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Covarrubias-Pazaran", "engine": "knitr::knitr", "headings": [ "SECTION 1: Theory", "1) Why reduce the cross-environment covariance", "2) The factor-analytic (FA) model", "3) The reduced-rank (RR) model", "4) Choosing k and comparing to other structures", "SECTION 2: Fitting factor-analytic and reduced-rank models", "1) Data", "2) Factor-analytic model with fam()", "3) Reduced-rank model with rrm()", "4) Comparing FA and RR", "SECTION 3: Extracting loadings, scores, and diagnostic plots", "1) Loadings and specific variances", "2) Genotype scores", "3) Why and how to rotate loadings and scores", "4) Percentage of variance explained", "5) Loadings plot", "6) Genotype scores plot", "7) Latent regression plots", "8) Heatmap of the fitted genetic correlation matrix", "Literature" ], "created": "2026-09-23 03:47:47", "modified": "2026-10-15 18:08:04", "commits": 4 }, { "source": "sommer.glmm.Rmd", "filename": "sommer.glmm.html", "title": "Generalized linear mixed models with sommer", "author": "sommer development team", "engine": "knitr::knitr", "headings": [ "Overview", "How the fit works", "PQL and IRLS", "Dispersion and covariance structures", "Offsets and precision weights", "Families and examples", "Gaussian", "Binomial", "Poisson", "Gamma", "Inverse Gaussian", "Quasi families", "Extracting results and controlling PQL", "Practical guidance" ], "created": "2026-09-25 15:36:15", "modified": "2026-10-17 05:25:18", "commits": 2 }, { "source": "sommer.genetic.evaluation.Rmd", "filename": "sommer.genetic.evaluation.html", "title": "Genetic evaluation with known variance components in sommer", "author": "sommer development team", "engine": "knitr::knitr", "headings": [ "Overview", "Simulated population", "Pedigree and relationship inverse", "Breeding values and phenotypes", "Step 1: REML on a subset of herds", "Step 2: evaluation of the whole population", "Accuracy of the predicted breeding values", "Other ways to give the variance components", "Practical notes" ], "created": "2026-10-02 21:08:27", "modified": "2026-10-02 21:08:27", "commits": 1 }, { "source": "sommer.gxe.Rmd", "filename": "sommer.gxe.html", "title": "Fitting genotype by environment models in sommer", "author": "Giovanny Covarrubias-Pazaran", "engine": "knitr::knitr", "headings": [ "1) Single environment model", "2) MET: main effect model", "3) MET: diagonal model (DG)", "4) MET: compund symmetry model (CS)", "5) MET: unstructured model (US)", "6) MET: random regression model", "7) Other GxE covariance structures", "8) Finlay-Wilkinson regression", "9) Factor analytic and reduced rank models", "10) Two stage analysis", "Literature" ], "created": "2025-04-01 20:56:50", "modified": "2026-09-28 06:09:54", "commits": 11 }, { "source": "sommer.machinery.Rmd", "filename": "sommer.machinery.html", "title": "Inside sommer: the ai_mme_sp2 engine", "author": "sommer development team", "engine": "knitr::knitr", "headings": [ "1. The problem the engine solves", "1.1 A structured linear mixed model", "1.2 What is and is not estimated here", "2. Henderson equations and the restricted likelihood", "2.1 The coefficient matrix", "2.2 The REML objective in Henderson form", "2.3 A useful connection to the textbook score", "3. Covariance parameters: legal coordinates for optimization", "3.1 Natural values and working values", "3.2 Derivatives belong to the covariance descriptor", "3.3 Fixed parameters and covariance validity", "4. How AI-REML proposes and accepts updates", "4.1 Score, information, and an update", "4.2 Why blend AI and EM update directions?", "ML posterior moments and fixed effects", "AI-first recovery", "Scalar parameter expansion", "Direct-engine EM and recovery", "4.3 Safeguards around the proposed step", "5. Three solvers for the MME system", "5.1 solver=\"ldlt\": sparse direct factorization", "5.2 solver=\"cholmod\": supernodal direct factorization", "5.3 solver=\"pcg\": iterative solves and stochastic traces", "5.4 At-a-glance comparison", "6. Structure-aware shortcuts and where the speed comes from", "6.1 Kronecker products: invert the factors, not the product", "6.2 Diagonal and repeated-block residuals", "6.3 Selected inverse instead of full inverse", "6.4 Reuse what does not change across iterations", "6.5 Matrix-free PCG for compatible REML models", "6.6 Why dense relationship matrices are a different regime", "7. The C++ numerical libraries", "8. A complete small Henderson solve: two environments and three entries", "8.1 Data, ordering, and design matrices", "8.2 The entry relationship and the supplied Ai", "8.3 The environment covariance and the full random covariance", "8.4 Assemble Henderson's equations", "8.5 What the CHOLMOD solve returns", "8.6 Quadratic form and one likelihood evaluation", "8.7 How the four covariance coordinates affect this example", "8.8 The converged fit is a different point", "8.9 What this six-observation example teaches", "9. Choosing settings and interpreting results" ], "created": "2026-09-28 16:20:30", "modified": "2026-10-17 18:40:35", "commits": 3 }, { "source": "sommer.blas.threads.Rmd", "filename": "sommer.blas.threads.html", "title": "Installing and configuring BLAS thread control", "author": "sommer development team", "engine": "knitr::knitr", "headings": [ "What the error means", "Identify the R installation and BLAS", "Install the appropriate