pylmm3 0.2.3

Python 3 linear mixed-model solver for genome-wide association studies

pylmm3

A fast, lightweight linear mixed-model solver for genome-wide association studies.

pylmm3 is a Python 3 implementation of the EMMA/fastLMM linear mixed model (LMM) framework. It corrects for population stratification and cryptic relatedness in GWAS by modeling pairwise genetic similarity (kinship) as a random effect, then tests each SNP for an additional fixed effect on top of that background.

Two command-line tools and a clean Python API:

• pylmmKinship — compute the realized relationship matrix (GRM) from PLINK genotype files
• pylmmGWAS — run the genome-wide association scan given a kinship matrix and phenotype file

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Contents

• Quick Start
• Installation
• Running the Tools
  • Option 1 — uv run (no activation)
  • Option 2 — Activate the virtual environment
• Two-Stage Workflow
• Python API
• CLI Reference
• Logging
• Output Format
• Testing
• How It Works
• Known Limitations
• Authors
• License

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Quick Start

git clone https://github.com/TheJacksonLaboratory/pylmm3.git
cd pylmm3
uv sync

# Stage 1 — build the kinship matrix
uv run pylmmKinship --bfile /path/to/study study.kin

# Stage 2 — run the GWAS
uv run pylmmGWAS --bfile /path/to/study --kfile study.kin --phenofile study.phenos results.tsv

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Installation

Choose the path that fits your situation. All three install numpy and scipy automatically.

Install uv first (if you don't have it):

curl -LsSf https://astral.sh/uv/install.sh | sh

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Tier 1 — Just run the CLI tools (no clone, no project setup)

uv tool install puts pylmmGWAS and pylmmKinship on your PATH in an isolated environment. This is the right path for anyone who just wants to run GWAS jobs.

uv tool install git+https://github.com/TheJacksonLaboratory/pylmm3.git

# Commands are now available globally:
pylmmKinship --bfile /data/study study.kin
pylmmGWAS    --bfile /data/study --kfile study.kin --phenofile study.phenos out.tsv

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Tier 2 — Use pylmm3 as a library inside your own project

# uv project
uv add git+https://github.com/TheJacksonLaboratory/pylmm3.git

# pip / any other tool
pip install git+https://github.com/TheJacksonLaboratory/pylmm3.git

Then import:

from pylmm3 import LMM, calculateKinship, runGWAS

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Tier 3 — Local development (clone and edit source)

git clone https://github.com/TheJacksonLaboratory/pylmm3.git
cd pylmm3
uv sync          # creates .venv, installs all dependencies + pylmm3 in editable mode

uv sync reads pyproject.toml and uv.lock for a fully reproducible environment. See Running the Tools below for how to invoke the CLIs after sync.

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Running the Tools

After uv sync there are two equally valid ways to run pylmm3.

Option 1 — uv run (no activation)

uv run transparently invokes commands inside .venv without requiring you to activate anything first. Works from any shell, any directory — no PATH changes needed.

# CLI entry points (registered in pyproject.toml)
uv run pylmmKinship --bfile /data/study study.kin
uv run pylmmGWAS   --bfile /data/study --kfile study.kin --phenofile study.phenos out.tsv

# Module invocation (identical result)
uv run python -m pylmm3.scripts.pylmmKinship --bfile /data/study study.kin
uv run python -m pylmm3.scripts.pylmmGWAS   --bfile /data/study --kfile study.kin out.tsv

# Interactive Python with pylmm3 available
uv run python

Option 2 — Activate the virtual environment

Activate once per shell session; then call the tools directly.

source .venv/bin/activate

pylmmKinship --bfile /data/study study.kin
pylmmGWAS    --bfile /data/study --kfile study.kin --phenofile study.phenos out.tsv

python -c "from pylmm3 import LMM, calculateKinship, runGWAS; print('ready')"

deactivate   # when done

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Two-Stage Workflow

The kinship matrix is the bridge between the two tools. Once computed it can be reused across multiple GWAS runs on the same cohort — testing different phenotypes or covariate configurations without re-building kinship.

