Fits structural equation models to GWAS summary statistics using GenomicSEM (Grotzinger 2019), including common-factor models, confirmatory factor models, ESEM, common-factor GWAS with Q_SNP heterogeneity, multivariate Wald tests, and stratified GenomicSEM partitioned heritability. Reconciles results against MTAG multi-trait analysis. Handles sample overlap via the LDSC sampling-covariance matrix, identifies and resolves Heywood cases, and verifies model fit with CFI / RMSEA. Use when modeling latent genetic architecture across correlated traits, running multivariate GWAS on a shared factor, distinguishing factor-mediated from trait-specific SNP effects, or comparing GenomicSEM common-factor results against MTAG when both depend on accurate sampling covariance.
Fits structural equation models to GWAS summary statistics using GenomicSEM (Grotzinger 2019), including common-factor models, confirmatory factor models, ESEM, common-factor GWAS with Q_SNP heterogeneity, multivariate Wald tests, and stratified GenomicSEM partitioned heritability. Reconciles results against MTAG multi-trait analysis. Handles sample overlap via the LDSC sampling-covariance matrix, identifies and resolves Heywood cases, and verifies model fit with CFI / RMSEA. Use when modeling latent genetic architecture across correlated traits, running multivariate GWAS on a shared factor, distinguishing factor-mediated from trait-specific SNP effects, or comparing GenomicSEM common-factor results against MTAG when both depend on accurate sampling covariance.
tool_type
r
primary_tool
GenomicSEM
Version Compatibility
Reference examples tested with: GenomicSEM 0.0.5+ (GitHub GenomicSEM/GenomicSEM), lavaan 0.6-17+, LDSC v1.0.1+ (Python 3; prefer abdenlab/ldsc-python3 v2.0.0 -- belowlab/ldsc v3.0.1 README states the CLI is broken; Docker jtb114/ldsc:latest is the belowlab fallback), baselineLD_v2.2 annotations (alkesgroup.broadinstitute.org/LDSCORE), MTAG 1.0.8+ (Python; JonJala/mtag), R 4.4+.
Before using code patterns, verify installed versions match. If versions differ:
R: packageVersion('GenomicSEM') then ?ldsc, ?commonfactor, ,
?usermodel
?commonfactorGWAS
Python (LDSC, MTAG): <tool>.py -h and inspect the source under ldsc/ or mtag/
GenomicSEM is GitHub-only (never on CRAN). If ldsc() or usermodel() throws an error about lavaan syntax or non-positive-definite covariance, introspect the installed API (getMethod('ldsc')) and adapt rather than retrying.
Genomic SEM
"Model the latent genetic architecture across several correlated GWAS" -> Treat each GWAS as a measured indicator of one or more latent genetic factors and fit a structural equation model to the LDSC-derived genetic covariance matrix S and its sampling covariance V (Grotzinger 2019 Nat Hum Behav 3:513). The framework extends naturally to a multivariate GWAS in which a SNP is regressed on a latent factor (common-factor GWAS), with Q_SNP testing whether the SNP effect is homogeneous across factor loadings. Sample overlap between input GWAS is absorbed by the off-diagonals of V; ignoring V inflates Type-I.
R: GenomicSEM::ldsc() produces the (S, V) covariance pair from munged sumstats
R: GenomicSEM::commonfactor() fits a single-factor CFA across all traits in S
R: GenomicSEM::usermodel() fits an arbitrary lavaan-syntax model
R: GenomicSEM::commonfactorGWAS() runs SNP -> factor multivariate GWAS with Q_SNP
R: GenomicSEM::userGWAS() runs arbitrary multivariate SNP regression with per-path Q_SNP
Python (alternative): mtag.py --sumstats t1,t2,t3 --out mtag_out (multi-trait power boost on individual traits)
Methodology evolves; verify the current Grotzinger 2023+ tutorials at github.com/GenomicSEM/GenomicSEM/wiki before locking a method. ESEM rotation choice (geomin vs target rotation) is an active area; report sensitivity to rotation.