R packages", "Route A: R uses FlexiBLAS", "Route B: R uses a recognized OpenBLAS or MKL library directly", "If R still uses a reference BLAS", "Verify control with a small model", "Retry your model", "Cluster allocations and startup configuration", "Troubleshooting and interpreting usage", "References" ], "created": "2026-10-06 08:44:09", "modified": "2026-10-06 08:44:09", "commits": 1 }, { "source": "sommer.qg.Rmd", "filename": "sommer.qg.html", "title": "Quantitative genetics using the sommer package", "author": "Giovanny Covarrubias-Pazaran", "engine": "knitr::knitr", "headings": [ "SECTION 1: Introduction", "Backgrounds in linear algebra", "SECTION 2: Topics in quantitative genetics", "1) Marker and non-marker based heritability calculation", "2) Specifying heterogeneous variances in univariate models", "3) Using the vpredict calculator", "3.1) Standar error for heritability", "4) Half and full diallel designs (use of the overlay)", "5) Genomic selection: predicting mendelian sampling", "6) Indirect genetic effects", "7) Genomic selection: single cross prediction", "8) Multivariate genetic models and genetic correlations", "9) Bivariate model with repeated records", "SECTION 3: Special topics in Quantitative genetics", "1) Partitioned model", "2) UDU' decomposition", "3) Mating designs", "North Carolina Design I (Nested design)", "North Carolina Design II (Factorial design)", "4) GWAS by GBLUP", "Final remarks", "Literature" ], "created": "2025-04-01 20:56:50", "modified": "2026-09-30 17:46:11", "commits": 13 }, { "source": "sommer.spatial.Rmd", "filename": "sommer.spatial.html", "title": "Spatial modeling using the sommer package", "author": "Giovanny Covarrubias-Pazaran", "engine": "knitr::knitr", "headings": [ "1. Where does the spatial part go?", "2. The building block: AR1 correlation", "3. A single trial", "3.1 A field where we know the truth", "3.2 Five candidate models", "3.3 Comparing the models", "3.4 Reading the estimated parameters", "3.6 Reproducing SpATS with P-spline ANOVA", "4. Several trials at once", "4.1 Three simulated trials", "4.2 Shared correlations: a Kronecker product with vsm()", "4.3 Trial-specific correlations: a direct sum with dsumm()", "4.4 Which model should I use?", "4.5 Trials without spatial information: levels=", "4.6 Spatial effects on the G side for several trials", "5. Practical advice", "Translating from ASReml-R", "Literature" ], "created": "2025-04-01 20:56:50", "modified": "2026-09-30 05:32:29", "commits": 7 }, { "source": "sommer.theory.Rmd", "filename": "sommer.theory.html", "title": "Theory: how sommer parameterizes and optimizes covariance structures", "author": "sommer development team", "engine": "knitr::knitr", "headings": [ "Chapter 1: The linear mixed model and Henderson's equations", "1.1 The model", "1.2 Henderson's Mixed Model Equations (MME)", "$$C\\begin", "1.3 Where covariance structures come in", "1.4 Preview of the key distinction (developed in Chapter 4)", "Chapter 2: Parameterization theory, explained from first principles", "2.1 Why we can't just let the computer search freely", "2.2 The working-parameter vector", "2.3 Transform family 1 — variances: the exponential map", "2.4 Transform family 2 — bounded quantities: logit and tanh", "2.5 Transform family 3 — many correlated quantities at once (factorizations)", "2.6 Why the reference level matters: avoiding scale confounding", "Chapter 3: Catalog of covariance structures", "3.1 ism(x) — identity", "3.2 dsm(x, values, fixed, theta) / atm(x, levs, values, fixed) — heterogeneous diagonal variances", "3.3 csm(x, rho, fixed, variance, values) — compound symmetry", "3.4 ar1m/ar2m/ar3m/toeplitzm — autoregressive & general Toeplitz correlation", "3.5 mam/ma1m/ma2m — moving-average covariance", "3.6 corgm(x, theta, fixed) — general correlation matrix", "3.7 usm(x, theta, fixed) — general unstructured covariance", "3.8 fam(x, k, loadings, specific, fixed, variance) / rrm(x, k, loadings, fixed) — factor-analytic covariance", "3.9 antem(x, order, beta, innovations, fixed) — antedependence", "3.10 maternm(x, range, nu, fixed, distance) — Matérn spatial correlation", "3.11 sar(x, W, rho, fixed) — simultaneous autoregressive spatial covariance", "3.12 car(x, W, rho, fixed) — proper conditional autoregressive covariance", "3.13 ownm(x, K, fun, par, fixed, dfun) — user-defined shape", "3.14 covm(ran1, ran2, thetaC, theta, ...) — legacy two-random-effect helper", "3.15 Summary table", "Chapter 4: REML, AI-REML, and ai_mme_sp2()", "4.1 The REML log-likelihood sommer maximizes", "4.2 The AI-REML update", "4.3 The core object: precision and its derivative", "4.4 Variance-type parameters: sparse/diagonal $B_k$", "4.5 Correlation-type parameters: dense $B_k$", "4.6 trust_cap: a second REML-stability mechanism tied to parameter type", "4.7 Summary: the full chain per parameter type", "Chapter 5: Worked examples, one per structure", "5.1 ism()", "5.2 dsm()", "5.3 csm(), homogeneous", "5.4 csm(), heterogeneous", "5.5 ar1m()", "5.6 ar2m() / ar3m() / toeplitzm()", "5.7 mam() / ma1m() / ma2m()", "5.8 usm()", "5.9 corgm()", "5.10 fam() / rrm()", "5.11 antem()", "5.12 maternm()", "5.13 sar()", "5.14 car()", "5.15 ownm()", "Chapter 6: End-to-end numerical trace, from $\\eta$ to the REML objective", "6.1 A 4-observation, 2-line x 2-trait toy data set", "6.2 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