Genotype files (.bed / .bim / .fam)
Phenotype file  (.phenos)
         │
         ▼
  ┌─────────────────┐
  │  pylmmKinship   │  ← reads genotypes, normalizes SNPs, builds K = W·Wᵀ / m
  └─────────────────┘
         │
     study.kin              (reusable across phenotypes)
     study.kin.kva/.kve     (optional; skip O(n³) eigen on next run)
         │
         ▼
  ┌─────────────────┐
  │   pylmmGWAS     │  ← fits null LMM once, then tests each SNP
  └─────────────────┘
         │
         ▼
  results.tsv
  SNP_ID  BETA  BETA_SD  F_STAT  P_VALUE

Typical run — with logging and saved eigendecomposition

# Build kinship, save eigenvectors for reuse (INFO shows milestones + timing)
uv run pylmmKinship \
  --bfile /data/study \
  --efile study.eigen \
  --log-level INFO \
  study.kin

# Run GWAS — load saved eigens, skip the O(n³) decomposition at startup
uv run pylmmGWAS \
  --bfile     /data/study \
  --kfile     study.kin \
  --eigen     study.eigen \
  --phenofile study.phenos \
  --log-level INFO \
  results.tsv

---

Python API

The public API exports four symbols:

from pylmm3 import LMM, calculateKinship, runGWAS, load_snp_matrix

Build a kinship matrix

import numpy as np
from pylmm3 import input as plink_input, calculateKinship

# Load genotypes from a PLINK binary fileset (.bed/.bim/.fam)
reader = plink_input.plink("study", type='b')
W = plink_input.load_snp_matrix(reader)   # (n_individuals, n_snps), np.nan for missing

K = calculateKinship(W)                   # (n, n) realized relationship matrix
np.savetxt("study.kin", K)                # plain-text format read by pylmmGWAS

Run a GWAS scan

from pylmm3 import runGWAS          # vectorized fast path (gwas_fast)
from pylmm3 import input as plink_input
import numpy as np

# Load data
reader = plink_input.plink("study", type='b', phenoFile="study.phenos")
Y = reader.phenos[:, 0]              # first phenotype column
K = np.loadtxt("study.kin")

# Fit null LMM once, scan all SNPs
results = runGWAS(Y, K, reader)      # numpy structured array

# Access results
import pandas as pd
df = pd.DataFrame(results)
print(df.sort_values("P_VALUE").head(10))

Reference vs fast path: from pylmm3 import runGWAS is the vectorized implementation (gwas_fast.py), which is the same default used by the CLI. The reference per-SNP loop is available as from pylmm3.gwas import runGWAS and produces numerically identical results (max relative error < 3×10⁻⁹).

Use the LMM class directly

from pylmm3 import LMM
from pylmm3 import input as plink_input
import numpy as np

# Load genotypes and phenotypes via the PLINK reader
reader = plink_input.plink("study", type='b', phenoFile="study.phenos")
Y = reader.phenos[:, 0]              # first phenotype column

# Kinship is plain text written by pylmmKinship / np.savetxt
K = np.loadtxt("study.kin")

# Initialize — eigendecomposition computed here if Kva/Kve not provided
model = LMM(Y, K)

# Fit the null model
model.fit(REML=True)
print(f"Heritability: {model.optH:.3f}  σ²: {model.optSigma:.4f}")

# Test a single SNP (genotype vector, length N, values in {0.0, 0.5, 1.0, nan})
# Apply model.nonmissing mask — LMM removes individuals with missing phenotype,
# so the SNP vector must be subset to the same individuals before calling association().
snp, snp_id = next(iter(reader))
ts, ps = model.association(snp[model.nonmissing].reshape(-1, 1))
print(f"{snp_id}: t = {ts:.4f}  p = {ps:.2e}")

Note: The verbose parameter on LMM() is accepted for backward compatibility but is ignored. Use PYLMM3_LOG_LEVEL=DEBUG or --log-level DEBUG to see internal detail. See Logging below.