MTAG vs GenomicSEM Common-Factor GWAS
Both methods exploit genetic correlation among input GWAS, but their goals and outputs differ.
Property
MTAG
GenomicSEM commonfactorGWAS
Output
Per-trait shrunk z-scores
SNP effect on latent factor
Sample-overlap handling
Bivariate LDSC intercept
Full LDSC sampling-covariance matrix V
Heterogeneity diagnostic
MaxFDR (Turley 2018)
Q_SNP (Grotzinger 2019)
Interpretation
"Boosted power for trait k"
"Effect on what the traits share"
Min traits
2
3 (otherwise factor not identified)
Best when
Power-boost an individual trait
Common factor hypothesized
Both depend on accurate sampling covariance. MTAG fails (MaxFDR > 5%) under the same heterogeneity that produces large Q_SNP in GenomicSEM. The two methods should be reported together when the prior on a common factor is non-trivial; agreement increases confidence, disagreement points to architecture-specific SNPs.
Decision Tree by Scenario
Scenario
Recommended
Why
Multi-trait GWAS power boost for one focal trait
MTAG
Optimized for per-trait marginal power
Common-factor architecture hypothesized
GenomicSEM commonfactorGWAS
Tests SNP -> factor; reports Q_SNP heterogeneity
Heterogeneous architecture (>1 latent factor)
ESEM, then confirmatory usermodel
Exploratory first, then confirm
Confirming a pre-specified factor structure
usermodel with lavaan syntax
Confirmatory factor analysis
Partition heritability of factor across annotations
Stratified GenomicSEM
Combines sLDSC + factor model
Mediation in a SEM framework
usermodel with indirect path
Path coefficients + delta-method SE
Sample overlap unknown or any-overlap suspected
Always use ldsc() output as input
V matrix off-diagonals absorb overlap
Cross-ancestry common-factor analysis
Run per-ancestry, compare loadings; no published cross-ancestry SEM as of 2026
Method not yet validated for mixed-ancestry V
Single biobank for all traits (e.g., UKB only)
GenomicSEM with ldsc(); the V matrix will reflect overlap
Equivalent to one-sample MR -- the V matrix is the correction
Trigger: A residual variance estimate is < 0, or a standardized loading exceeds 1.
Mechanism: Empirical underidentification; the genetic covariance matrix S is near-singular OR a trait has near-zero specific variance under the model. The maximum-likelihood / DWLS estimator runs past the boundary of the parameter space.
Symptom:lavaan warning "some estimated lv variances are negative" or "covariance matrix is not positive definite"; standardized loading > 1; non-convergence.
Fix: First, inspect the LDSC S matrix for genetic correlations near 1 (multicollinearity). Drop or merge near-identical traits. Second, constrain the offending residual variance to be non-negative in the lavaan syntax (trait1 ~~ a*trait1; a > 0). Third, verify the V matrix is positive definite via chol(V_LD); if not, the bivariate LDSC inputs disagree on intercept signs and need re-munging. Never re-fit without diagnosing the cause.
Sample overlap mis-specified
Trigger: Using LDSC intercept manually or supplying covariance from non-ldsc() source.
Mechanism: GenomicSEM's ldsc() function returns a list with S (genetic covariance) AND V (sampling covariance of the lower-triangle of S). The V off-diagonals capture sample overlap via cross-trait LDSC intercept. Skipping V and supplying only S treats all inputs as independent samples; Type-I error inflates because the sampling distribution under H0 is wrong.
Symptom: SE on factor loadings far too small; many SNPs significant in common-factor GWAS that don't replicate; comparison to MTAG shows disagreement consistent with overlap.
Fix: Always pass the full output of ldsc() -- both S and V -- to commonfactor(), usermodel(), and commonfactorGWAS(). Never construct S manually from rg estimates.
Q_SNP not reported in commonfactorGWAS
Trigger: Running commonfactorGWAS() and reporting only the factor p-value per SNP.
