Discrepancy Analysis

Discrepancy analysis asks whether groups or covariates explain part of the discrepancy among trajectories, and whether this association changes across time windows, when sequences are summarized by a pairwise dissimilarity matrix. Instead of comparing one number per person, you compare whole trajectories in the space defined by your chosen dissimilarity measure.

These pages walk through the main functions in sequenzo.discrepancy_analysis, Sequenzo's module for distance-based group comparison. The workflow follows the TraMineR diss* family described in Studer et al. (2011).

What You Need Before You Start

Most pages in this section assume that you already have:

1. A SequenceData object with one row per case and one column per time point.

2. A square symmetric distance matrix from get_distance_matrix() in sequenzo.dissimilarity_measures.

How This Section Is Organized

Topic	Main Sequenzo function	Typical question
Overall trajectory spread	overall_discrepancy()	How much discrepancy is there among all sequences?
One grouping variable	single_factor_association()	Does group membership explain part of the discrepancy among sequences?
Several covariates at once	multifactor_association()	After other covariates are included, how much discrepancy does each factor explain?
One factor at a time	marginal_factor_association()	What is each factor's raw association with discrepancy when tested alone?
Window-wise comparison along time	compare_groups_across_positions()	At which time windows does between-group separation stand out?
Distance-based tree	distance_tree()	Which covariates partition the sample into subgroups with lower within-node discrepancy?
Sequence-based tree	sequence_tree()	Same tree workflow, starting from SequenceData
Permutation inference	permutation_test(), association_permutation_test()	Are observed associations larger than chance?

multifactor_association() follows Type II logic from multifactor ANOVA (Shaw & Mitchell-Olds, 1993). In a model with several covariates, Type II asks: if I remove one covariate while keeping all the others, how much of the explained discrepancy disappears? Each reported contribution is therefore conditional on the remaining predictors, and it does not depend on the order in which variables were entered (unlike Type I incremental sums). marginal_factor_association() is different: it runs separate single-factor tests, one variable at a time, with no adjustment for the others. Do not treat those two summaries as interchangeable.

The pages below focus on the most common workflow functions. The package also exports helper functions such as get_leaf_membership(), plot_tree(), and plot_group_differences_across_positions().

A Beginner-Friendly Workflow

Follow these steps when you compare predefined groups:

1. Prepare sequence data. Build SequenceData with the correct state alphabet, time columns, and optional survey weights.
2. Choose a distance measure. Call get_distance_matrix() with the same method you would use for clustering or visualization. By default, keep squared=False so the analysis uses nonsquared dissimilarities (exponent v = 1), as Studer et al. (2011) recommend for OM, LCS, and other non-Euclidean sequence distances.
3. Run a single-factor association test. Pass the distance matrix and group labels to single_factor_association().
4. Read pseudo R² and permutation p-values. Pseudo R² is the share of total discrepancy explained by the grouping variable. The permutation p-value asks whether that explained share is larger than expected under random label shuffles.
5. Localize differences if needed. Use compare_groups_across_positions() when you want to know where along the time axis groups separate in window-wise local discrepancy.
6. Explore covariate structure if needed. Use distance_tree() or sequence_tree() when you want a regression-tree summary of which predictors split the sample into more homogeneous trajectory subgroups.

How This Differs from Group Comparison (BIC / LRT)

Sequenzo also provides group comparison tools based on the BIC and LRT framework in Liao and Fasang (2021). That workflow compares two predefined groups with a different statistical setup.

Discrepancy analysis is the TraMineR-style pseudo-ANOVA on dissimilarities. It decomposes total discrepancy into between-group and within-group parts, supports more than two groups, and extends to trees, multifactor models, and window-wise scans.

Use discrepancy analysis when you want TraMineR-compatible dissassoc, disstree, and seqdiff-style inference. Use group comparison when your research design matches the two-group BIC/LRT framework.

Included Pages

• Conceptual Guide — core ideas in plain language
• Sequenzo-TraMineR Mapping — function correspondence with TraMineR
• single_factor_association() — test association between distances and one grouping variable
• compare_groups_across_positions() — scan group differences along moving time windows
• Permutation Tests — how randomization is used in this module
• distance_tree() — build a distance-based regression tree
• sequence_tree() — build the same tree from SequenceData

Authors

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.

McArdle, B. H., & Anderson, M. J. (2001). Fitting multivariate models to community data: A comment on distance-based redundancy analysis. Ecology, 82(1), 290–297.

Mielke, P. W., & Berry, K. J. (2007). Permutation Methods: A Distance Function Approach (2nd ed.). Springer.

Liao, T. F., & Fasang, A. E. (2021). Comparing groups of life-course sequences using the Bayesian information criterion and the likelihood-ratio test. Sociological Methodology, 51(1), 44-85.

Shaw, R. G., & Mitchell-Olds, T. (1993). ANOVA for unbalanced data: an overview. Ecology, 74(6), 1638-1645.