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  "Title": "Item Response Theory for Large Sparse Data",
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  "Description": "Fits binary item response theory (IRT) models for large\nand sparse data in long format, by marginal maximum likelihood\nwith a Laplace approximation to the integral over person\nabilities, or by the joint posterior mode over items and\npersons. Supports 1PL to 4PL models, multidimensional and\nconfirmatory loading structures with an estimated latent\ncorrelation, covariate effects on ability and on each item\nparameter, empirical-Bayes prior adaptation, and\npost-estimation tools for information, reliability, item fit,\nheld-out prediction and simulation.",
  "License": "MIT + file LICENSE",
  "Encoding": "UTF-8",
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  "SystemRequirements": "GNU make",
  "URL": "https://github.com/cdriveraus/bigIRT",
  "BugReports": "https://github.com/cdriveraus/bigIRT/issues",
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  "Repository": "https://cdriveraus.r-universe.dev",
  "Date/Publication": "2026-10-21 11:56:04 UTC",
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  "Author": "Charles Driver [aut, cre] (ORCID:\n<https://orcid.org/0000-0002-4174-2970>)",
  "Maintainer": "Charles Driver <charles.driver@psychologie.uzh.ch>",
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    "message": "Merge ci-fixes: strucchange functional, withr in Suggests, seed 3's verdict unasserted\n\nCo-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>\n",
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    "as.mirt",
    "augmentIRT",
    "checkConvergence",
    "checkMirtBridge",
    "compareIRTmodels",
    "dropPerfectScores",
    "empiricalICC",
    "extractMIRTpars",
    "fitIRT",
    "glanceIRT",
    "heldoutLogLik",
    "heldoutMetrics",
    "improveModel",
    "IRTcurve",
    "IRTic",
    "itemFit",
    "itemInformation",
    "looIRT",
    "modificationTests",
    "normaliseIRT",
    "normaliseMIRT",
    "personCovarianceMatrices",
    "personCovarianceMatrices_R",
    "plotLaplaceDiagnostics",
    "reliability",
    "reportIRT",
    "rowLoadingsToSparse",
    "scoreContributions",
    "scoreTest",
    "simIRT",
    "testInformation",
    "tidyIRT",
    "wleIRT"
  ],
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    {
      "page": "as.mirt",
      "title": "Coerce a fit to a fixed-parameter mirt object",
      "topics": [
        "as.mirt"
      ]
    },
    {
      "page": "augmentIRT",
      "title": "Per-response fitted values and residuals",
      "topics": [
        "augmentIRT"
      ]
    },
    {
      "page": "checkConvergence",
      "title": "Convergence, resolved by parameter block",
      "topics": [
        "checkConvergence"
      ]
    },
    {
      "page": "checkMirtBridge",
      "title": "Verify the mirt coercion reproduces this fit's curves",
      "topics": [
        "checkMirtBridge"
      ]
    },
    {
      "page": "compareIRTmodels",
      "title": "Compare IRT Model Parameterizations",
      "topics": [
        "compareIRTmodels"
      ]
    },
    {
      "page": "dropPerfectScores",
      "title": "Drop subjects and items with all perfect scores",
      "topics": [
        "dropPerfectScores"
      ]
    },
    {
      "page": "empiricalICC",
      "title": "Observed against model-implied response curves",
      "topics": [
        "empiricalICC"
      ]
    },
    {
      "page": "estfun.bigIRT_scores",
      "title": "Score contributions as an estimating-function matrix",
      "topics": [
        "estfun.bigIRT_scores"
      ]
    },
    {
      "page": "extractMIRTpars",
      "title": "Extract Comparable MIRT Parameters",
      "topics": [
        "extractMIRTpars"
      ]
    },
    {
      "page": "fitIRT",
      "title": "Fit a binary Item Response Theory (IRT) model",
      "topics": [
        "fitIRT"
      ]
    },
    {
      "page": "glanceIRT",
      "title": "One-row model summary",
      "topics": [
        "glanceIRT"
      ]
    },
    {
      "page": "heldoutLogLik",
      "title": "Held-out marginal log-likelihood",
      "topics": [
        "heldoutLogLik"
      ]
    },
    {
      "page": "heldoutMetrics",
      "title": "Predictive performance on held-out responses",
      "topics": [
        "heldoutMetrics"
      ]
    },
    {
      "page": "improveModel",
      "title": "Improve a model by score tests and held-out likelihood",
      "topics": [
        "improveModel"
      ]
    },
    {
      "page": "IRTcurve",
      "title": "Evaluate IRT Item Response Curves",
      "topics": [
        "IRTcurve"
      ]
    },
    {
      "page": "IRTic",
      "title": "Information criteria for a marginal fit",
      "topics": [
        "IRTic"
      ]
    },
    {
      "page": "itemFit",
      "title": "Item fit by standardised residuals",
      "topics": [
        "itemFit"
      ]
    },
    {
      "page": "itemInformation",
      "title": "Item information, standard errors and effective parameters",
      "topics": [
        "itemInformation"
      ]
    },
    {
      "page": "logLik.bigIRT_fit",
      "title": "Marginal log-likelihood of a fit",
      "topics": [
        "logLik.bigIRT_fit"
      ]
    },
    {
      "page": "looIRT",
      "title": "Approximate leave-one-out cross-validation",
      "topics": [
        "looIRT"
      ]
    },
    {
      "page": "modificationTests",
      "title": "Score tests for modifying a fitted model",
      "topics": [
        "modificationTests"
      ]
    },
    {
      "page": "normaliseIRT",
      "title": "normaliseIRT",
      "topics": [
        "normaliseIRT"
      ]