Mechanism: Q_SNP tests heterogeneity of the SNP's effect across factor loadings (Grotzinger 2019 supplement). A SNP with significant Q_SNP violates the common-factor assumption: its effect is NOT mediated by the factor, and the factor estimate is meaningless for that SNP.
Symptom: Top "common-factor SNPs" are dominated by trait-specific effects; replication in independent cohorts is poor for SNPs with high Q_SNP.
Fix: Always report Q_SNP p-value alongside the factor p-value. Flag SNPs with Q_SNP p < 5e-8 / N_factor_SNPs (Bonferroni for the discovered set) as architecture-violating and exclude from "common-factor SNP" claims. Re-fit those SNPs in userGWAS() with separate paths to each trait.
Trait inclusion under heterogeneous factor structure
Trigger: Forcing a common-factor model on traits that don't share a single latent factor.
Mechanism: When two or more traits load on a different factor than the rest, the single-factor model misfits. lavaan still returns parameter estimates but model fit is poor.
Symptom: CFI < 0.9; RMSEA > 0.08; some standardized loadings near 0 while others near 1; chi-square highly significant even after accounting for N.
Fix: Run ESEM first (commonfactor then usermodel with cross-loadings allowed) to discover structure. If two factors emerge, fit a two-factor usermodel. Drop traits with near-zero loadings on all factors. Document the model search.
MTAG MaxFDR > 5%
Trigger: Running MTAG on traits with low pairwise genetic correlation or with one trait that has a very different architecture.
Mechanism: MTAG assumes a homogeneous variance-covariance structure across SNPs. When heterogeneity dominates, the empirical-Bayes shrinkage can over-claim SNPs in the focal trait. Turley 2018 defines MaxFDR as the maximum estimated false discovery rate under worst-case heterogeneity; > 5% invalidates the published trait-specific summary statistics.
Fix: Check pairwise rg via LDSC; if any pair is < 0.7, MTAG is risky. Drop the most heterogeneous trait and re-run. Alternatively, switch to GenomicSEM's commonfactorGWAS which models heterogeneity explicitly via Q_SNP.
Non-positive-definite V_LD matrix
Trigger: LDSC inputs from different ancestry GWAS, or one trait with very low mean chi-square (< 1.02).
Mechanism: V is the sampling covariance of vech(S); when individual entries of S have huge SE relative to off-diagonal covariance, the resulting V is not positive definite (negative eigenvalues).
Symptom:commonfactor() errors with "matrix is not positive definite" before fitting; eigen(LDSCoutput$V)$values shows negative values.
Fix: Verify per-trait mean chi-square via ldsc() log; below 1.02, exclude that trait. Verify all GWAS are EUR ancestry (or match ancestry of LD scores). Apply nearest-PD smoothing via Matrix::nearPD(V)$mat ONLY as a last resort and document the approximation in methods.
Model Fit Diagnostics
Index
Acceptable
Good
Source
CFI
>= 0.90
>= 0.95
Hu & Bentler 1999 Struct Equ Model 6:1
TLI / NNFI
>= 0.90
>= 0.95
Hu & Bentler 1999
RMSEA
<= 0.08
<= 0.05
Hu & Bentler 1999
SRMR
<= 0.08
<= 0.05
Hu & Bentler 1999
chi-square p-value
(less informative at large N)
n/a
Penalize for N inflation
AIC / BIC are used for nested-model comparison (lower is better); only compare nested models fit on the same S.
Quantitative Thresholds
Threshold
Source
Rationale
CFI >= 0.95
Hu & Bentler 1999
Conventional good fit; SEM literature default
RMSEA <= 0.05
Hu & Bentler 1999
Conventional good fit
RMSEA 0.05 - 0.08
Hu & Bentler 1999
Acceptable; flag as "adequate" not "good"
Q_SNP p < 0.05 / N_SNP_factor
Grotzinger 2019 Nat Hum Behav 3:513
Bonferroni for heterogeneity among factor-significant SNPs
MTAG MaxFDR < 5%
Turley 2018 Nat Genet 50:229
Above this, MTAG marginal trait results invalid
Per-trait LDSC mean chi-square > 1.02
LDSC documentation
Below this, V entries too noisy; factor SE inflated
Single factor with k traits has k(k+1)/2 moments; needs k>=3 to identify
Standard Workflow
Goal: Fit a common-factor model across correlated GWAS and run a multivariate GWAS on the factor with Q_SNP.
