate three-tree subsets to retain (default 40).

Details

See longitree for a description of the three single-tree construction procedures (ST1, ST2, ST3) corresponding to cv, alpha, and gamma.

Value

An object of class "longitrees". Pass to selectionplot to select the optimal three-tree combination.

References

Obata, R. and Sugimoto, T. (2026). A decision tree analysis for longitudinal measurement data and its applications. Advances in Data Analysis and Classification. doi:10.1007/s11634-025-00665-2

See Also

longitree, selectionplot, threetrees, treeplot

---

Sample longitudinal data for decision tree examples

Description

A sample balanced longitudinal dataset with 50 subjects observed at 10 equally spaced time points.

Usage

ltreedata

Format

A data frame with 500 rows and 7 variables:

y

Response variable (continuous).

subject

Subject identifier (integer, 1–50).

time

Time point (integer, 1–10).

x1

Baseline covariate 1 (integer, 1–10).

x2

Baseline covariate 2 (integer, 1–10).

x3

Baseline covariate 3 (integer, 1–6).

x4

Baseline covariate 4 (integer, 1–12).

---

Select Optimal Three-Tree Combination

Description

Plots the cross-validated prediction error against the maximum pairwise adjusted Rand index (ARI) for candidate three-tree subsets, and selects a subset based on either prediction performance or tree diversification. The selected combination is indicated by a red point on the plot, which corresponds to the three trees used in the subsequent threetrees step.

Usage

selectionplot(longitrees, metric, nth)

Arguments

longitrees	A longitrees object.
metric	"PE" to select the subset with the smallest cross-validated prediction error, or "ARI" to select the subset with the smallest maximum pairwise ARI (greatest tree diversification).
nth	Rank of the tree subset to select (1 = best).

Value

An object of class "selectionplot". Pass to threetrees to refit and evaluate the selected trees.

References

Obata, R. and Sugimoto, T. (2026). A decision tree analysis for longitudinal measurement data and its applications. Advances in Data Analysis and Classification. doi:10.1007/s11634-025-00665-2

See Also

longitrees, threetrees

---

Fit and Evaluate Three Selected Trees

Description

Refits the three trees selected by selectionplot on their original bootstrap samples.

Usage

threetrees(x, selection)

## S3 method for class 'threetrees'
summary(object, ...)

## S3 method for class 'threetrees'
print(x, ...)

## S3 method for class 'threetrees'
predict(object, tree = 1, ...)

## S3 method for class 'threetrees'
plot(x, tree = 1, ...)

Arguments

x	A threetrees object.
selection	A selectionplot object.
object	A threetrees object.
...	Additional arguments passed to treeplot.
tree	Integer 1, 2, or 3 selecting which tree to plot.

Value

An object of class "threetrees". Use summary.threetrees, predict.threetrees, or plot.threetrees to inspect the results.

Methods (by generic)

• summary(threetrees): Print a brief summary of a threetrees object.

• print(threetrees): Print method (calls summary).

• predict(threetrees): Extract predicted values and terminal node assignments from a threetrees object. Returns a data frame with columns predict (predicted values) and terminalnode (terminal node assignments).

• plot(threetrees): Plot one of the three trees. A convenience wrapper around treeplot.

References

Obata, R. and Sugimoto, T. (2026). A decision tree analysis for longitudinal measurement data and its applications. Advances in Data Analysis and Classification. doi:10.1007/s11634-025-00665-2

See Also

longitrees, selectionplot, treeplot

Examples

data(ltreedata)
set.seed(10)
trees_res <- longitrees(y ~ ., time = "time", random = "subject",
                           weight = 0.5, data = ltreedata, alpha = 0.01,
                           bootsize = 50, mins = 40)
sel <- selectionplot(trees_res, metric = "PE", nth = 1)
tt <- threetrees(trees_res, selection = sel)
summary(tt)
predict(tt, tree = 1)
predict(tt, tree = 2)
predict(tt, tree = 3)
plot(tt, tree = 1)
plot(tt, tree = 2)
plot(tt, tree = 3)

---

Decision Tree Plot Visualisation for Longitudinal Data

Description

Visualises the structure of a decision tree for longitudinal data. Built on ggparty. Each split node displays the node number, split variable, $p$-value, and weight $w$. Each terminal node displays the node number, sample size $N$, and the intercept ($\hat\beta_0$) and slope ($\hat\beta_1$) from a linear mixed-effects model fitted within that node. Individual longitudinal trajectories are shown as dashed lines; the predicted values (average at each time point) are shown as solid lines, with the response variable on the vertical axis and time on the horizontal axis.

Usage

treeplot(
  x,
  tree = NULL,
  snsize = 50,
  spsize = 5,
  plotsize = 80,
  linesize1 = 0.3,
  linesize2 = 1,
  tnsize = 60
)

Arguments

x	A longitree or threetrees object.
tree	Integer 1, 2, or 3 selecting which tree to plot when x is a threetrees object.
snsize	Split-node label size (default 50).
spsize	Split-point label size (default 5).
plotsize	Overall plot size (default 80).
linesize1	Branch line width (default 0.3).
linesize2	Main line width (default 1).
tnsize	Terminal-node label size (default 60).

Value

A ggplot2/ggparty object.

References

Obata, R. and Sugimoto, T. (2026). A decision tree analysis for longitudinal measurement data and its applications. Advances in Data Analysis and Classification. doi:10.1007/s11634-025-00665-2

See Also

longitree, threetrees

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