    },
    {
      "page": "normaliseMIRT",
      "title": "Normalize Multidimensional IRT Parameters",
      "topics": [
        "normaliseMIRT"
      ]
    },
    {
      "page": "personCovarianceMatrices",
      "title": "Compute person covariance matrices from row-level moderated IRT parameters",
      "topics": [
        "personCovarianceMatrices"
      ]
    },
    {
      "page": "personCovarianceMatrices_R",
      "title": "Compute person covariance matrices with a pure R reference implementation",
      "topics": [
        "personCovarianceMatrices_R"
      ]
    },
    {
      "page": "plotLaplaceDiagnostics",
      "title": "Plot Laplace diagnostics",
      "topics": [
        "plotLaplaceDiagnostics"
      ]
    },
    {
      "page": "reliability",
      "title": "Reliability of the fitted abilities",
      "topics": [
        "reliability"
      ]
    },
    {
      "page": "reportIRT",
      "title": "Render a model report",
      "topics": [
        "reportIRT"
      ]
    },
    {
      "page": "rowLoadingsToSparse",
      "title": "Convert row loadings to a sparse row representation",
      "topics": [
        "rowLoadingsToSparse"
      ]
    },
    {
      "page": "scoreContributions",
      "title": "Score contributions of a fitted model",
      "topics": [
        "scoreContributions"
      ]
    },
    {
      "page": "scoreTest",
      "title": "Score-based tests of covariate relations after a fit",
      "topics": [
        "scoreTest"
      ]
    },
    {
      "page": "simIRT",
      "title": "Simulate IRT data",
      "topics": [
        "simIRT"
      ]
    },
    {
      "page": "testInformation",
      "title": "Item and test information across the ability range",
      "topics": [
        "testInformation"
      ]
    },
    {
      "page": "tidyIRT",
      "title": "Tidy the item parameters",
      "topics": [
        "tidyIRT"
      ]
    },
    {
      "page": "wleIRT",
      "title": "Compute Weighted Likelihood Estimate (WLE) and Standard Error (SE)",
      "topics": [
        "wleIRT"
      ]
    }
  ],
  "_readme": "https://github.com/cdriveraus/bigIRT/raw/HEAD/README.md",
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      "name": "c++",
      "homepage": "http://gcc.gnu.org/",
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      "source": "score-tests.Rmd",
      "filename": "score-tests.html",
      "title": "Testing covariates after a fit: score-based DIF and ability screening",
      "engine": "knitr::rmarkdown",
      "headings": [
        "Data with impact and DIF",
        "The covariate belongs in the ability model",
        "DIF: one test per item",
        "Purification",
        "A covariate the fit does not have",
        "Covariates of ability",
        "Covariates that vary within person"
      ],
      "created": "2026-10-09 10:52:32",
      "modified": "2026-10-09 12:42:31",
      "commits": 2
    },
    {
      "source": "laplace-objective.Rmd",
      "filename": "laplace-objective.html",
      "title": "The Laplace objective and its gradient in bigIRT",
      "engine": "knitr::rmarkdown",
      "headings": [
        "Purpose",
        "4PL MIRT model",
        "Observation model",
        "$$\\Pr(Y_{ij} = 1 \\mid \\theta_i, \\psi_j)",
        "$$\\ell_{ij}(\\theta_i,\\psi_j)",
        "Parameterization used in bigIRT",
        "Latent distribution",
        "Marginal likelihood target",
        "Exact marginal likelihood",
        "$$\\log L(\\psi)",
        "Why Laplace",
        "Per-person posterior approximation",
        "$$f_i(\\theta_i;\\psi)",
        "$$H_i(\\psi)",
        "Direct Laplace objective used in bigIRT",
        "$$\\tilde L(\\psi)",
        "Value versus gradient",
        "Direct value",
        "Approximate gradient",
        "Item-side frozen-posterior gradient",
        "Why this can be reasonable",
        "Ability mean gradient",
        "Ability correlation gradient",
        "Why optimize in one direct stage?",
        "Advantages",
        "Disadvantages",
        "Current algorithm in words",
        "Identification",
        "Why the approximation can still work well",
        "1. The value tracks the intended target",
        "2. The frozen-posterior gradient is locally sensible",
        "3. Warm starts help",
        "4. Large-data settings help the local Gaussian approximation",
        "Important limitations",
        "Approximate direct gradient",
        "Sensitivity of $c$ and $d$",
        "Dependence on latent-distribution specification",
        "Expensive evaluations",
        "Alternative approaches",
        "1. Two-step Laplace EM",
        "Pros",
        "Cons",
        "2. Exact direct Laplace gradient via implicit differentiation",
        "3. Adaptive quadrature",
        "4. MHRM and related stochastic marginal methods",
        "5. Variational approximations",
        "6. JML / conditional optimization",
        "When laplace_direct is attractive",
        "When another method may be preferable",
        "Summary",
        "Measured behaviour of the frozen-posterior gradient",
        "What the weight is actually worth",
        "Why the near-correct weight loses, and what cannot fix it",
        "It is not the quality of the Gaussian approximation",
        "It is a bias-variance trade, concentrated where identification is weak",
        "Scaling the log-determinant cannot substitute for it",
        "What follows",
        "Resolution: the gradient was right, the objective was incomplete",
        "What this retracts"
      ],
      "created": "2026-08-27 15:35:03",
      "modified": "2026-09-23 18:43:04",
      "commits": 2
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