Approach: Munge sumstats -> LDSC for (S, V) -> common-factor CFA -> inspect fit -> prepare SNPs -> common-factor GWAS -> report factor effects with Q_SNP flags.
library(GenomicSEM)# Step 1: Munge sumstats (one-time; produces .sumstats.gz files)
files <-c('raw/trait1.txt','raw/trait2.txt','raw/trait3.txt')
hm3 <-'w_hm3.snplist'# HapMap3 SNP list
trait_names <-c('trait1','trait2','trait3')
N <-c(150000,200000,175000)
munge(files = files, hm3 = hm3, trait.names = trait_names, N = N)# Step 2: LDSC produces both S (genetic covariance) and V (sampling covariance)
traits <-c('trait1.sumstats.gz','trait2.sumstats.gz','trait3.sumstats.gz')
ldsc_results <- ldsc(
traits = traits,
sample.prev =c(0.5,0.5,NA),# case prevalence; NA for continuous
population.prev =c(0.05,0.05,NA),
ld ='eur_w_ld_chr/',
wld ='eur_w_ld_chr/',
trait.names = trait_names
)# ldsc_results$S = genetic covariance; ldsc_results$V = sampling covariance# Step 3a: Common-factor CFA via DWLS
cf_fit <- commonfactor(covstruc = ldsc_results, estimation ='DWLS')
print(cf_fit$modelfit)# CFI, RMSEA, SRMR, chi-square
print(cf_fit$results)# loadings + SEs# Step 3b: Alternative -- user-specified two-factor model (>=3 indicators per factor)# Identification rule: each factor needs >= 3 indicators OR one anchor loading fixed# to 1 plus factor variance free. A factor with a single indicator is NOT identified.
model_syntax <-'
F1 =~ NA*trait1 + trait2 + trait3
F2 =~ NA*trait4 + trait5 + trait6
F1 ~~ 1*F1
F2 ~~ 1*F2
F1 ~~ F2
'
user_fit <- usermodel(covstruc = ldsc_results, model = model_syntax, estimation ='DWLS')
estimation = 'DWLS' (diagonally weighted least squares) is the default and is required when V is large; 'ML' is faster but assumes a known V and can produce wrong SE under sample overlap.
ESEM (Exploratory Factor Structure)
When the factor structure is unknown, fit usermodel() with all loadings free across all factors, then apply a rotation post-fit. Rotation choices: geomin oblique (default; allows factor correlation), target rotation (Browne 2001 Multivariate Behav Res 36:111; uses a hypothesized loading template), quartimin (orthogonal; assumes factors are uncorrelated).
model_esem <-'
F1 =~ NA*trait1 + trait2 + trait3 + trait4
F2 =~ NA*trait1 + trait2 + trait3 + trait4
F1 ~~ 1*F1
F2 ~~ 1*F2
F1 ~~ F2
'
esem_fit <- usermodel(covstruc = ldsc_results, model = model_esem, estimation ='DWLS')# Rotate post-fit via GPArotation::GPForth/GPFoblq or lavaan::rotate()
Decision: ESEM for K-factor exploration when structure is unknown; CFA via usermodel() once a structure is confirmed. Report rotation sensitivity (geomin vs target vs quartimin) and treat as exploratory.