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CLI Reference

pylmmKinship

uv run pylmmKinship [options] --[bfile | tfile | emmaSNP] <base> <outfile>

Flag	Required	Description
--bfile <base>	one of three	Base path for PLINK binary files (.bed / .bim / .fam)
--tfile <base>	one of three	Base path for PLINK text files (.tped / .tfam)
--emmaSNP <file>	one of three	EMMA-format genotype file
--emmaNumSNPs <n>	with --emmaSNP	Number of SNPs in the EMMA file
-e, --efile <base>	no	Save eigendecomposition to <base>.kva and <base>.kve
--log-level LEVEL	no	Log verbosity: DEBUG, INFO, WARNING, ERROR (default: WARNING)
-v, --verbose	no	Shorthand for --log-level INFO
<outfile>	yes	Output path for the kinship matrix

pylmmGWAS

uv run pylmmGWAS [options] --kfile <kin> --[bfile | tfile | emmaSNP] <base> <outfile>

Basic options

Flag	Required	Default	Description
--bfile <base>	one of three	—	PLINK binary fileset base path
--tfile <base>	one of three	—	PLINK text fileset base path
--emmaSNP <file>	one of three	—	EMMA-format genotype file
--emmaPHENO <file>	no	—	EMMA-format phenotype file
--emmaCOV <file>	no	—	EMMA-format covariate file
--kfile <file>	yes	—	Pre-computed kinship matrix (.kin or .kin.gz)
--phenofile <file>	no	<bfile>.phenos	PLINK phenotype file
-p <int>	no	0	0-indexed phenotype column (counting from column 3)
--covfile <file>	no	—	PLINK covariate file
<outfile>	yes	—	Output path for GWAS results

Advanced options

Flag	Default	Description
--eigen <base>	—	Load pre-computed eigendecomposition (<base>.kva / <base>.kve); skips O(n³) decomp at startup
--REML	off	Use REML for per-SNP association tests (null model always uses REML regardless)
--refit	off	Re-estimate variance components at every SNP; more accurate, much slower
--removeMissingGenotypes	off	Drop individuals with missing genotypes per SNP instead of imputing with the mean
--noMean	off	Suppress automatic intercept when --covfile is provided
--orig	off	Use the reference per-SNP loop instead of the default vectorized scan
--log-level LEVEL	WARNING	Log verbosity: DEBUG, INFO, WARNING, ERROR
-v, --verbose	off	Shorthand for --log-level INFO

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Logging

pylmm3 follows the standard Python library logging contract: it attaches a NullHandler to the pylmm3 logger at import time and never calls basicConfig() or installs a handler of its own. All loggers are named pylmm3.<module> (e.g. pylmm3.gwas_fast, pylmm3.lmm) and propagate to the root logger. The calling application installs the handler and decides how loud each component should be.

Log levels

Level	Default?	What you see
ERROR	always	Unrecoverable failures — bad BED magic, unknown file type
WARNING	always	Dropped individuals, missing kinship entries, multiple optima during heritability optimization
INFO	off	Per-step timings — SNP load, LMM construction, null fit (h + σ²), scan throughput, total elapsed
DEBUG	off	Internal detail — eigendecomposition breakdown, BED bytes per SNP, per-10k-SNP throughput ticks

The default level is WARNING (nearly silent). A production run emits output only when something is wrong.

Running the pylmm3 CLIs directly

Via CLI flag:

uv run pylmmGWAS --log-level INFO  ... results.tsv   # milestones + timing
uv run pylmmGWAS --log-level DEBUG ... results.tsv   # full internal trace
uv run pylmmGWAS --verbose         ... results.tsv   # shorthand for INFO

Via environment variable — useful for one-off debugging without changing the command line:

PYLMM3_LOG_LEVEL=DEBUG uv run pylmmGWAS --bfile study --kfile study.kin results.tsv

Priority when running the CLI: --log-level flag > PYLMM3_LOG_LEVEL env var > WARNING default.

