fapa 0.1.1

Factor Analytic Profile Analysis of Ipsatized Data

fapa

Factor Analytic Profile Analysis of Ipsatized Data

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

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Overview

FAPA is a metric inferential framework for pattern detection and person-level reconstruction in multivariate profile data. After row-centering (ipsatization) to remove profile elevation, FAPA applies SVD to recover shared core profiles and individual pattern weights via a three-stage bootstrap verification framework.

The FAPA workflow

1. Ipsatization - remove person-level elevation to isolate within-person pattern structure
2. Core estimation - SVD recovers core profiles, person weights, and variance decomposition
3. Stage 1: Dimensionality - variance-matched Horn's parallel analysis
4. Stage 2: Subspace stability - bootstrap principal angles (Procrustes)
5. Stage 3: Profile replicability - Tucker's congruence coefficients
6. Inference - BCa bootstrap confidence intervals for core-profile coordinates
7. Reconstruction - person-level R2 and pattern weights

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Installation

pip install fapa

For pandas support: pip install "fapa[full]"

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

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Quick start

from fapa import (load_and_ipsatize, fapa_core, fapa_pa,
                  fapa_procrustes, fapa_tucker, fapa_bca,
                  fapa_person, print_pa, print_procrustes,
                  print_tucker, fapa_simdata)

# Step 1: Ipsatize
d = load_and_ipsatize(fapa_simdata)
Xt = d["ipsatized"]          # 500 x 22 EDI-2 matrix, row-sums = 0

# Stage 1: Parallel analysis
pa = fapa_pa(Xt, B=2000, seed=42)
print_pa(pa)
K = pa["n_retain"]           # e.g. 2

# Core estimation
fit = fapa_core(Xt, K=K)
print(f"Variance explained: {fit['cum_var'][-1]*100:.1f}%")

# Stage 2: Subspace stability
pr = fapa_procrustes(Xt, K=K, B=2000, angle_thresh=30, seed=42)
print_procrustes(pr, K_pa=K)

# Stage 3: Profile replicability
tc = fapa_tucker(Xt, K=K, B=2000, cc_thresh=0.85, seed=42)
print_tucker(tc, cc_thresh=0.85, K_pa=K)

# BCa confidence intervals
bca = fapa_bca(Xt, K=K, B=2000, alpha=0.05, seed=42)
print(bca["ci"][0].round(3))   # Core Profile 1 CI table

# Person reconstruction
person = fapa_person(Xt, fit, participants=[0, 1, 2])
print(f"Mean R2 = {person['R2_mean']:.3f}")

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Built-in dataset

fapa_simdata is a 500 x 22 matrix of simulated EDI-2 (Eating Disorder Inventory-2) subscale scores, with 11 pre-treatment and 11 post-treatment columns. The latent structure approximates two components: a normative symptom gradient (CP1) and a pre/post treatment change contrast (CP2).

from fapa import fapa_simdata, FAPA_COLS, FAPA_PRE_COLS, FAPA_POST_COLS
print(fapa_simdata.shape)    # (500, 22)
print(FAPA_PRE_COLS[:3])     # ['Before_1_Dt', 'Before_2_Bu', 'Before_3_Bd']

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R package

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

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Citation

Kim, S.-K. (2024). Factorization of person response profiles to identify summative profiles carrying central response patterns. Psychological Methods, 29(4), 723-730. doi:10.1037/met0000568

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License

MIT

Author

Se-Kang Kim, Ph.D. Baylor College of Medicine / Texas Children's Hospital [e-mail]