alsi-kim 0.1.0

Aggregated Latent Space Index for Binary, Ordinal, and Continuous Data

alsi

Aggregated Latent Space Index for Binary, Ordinal, and Continuous Data

Python port of the R alsi package (CRAN, Kim 2026).

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Overview

Multivariate data in behavioral and clinical research frequently exhibit dimensional multiplicity - association structure that distributes across several non-trivial dimensions rather than concentrating in one. The Aggregated Latent Space Index (ALSI) collapses this structure into a single, stability-validated person-level scalar via three automatic stages:

1. Parallel analysis (Horn 1965) - how many dimensions exceed chance?
2. Bootstrap Procrustes stability - dual criterion: principal angle < 20 deg AND Tucker phi >= 0.85
3. Variance-weighted aggregation: alpha_i = sqrt(sum_k w_k * f_ik^2)

Three complete pipelines cover every common data type:

Pipeline	Data type	Method	Index
alsi_workflow()	Binary (0/1)	Multiple Correspondence Analysis	ALSI (non-negative)
alsi_workflow_ordinal()	Likert / ordinal	ALS optimal scaling	Ordinal ALSI (signed)
calsi_workflow()	Continuous	Ipsatized SVD	cALSI (non-negative)

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Installation

pip install alsi

Requirements: Python >= 3.9, numpy >= 1.24, scipy >= 1.10

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Quick start

Continuous data (cALSI)

from alsi import calsi_workflow, wawm4, WAWM4_DOMAINS

result = calsi_workflow(
    wawm4,
    B_pa=2000, B_boot=2000, q=0.95,
    seed=20260206,
    domains=WAWM4_DOMAINS,
)
print(result.summary())

Binary data (ALSI)

from alsi import alsi_workflow, ANR2, ANR2_VARS

result = alsi_workflow(
    ANR2, vars=ANR2_VARS,
    B_pa=2000, B_boot=2000,
    seed=20260123,
)
print(result.summary())

Ordinal data (Ordinal ALSI)

from alsi import alsi_workflow_ordinal, BFI_Extraversion, BFI_ITEMS, BFI_REVERSED_ITEMS

result = alsi_workflow_ordinal(
    BFI_Extraversion,
    items=BFI_ITEMS,
    reversed_items=BFI_REVERSED_ITEMS,
    scale_min=1, scale_max=5,
    n_permutations=100, B_boot=1000,
    seed=12345,
)
print(result.summary())

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Result fields (consistent across all three pipelines)

result.alphas      # (n,) person-level ALSI values - the main output
result.F           # (n, K*) person coordinates in the retained subspace
result.weights     # (K*,) variance weights w_k = lambda_k / sum(lambda_j)
result.K_PA        # dimensions retained by parallel analysis
result.K_star      # dimensions passing dual stability criterion
result.stability   # full bootstrap Procrustes diagnostics dict
result.summary()   # formatted text summary

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Lower-level functions

All lower-level functions from the R package are also available:

from alsi import (
    mca_pa,         # parallel analysis for MCA
    mca_bootstrap,  # bootstrap stability for MCA
    mca_align,      # Procrustes alignment for category coordinates
    svd_pa,         # parallel analysis for ipsatized SVD
    svd_bootstrap,  # bootstrap stability for SVD
    svd_align,      # Procrustes alignment for domain loadings
)

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Built-in datasets

Name	Shape	Pipeline	Description
ANR2	1261 x 13	Binary	Psychiatric diagnostic indicators + EDI/BMI outcomes
BFI_Extraversion	500 x 10	Ordinal	Big Five Inventory Extraversion items (Likert 1-5)
wawm4	900 x 9	Continuous	WAIS-IV / WMS-IV cognitive domain scores

from alsi import ANR2, ANR2_VARS   # ANR2_VARS = the 9 binary columns
from alsi import BFI_Extraversion, BFI_ITEMS, BFI_REVERSED_ITEMS
from alsi import wawm4, WAWM4_DOMAINS

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R package

CRAN: https://cran.r-project.org/package=alsi GitHub: https://github.com/sekangakim/alsi

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Citation

Kim, S.-K. (2026). The Aggregated Latent Space Index: A stability-validated framework for person-level aggregation across binary, ordinal, and continuous data. Manuscript submitted for publication.

Kim, S.-K. (2026). alsi: Aggregated Latent Space Index (v0.1.0) [Python package]. PyPI. https://pypi.org/project/alsi/

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License

GPL-3.0

Author

Se-Kang Kim, Ph.D. Psychology Division, Department of Pediatrics Baylor College of Medicine / Texas Children's Hospital ORCID: 0000-0003-0928-3396 [e-mail]