Cross-loadings. Cross-loadings (one trait loads on > 1 factor) are common in psychiatric and behavioral GWAS. Brown 2015 Confirmatory Factor Analysis for Applied Research recommends allowing cross-loadings first and using modification indices to guide simplification. Allow a cross-loading when constraining residual variance otherwise forces a Heywood case. Constrain when CFI < 0.9 and modification indices instead suggest a correlated residual between two indicators (which is the more parsimonious fix).
userGWAS for Custom Path Models
userGWAS() fits arbitrary lavaan-syntax SNP regressions and is the right tool when the SNP needs to be tested on multiple paths simultaneously (e.g. factor-mediated effect AND a direct effect on one indicator).
# Test SNP -> F path + SNP -> trait1 direct path simultaneously
model <-'
F =~ NA*trait1 + trait2 + trait3
F ~~ 1*F
F ~ SNP
trait1 ~ SNP # direct effect on trait1, partialed out of F
'
user_results <- userGWAS(covstruc = ldsc_results,
SNPs = ss,
estimation ='DWLS',
model = model,
sub =c('F~SNP','trait1~SNP'),
parallel =TRUE,
cores =8)# Output columns include: lhs, op, rhs, est, SE, Z, Pvalue, Q_pval, Q_df.# Q_pval per SNP measures heterogeneity across loadings AFTER conditioning on# the direct path; remaining Q_SNP signal indicates a third path is needed.
Higher-Order / Bifactor / p-Factor Models
Use case: psychiatric genetics p-factor (Caspi 2014 Clin Psychol Sci 2:119; Grotzinger 2022 Nat Genet 54:548 cross-disorder), cognitive g-factor (de la Fuente 2021 Nat Hum Behav 5:49).
Hierarchical template -- first-order factors load on a single second-order p-factor:
Bifactor alternative: p =~ all traits directly, with INT/EXT/THT as orthogonal residual factors. Bifactor typically gives tighter CFI/RMSEA but the substantive interpretation of the residual factors is harder; bifactor is also prone to over-fitting at modest trait counts (Bonifay W & Cai L 2017 Multivariate Behav Res 52:465). Cite Grotzinger 2022 Nat Genet 54:548 and Karlsson Linner R, Mallard TT et al 2021 Nat Neurosci 24:1367 for the canonical psychiatric implementations.
Common-Factor GWAS with Q_SNP
Goal: Identify SNPs that affect the latent factor and flag SNPs whose effect is heterogeneous across loadings.
Approach: Build SNP-by-trait effect-and-SE matrix via sumstats(), then fit the SNP-augmented model genome-wide via commonfactorGWAS(). Report both factor p-value and Q_SNP p-value per SNP.
sumstats() flips effect signs based on the reference panel A1/A2 to enforce consistent allele coding across input GWAS. Required input columns (case-sensitive) are SNP, A1, A2, BETA/Z/OR, SE, P, N, MAF; some are conditional on se.logit / OLS. Silent failures are almost always column-name mismatches (e.g. EA/NEA instead of A1/A2 -> 0% SNPs retained) or a missing N column -> SNPs dropped. Always run head(read.table(file, header=TRUE, nrow=2)) per input before the sumstats() call.
# Prepare per-SNP betas and SEs across all input GWAS
ss <- sumstats(
files =c('raw/trait1.txt','raw/trait2.txt','raw/trait3.txt'),
ref ='reference.1000G.maf.0.005.txt',
trait.names = trait_names,
se.logit =c(TRUE,TRUE,FALSE),# TRUE if trait is logistic-scale (case-control); FALSE if continuous
OLS =c(FALSE,FALSE,TRUE),
linprob =c(FALSE,FALSE,FALSE),
N = N,
info.filter =0.9,# standard imputation INFO threshold
maf.filter =0.01)# GenomicSEM internally detects the OS via Sys.info()[['sysname']] and chooses# PSOCK (Windows) vs FORK (Linux/Mac) clusters automatically; there is no user# `Operating=` argument. MPI=TRUE switches to an mpirun-based strategy for# cluster job submission. parallel=TRUE is the default.
