distance_tree()

distance_tree() builds a regression tree that partitions the sample into subgroups with lower within-node sequence discrepancy. Each split is chosen to maximize pseudo-R² and is kept only when a pseudo-F permutation test supports it.

Function Usage

distance_tree(
    distance_matrix,
    predictors,
    weights=None,
    min_size=0.05,
    max_depth=5,
    R=1000,
    pval=0.01,
    weight_permutation=None,
    squared=False,
    first_split=None
)

TraMineR Parameter Mapping

• distance_matrix -> TraMineR diss
• predictors -> TraMineR formula predictors
• weights -> TraMineR weights
• min_size -> TraMineR min.size
• max_depth -> TraMineR maxdepth
• R -> TraMineR R
• pval -> TraMineR pval
• weight_permutation -> TraMineR weight.perm
• squared -> TraMineR squared
• first_split -> TraMineR first.split

Entry Parameters

Parameter	Required	Type	Description
distance_matrix	✓	np.ndarray / pd.DataFrame	Square symmetric distance matrix with shape (n, n).
predictors	✓	pd.DataFrame	Covariates with one row per sequence and one column per predictor.
weights	✗	np.ndarray	Optional sequence weights with shape (n,). If omitted, equal weights are used.
min_size	✗	float / int	Minimum node size. Values below 1 are treated as a fraction of total weight. Default: 0.05.
max_depth	✗	int	Maximum tree depth. Default: 5.
R	✗	int	Number of permutations for split significance. Default: 1000.
pval	✗	float	Maximum p-value required to keep a split. Default: 0.01.
weight_permutation	✗	str / None	Permutation mode: "replicate", "diss", "group", or "none". Default: None (resolved to "none" without weights, otherwise "replicate").
squared	✗	bool	If True, use exponent v = 2 on dissimilarities before tree fitting. Default: False (v = 1).
first_split	✗	str	Optional predictor name forced at the root split.

What It Returns

A dictionary with the fitted tree and supporting metadata.

Key	Type	Description
root	DissTreeNode	Root node of the fitted tree.
fitted	pd.DataFrame	Leaf membership for each sequence in column (fitted).
info	dict	Method name, sample size, tree parameters, global adjustment statistics, and permutation settings.
data	pd.DataFrame	Copy of the predictor data frame used for fitting.
weights	np.ndarray	Weights used during fitting.

The info["adjustment"] entry stores a global single_factor_association() result computed on the final leaf labels. Use it as a compact summary of how well the tree partitions total discrepancy.

Examples

Step 1: Compute a distance matrix

import pandas as pd
from sequenzo import SequenceData, load_dataset
from sequenzo.dissimilarity_measures import get_distance_matrix

df = load_dataset("mvad")
time_list = [c for c in df.columns if str(c).isdigit()]
seqdata = SequenceData(df, time=time_list, states=sorted(df[time_list].stack().unique()))

dist = get_distance_matrix(seqdata=seqdata, method="LCS", norm="auto")

Step 2: Prepare predictors

predictors = df[["male", "fmpr", "emp97"]].copy()

Step 3: Fit the tree

from sequenzo.discrepancy_analysis import distance_tree

tree = distance_tree(
    distance_matrix=dist,
    predictors=predictors,
    R=1000,
    pval=0.05,
    max_depth=4,
)

Step 4: Inspect leaves and rules

from sequenzo.discrepancy_analysis import (
    get_leaf_membership,
    get_classification_rules,
    print_tree,
    plot_tree,
)

print_tree(tree)
leaf_ids = get_leaf_membership(tree)
rules = get_classification_rules(tree)
plot_tree(tree, filename="distance_tree.png")

R Counterpart

• Closest R function: disstree
• Mapping note: Sequenzo uses the same pseudo-R² split criterion, medoid labeling, and permutation-gated splitting strategy as the TraMineR distance-tree workflow.

Notes

• predictors must contain exactly one row per sequence represented in distance_matrix.
• If R <= 1, split retention is effectively permissive because no permutation threshold is applied.
• min_size is interpreted on total weight, not only raw row count.
• The tree is binary because pseudo-R² does not penalize the number of groups.
• Use export_tree_to_dot() when you need a Graphviz representation.
• Use assign_to_leaves() when you want to classify new rows with the fitted tree rules.
• By default, Sequenzo uses nonsquared dissimilarities (v = 1). Set squared=True mainly when the dissimilarity is Euclidean, or as a sensitivity check.
• Use weight_permutation="diss" for survey or calibration weights. The default "replicate" matches TraMineR and is appropriate only for integer frequency weights.

Authors

Code: Yuqi Liang

Documentation: Yuqi Liang

References

Studer, M., Ritschard, G., Gabadinho, A., & Müller, N. S. (2011). Discrepancy analysis of state sequences. Sociological Methods & Research, 40(3), 471–510.

Batagelj, V. (1988). Generalized Ward and related clustering problems. In H. H. Bock (Ed.), Classification and Related Methods of Data Analysis (pp. 67–74). North-Holland.