Running pylmm3 through an orchestrator (e.g. plinkformatter)

When plinkformatter calls pylmm3 in-process, plinkformatter's configure() owns the root handler and controls both packages. PYLMM3_LOG_LEVEL provides independent per-package control:

Command	plinkformatter	pylmm3
default	WARNING (silent)	WARNING (silent)
--verbose	INFO	INFO — timings visible
--log-level DEBUG	DEBUG	DEBUG
PYLMM3_LOG_LEVEL=DEBUG ./run.sh	WARNING	DEBUG — pylmm3 only
PYLMM3_LOG_LEVEL=WARNING --log-level DEBUG	DEBUG	WARNING — plinkformatter only

Using pylmm3 as a library in your own code

pylmm3 is silent by default (NullHandler). Configure your application's root handler once at startup and pylmm3 loggers flow through it automatically. Call pylmm3.log.configure() to set pylmm3's verbosity independently:

import logging
from pylmm3.log import configure as configure_pylmm3

# Your application installs the handler once
logging.basicConfig(level=logging.INFO, format="%(levelname)s %(name)s %(message)s")

# Set pylmm3 to a different level if you want more or less detail
configure_pylmm3(logging.DEBUG)   # or logging.WARNING to silence it

from pylmm3 import runGWAS        # pylmm3 logs now flow through your handler

What INFO timing looks like

At --verbose (INFO) a typical GWAS run emits:

[INFO   ] 2026-06-01 09:12:04.123  pylmm3.gwas_fast  Read input for 1223 individuals in 0.041s
[INFO   ] 2026-06-01 09:12:06.441  pylmm3.gwas_fast  Read 231164x1223 kinship in 2.318s
[INFO   ] 2026-06-01 09:12:06.892  pylmm3.gwas_fast  LMM ready in 0.451s (eigendecomposition included unless precomputed)
[INFO   ] 2026-06-01 09:12:07.204  pylmm3.gwas_fast  Null fit: h=0.412  sigma=1.834  (0.312s)
[INFO   ] 2026-06-01 09:12:14.817  pylmm3.gwas_fast  Scanned 231164 SNPs in 7.613s — skipped 159 (0.1%) due to missing genotypes or low variance
[INFO   ] 2026-06-01 09:12:14.819  pylmm3.gwas_fast  Total: 9.003s

All output goes to stderr. The [LEVEL ] field is always 9 characters wide so columns align across log lines.

Why %s-style formatting in logger calls

All logger calls in pylmm3 use %-style arguments, not f-strings:

# Correct — lazy: the string is never formatted if the level is disabled
logger.debug("BED bytes per SNP: %d", self.BytestoRead)

# Wrong — eager: the f-string is evaluated at the call site regardless of level
logger.debug(f"BED bytes per SNP: {self.BytestoRead}")

Python's logging module defers % substitution to Formatter.format(), which is only called when a handler will actually emit the record. With f-strings the interpolation happens before the level check — wasted work on every suppressed call. In a tight loop over 250,000 SNPs this adds up.

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Output Format

Kinship matrix (<outfile>)

Space-delimited n×n matrix written by numpy.savetxt. No header. Row and column order matches the FAM/TFAM file exactly. Values near 0 indicate unrelated pairs; values near 1 indicate identical individuals.

Eigendecomposition (<base>.kva, <base>.kve)

Written when -e <base> is passed to pylmmKinship. Plain-text files:

• <base>.kva — eigenvalues of K, length n
• <base>.kve — eigenvectors of K, n × n

Pass to pylmmGWAS --eigen <base> to skip the decomposition on subsequent runs.

GWAS results (<outfile>)

Tab-separated. One header row, then one row per SNP. Monomorphic or all-missing SNPs are written as nan across all value columns rather than being silently dropped.

Column	Type	Description
SNP_ID	string	RS identifier from the .bim file
BETA	float	Effect size estimate — phenotype change per unit dosage
BETA_SD	float	Standard error of the effect estimate
F_STAT	float	t-statistic for the SNP association test (column name is a historical artifact — this is a t-statistic)
P_VALUE	float	Two-tailed p-value from the t-distribution with n − q degrees of freedom

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Testing

The test suite lives in tests/ and uses pytest. It is fully self-contained — synthetic data is generated from a fixed random seed and temporary PLINK filesets are written per test, so no external fixture files are required.

uv run pytest -q          # quiet — one line of summary
uv run pytest -v          # verbose — one line per test

Run a subset while developing:

uv run pytest tests/test_gwas.py                                  # one file
uv run pytest tests/test_lmm.py::test_tstat_matches_scipy         # one test
uv run pytest -k gwas                                             # by name pattern
uv run pytest -x                                                  # stop at first failure