cfgwas <- commonfactorGWAS(
covstruc = ldsc_results,
SNPs = ss,
estimation ='DWLS',
parallel =TRUE,
cores =8,
MPI =FALSE)# cfgwas columns include rsID/chr/BP/MAF/A1/A2/est/se_c/Z_Estimate/Pval_Estimate (factor effect)# plus heterogeneity columns Q / Q_df / Q_pval. Q_pval IS the per-SNP heterogeneity# test (often referred to as Q_SNP in the literature; the column name in the data.frame is Q_pval).
cfgwas$factor_sig <- cfgwas$Pval_Estimate <5e-08
cfgwas$qsnp_sig <- cfgwas$Q_pval <(0.05/sum(cfgwas$factor_sig))
cfgwas$factor_only <- cfgwas$factor_sig &!cfgwas$qsnp_sig
The "factor-only" subset (factor-significant AND Q_SNP non-significant) is the publication-grade set of common-factor SNPs.
MTAG Comparison
Goal: Cross-check GenomicSEM common-factor results against MTAG per-trait shrunk z-scores.
Approach: Run MTAG CLI on the same input sumstats; compare top hits with GenomicSEM factor hits. Report MaxFDR.
# MTAG CLI (Python)
python mtag.py \
--sumstats trait1.txt,trait2.txt,trait3.txt \
--n_min 0 \
--out mtag_results
# MTAG uses the signed Z by default; --use_beta_se was disabled upstream (raises a# RuntimeError since Dec 2021 due to beta-se bugs), so supply a Z column and omit it.# Check MaxFDR per trait
grep -iE 'max ?fdr' mtag_results.log # matches both the section header and the 'Max FDR of Trait' value lines# Each per-trait MTAG file: mtag_results_trait_<k>.txt
If MaxFDR > 0.05 for any trait, MTAG results for that trait are unreliable; GenomicSEM with Q_SNP filtering is the more defensible report.
Stratified GenomicSEM (Partitioned Heritability of Factor)
For partitioning the heritability of the latent factor across functional annotations, use s_ldsc() (stratified LDSC inside GenomicSEM) and pass the multi-annotation output to a stratified model fit.
# Stratified LDSC across baseline + custom annotations
s_results <- s_ldsc(
traits = traits,
sample.prev =c(0.5,0.5,NA),
population.prev =c(0.05,0.05,NA),
ld ='baselineLD_v2.2.',
wld ='weights.hm3_noMHC.',
frq ='1000G.EUR.QC.',
trait.names = trait_names
)# enrich() inventory:# params: lavaan syntax of the parameter under enrichment (loading, residual var, or F~~F latent var)# fix='regressions': hold regression paths fixed at the genome-wide estimate during stratified fit# std.lv=FALSE: do not standardize the latent variance# rm_flank=TRUE: drop flanking-window contributions (default)# tau=FALSE: use the baseline-annotation S/V matrices (TRUE switches to the V_Tau/S_Tau tau parametrization)# base=TRUE: include baseline annotation contributions in the partition# toler=NULL: matrix-inversion tolerance (let GenomicSEM choose; supply a small value when S is near-singular)
strat_factor <- enrich(s_covstruc = s_results,
model ='',
params ='F =~ trait1',
fix ='regressions',
std.lv =FALSE,
rm_flank =TRUE,
tau =FALSE,
base =TRUE,
toler =NULL)
The output gives per-annotation enrichment of the factor h2 -- the analog of cell-type S-LDSC for the latent factor (Grotzinger AD et al 2022 Nat Genet 54:548).
Computational Footprint
Step
Runtime
Hardware
ldsc() multi-trait sampling covariance
minutes
laptop
commonfactor() / usermodel() (no SNP loop)
seconds
laptop
commonfactorGWAS() over 6-8M SNPs
4-24h depending on cores
cluster recommended
userGWAS() over 6-8M SNPs with complex path model
8-48h
cluster recommended
Stratified GenomicSEM with 50+ annotations
1-3 days
cluster
MTAG over 6-8M SNPs
1-2h
laptop or cluster
Cluster runs of commonfactorGWAS() / userGWAS() should use MPI=TRUE when submitting via mpirun; GenomicSEM detects the OS internally (via Sys.info()[['sysname']]) and selects FORK (Linux/Mac) vs PSOCK (Windows) cluster types automatically -- there is no Operating= user argument. On a Mac/Windows workstation, reduce cores to the physical-core count to avoid PSOCK fork failures.
