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  "Title": "GEMMA Multivariate Linear Mixed Model",
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  "Description": "Fits a multivariate linear mixed effects model that uses a\npolygenic term, after Zhou & Stephens (2014)\n(<https://www.nature.com/articles/nmeth.2848>). Of particular\ninterest is the estimation of variance components with\nrestricted maximum likelihood (REML) methods. Genome-wide\nefficient mixed-model association (GEMMA), as implemented in\nthe package 'gemma2', uses an expectation-maximization\nalgorithm for variance components inference for use in\nquantitative trait locus studies.",
  "License": "MIT + file LICENSE",
  "Encoding": "UTF-8",
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    "calc_qi",
    "calc_XHiY",
    "center_kinship",
    "eigen_proc",
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    "MphEM",
    "stagger_mats",
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      "page": "calc_omega",
      "title": "Calculate Omega matrices",
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      "title": "Calculate Qi (inverse of Q) and log determinant of Q",
      "topics": [
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    {
      "page": "calc_sigma",
      "title": "Calculate Sigma_ee and Sigma_uu matrices",
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      "title": "Calculate XHiY",
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    {
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      "title": "Eigendecomposition procedure for Vg and Ve",
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      "page": "eigen2",
      "title": "Calculate eigendecomposition and return ordered eigenvalues and eigenvectors",
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      "page": "gemma2",
      "title": "gemma2",
      "topics": [
        "gemma2"
      ]
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    {
      "page": "MphCalcLogL",
      "title": "Calculate log likelihood",
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    },
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      "page": "MphEM",
      "title": "Perform expectation-maximization algorithm to infer Vg and Ve values for a pair of traits.",
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      "title": "Stagger matrices within a larger, block-diagonal matrix",
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        "stagger_mats"
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    },
    {
      "page": "update_e",
      "title": "Update E",
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    },
    {
      "page": "UpdateRL_B",
      "title": "Update B for restricted log likelihood",
      "concept": [
        "expectation-maximization functions"
      ],
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        "UpdateRL_B"
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    "Matrix"
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      "title": "Comparing gemma2 output with that of Zhou's GEMMA",
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        "Writing gemma2",
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        "Running gemma2 with example data",
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