What the suite covers

File	Module under test	Focus
tests/test_lmm.py	pylmm3.lmm	Missing-phenotype removal, eigendecomposition + clamping, fit(), single-SNP association(), tstat vs scipy.stats, and the REML log-likelihood staying finite when det(XᵀX) overflows (slogdet regression guard)
tests/test_kinship.py	pylmm3.kinship	Shape/symmetry, center=True → trace(K) = n − 1, invariant-SNP dropping, NaN imputation
tests/test_input.py	pylmm3.input	Genotype normalization, TPED/BED decoding, end-to-end EMMA/TPED/BED readers, phenotype NA/-9 → NaN
tests/test_gwas.py	pylmm3.gwas, pylmm3.gwas_fast	Output structure, signal recovery, monomorphic/missing handling, and a cross-validation that the vectorized gwas_fast is numerically identical to the reference gwas

Shared fixtures (seeded RNG, synthetic genotypes/kinship/phenotype, and temporary PLINK filesets) live in tests/conftest.py.

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How It Works

Kinship matrix

Each SNP is imputed (missing → column mean), standardized to zero mean and unit variance, and invariant SNPs are dropped. If every SNP is invariant (a genetically uniform cohort, e.g. a single strain), there is nothing to build K from and calculateKinship raises NoVariantSNPsError (a ValueError subclass) rather than returning a degenerate matrix. The realized relationship matrix is:

K = W · Wᵀ / m

where W is the (n × m) matrix of standardized genotypes and m is the number of valid SNPs retained. With center=True, K is further normalized so that trace(K) = n − 1 (EMMA-style).

LMM and heritability estimation

The model is Y = X·β + u + ε where u ~ N(0, h·σ²·K) captures population structure and ε ~ N(0, (1−h)·σ²·I) is the residual. Fitting requires optimizing over the single free parameter h (heritability).

The key computational trick: K is decomposed once as K = V·Λ·Vᵀ via scipy.linalg.eigh. Rotating Y and X into this eigenbasis diagonalizes the covariance, reducing the O(n³) log-likelihood evaluation to O(n) per heritability value. The profile likelihood is then maximized over a 100-point grid, with Brent's method applied to refine each local maximum.

Vectorized GWAS scan

The default scan (gwas_fast.py) batches fully-observed SNPs into blocks of 2000 and processes each block with a single BLAS dgemm call (Kve.T @ G), then applies the Schur complement of the fixed covariate block — which is constant across SNPs at the null-fit h — to compute per-SNP effect sizes and t-statistics entirely in NumPy. This is algebraically identical to the reference per-SNP loop in gwas.py (validated: max relative error < 3×10⁻⁹ across 231,164 SNPs) and runs 50–200× faster in practice.

SNPs with missing genotypes or when --refit is active automatically fall back to the per-SNP path.

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Known Limitations

Limitation	Detail
Memory	K is an n×n float64 matrix where n is the number of individuals in the cohort. At n = 10,000 that is ~800 MB; at n = 100,000 it is ~80 GB.
Single-threaded	No parallelism across SNPs.
REML with many covariates	--REML on the per-SNP path uses linalg.det(), which overflows when the covariate count q ≥ ~100. The null model uses slogdet and is safe. In practice GWAS runs use q = 2 (intercept + genotype) and are unaffected.
--removeMissingGenotypes cost	Dropping missing individuals triggers an O(n³) eigendecomposition recompute per affected SNP. Avoid this flag on cohorts with high missing-genotype rates.
Covariate missing values	The covariate file does not support missing values. Impute externally before passing to pylmmGWAS.
--kfile2	Accepted by the parser but immediately exits with an error — the two-kinship confounding path is not implemented.

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Authors

pylmm3 is developed and maintained at The Jackson Laboratory:

Name	Email
Matt Vincent	[e-mail]
Nick Sebasco	[e-mail]

pylmm3 is a Python 3 port of the original pylmm by Nicholas A. Furlotte.

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License

Copyright © 2015 Nicholas A. Furlotte
Copyright © 2024–2026 The Jackson Laboratory

pylmm3 is free software licensed under the GNU Affero General Public License v3.0 or later.

This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.