Reconciliation: When GenomicSEM and MTAG Disagree
Pattern
Likely cause
Action
GenomicSEM factor SNP sig, MTAG sig for all traits
Genuine common-factor SNP
Report; high confidence
GenomicSEM factor SNP sig, MTAG sig in only 1 trait
Q_SNP heterogeneity likely; one-trait-dominant
Check Q_SNP; if sig, this is NOT a factor SNP
MTAG sig, GenomicSEM factor null, Q_SNP sig
Trait-specific SNP captured by MTAG shrinkage
Report as trait-specific, not common-factor
Both null but per-trait univariate sig
Power loss from multivariate parameterization
Re-check sample overlap V matrix
GenomicSEM and MTAG both sig but opposite direction
Sample-overlap mis-specification OR sign error in munging
Re-munge with same allele convention; re-run ldsc()
MTAG MaxFDR > 5%, GenomicSEM with Q_SNP works
MTAG assumption violated
Prefer GenomicSEM as primary
One-trait GWAS sig but common-factor not
Trait-specific architecture
Don't force into common-factor frame
Operational rule for publication: A common-factor SNP claim requires (1) factor p < 5e-8, (2) Q_SNP p > 0.05 / N_factor_SNPs (non-heterogeneous), and (3) replication in an independent set of traits or cohorts. Trait-specific SNPs from MTAG require MaxFDR < 5% for the trait. Reporting only the factor effect without Q_SNP is the most common reviewer-flagged error.
Common Errors
Error / symptom
Cause
Solution
commonfactor() complains "S not positive definite"
Genetic correlations near +/-1 among inputs
Drop redundant traits; verify rg < 0.95 pairwise
Standardized loading > 1
Heywood case; under-identification
Constrain residual variance >= 0; inspect S for collinearity
Factor p-value reported, Q_SNP not reported
Default focus is on factor effect
Always report Q_SNP from commonfactorGWAS output
ldsc() fails with "category not found"
Wrong LD score column names (legacy format)
Use Python 3 LDSC fork; download eur_w_ld_chr/ from alkesgroup
lavaan says "model not identified"
Too few traits for too many parameters
Need >= 3 traits per factor; constrain factor variance to 1
MTAG MaxFDR not in log
Older MTAG version (< 1.0.7)
Update MTAG; MaxFDR reporting added late 2019
Singular V matrix on smooth nearPD
One trait has near-zero h2 or mean chi-square < 1.02
Drop the trait; do not smooth as a fix
usermodel() slow or fails
Complex syntax + many traits
Simplify model; estimate with estimation = 'DWLS', not 'ML', when V is informative
Sumstats output has zero overlap with reference
Allele coding mismatch in sumstats()
Check se.logit and OLS settings per trait; align A1/A2
GenomicSEM and TwoSampleMR give different rg
TwoSampleMR uses bivariate LDSC; GenomicSEM uses the same S
Match the underlying LDSC reference panel and weights
MTAG maxFDR reported per trait; > 5% invalidates MTAG for that trait -> GenomicSEM common-factor used instead
"Sample overlap absorbed?"
Full V matrix from ldsc() is the input to all model fits; S is never constructed manually from pairwise rg estimates
"Model fit?"
CFI >= 0.95, RMSEA <= 0.08, SRMR <= 0.08 reported; AIC / BIC for nested comparison; chi-square reported but treated as inflated at large N
"Why a factor model and not MTAG?"
Factor structure tested first; if traits load on a common factor with CFI > 0.95, common-factor GWAS preferred -- explicitly models heterogeneity via Q_SNP
"Heywood case?"
Negative residual variance constrained >= 0; OR the offending indicator dropped and the model re-specified; the choice is documented in methods
"Cross-ancestry?"
Run per-ancestry; no validated cross-ancestry V matrix as of 2026; loadings compared qualitatively
"Why DWLS and not ML?"
ML assumes V is known; DWLS uses the empirical V from ldsc() and is the appropriate estimator under sample overlap
Tool Installation
# GenomicSEM is GitHub-only
remotes::install_github('GenomicSEM/GenomicSEM')# Dependencies
install.packages(c('lavaan','Matrix','gdata'))# Optional companions
remotes::install_github('MRCIEU/TwoSampleMR')# for downstream MR using factor GWAS as exposure
For Python tools:
# LDSC python3 fork (GenomicSEM input format). belowlab/ldsc v3.0.1 broke the# --h2/--rg/--h2-cts CLI per its README; use abdenlab/ldsc-python3 (v2.0.0)# for a working CLI. Docker jtb114/ldsc:latest is the belowlab fallback.
git clone https://github.com/abdenlab/ldsc-python3.git
cd ldsc-python3 && pip install . # Poetry project (pyproject.toml); no requirements.txt# MTAG
git clone https://github.com/JonJala/mtag.git
cd mtag && pip install -r requirements.txt
Pre-downloaded reference files: eur_w_ld_chr/, baselineLD_v2.2.*, w_hm3.snplist, and 1000G allele-frequency files are hosted at alkesgroup.broadinstitute.org/LDSCORE/.
References
Grotzinger AD et al 2019 Nat Hum Behav 3:513 (GenomicSEM, common-factor GWAS, Q_SNP)
Grotzinger AD et al 2022 Nat Genet 54:548 (Stratified GenomicSEM)
Turley P et al 2018 Nat Genet 50:229 (MTAG; MaxFDR)
Bulik-Sullivan B et al 2015 Nat Genet 47:291 (LDSC for genetic covariance)
Bulik-Sullivan B et al 2015 Nat Genet 47:1236 (bivariate LDSC, sample overlap)
Rosseel Y 2012 J Stat Softw 48:1-36 (lavaan package)
Hu LT & Bentler PM 1999 Struct Equ Model 6:1 (CFI / RMSEA cutoffs)
Asparouhov T & Muthen B 2009 Struct Equ Model 16:397 (ESEM framework)
Finucane HK et al 2015 Nat Genet 47:1228 (S-LDSC, foundation for stratified GenomicSEM)
Gazal S et al 2017 Nat Genet 49:1421 (baseline-LD annotations)
Demange PA et al 2021 Nat Genet 53:35 (GenomicSEM GWAS-by-subtraction for noncognitive skills; Q_SNP in practice)
Karlsson Linner R, Mallard TT et al 2021 Nat Neurosci 24:1367 (multivariate externalizing GWAS via GenomicSEM)
de la Fuente J et al 2021 Nat Hum Behav 5:49 (GenomicSEM for cognitive g factor)
Skrivankova VW et al 2021 JAMA 326:1614 (STROBE-MR; relevant when downstream MR uses factor GWAS)
Related Skills
causal-genomics/mendelian-randomization - Use factor-GWAS effect sizes as MR exposure
causal-genomics/genetic-correlation - Bivariate LDSC produces the off-diagonals of the S matrix; GenomicSEM is the multi-trait extension
causal-genomics/heritability-partitioning - LDSC and S-LDSC foundations for stratified GenomicSEM
causal-genomics/colocalization-analysis - Cross-trait colocalization at common-factor loci
causal-genomics/pleiotropy-detection - Q_SNP is a per-SNP pleiotropy diagnostic; sibling concept
causal-genomics/fine-mapping - Resolve factor-significant loci to credible sets
causal-genomics/mediation-analysis - SEM mediation paths overlap with usermodel indirect effects
causal-genomics/transcriptome-wide-association - TWAS on factor sumstats from commonfactorGWAS
population-genetics/association-testing - GWAS sumstats are the input format
