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* Add postposterior covariance matrix based mirt rules * Qualify usage of even_grid in dt test * Formatting of ability_estimator * Add todo note to comparison.jl * Refactor dispersion around ScalarizedStateCriteron * Apply formatting
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,65 @@ | ||
| #= | ||
| This file contains some specialised ways to calculate information. | ||
| For some models analytical solutions are possible for information. | ||
| Most are simple applications of the chain rule | ||
| However, I haven't taken a systematic approach yet yet. | ||
| So these are just from equations in the literature. | ||
| There aren't really any type guards on these so its up to the caller to make sure they are using the right ones. | ||
| =# | ||
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| function alt_expected_1d_item_information(ir::ItemResponse, θ) | ||
| """ | ||
| This is a special case of the expected_item_information function for | ||
| * 1-dimensional ability | ||
| * Dichotomous items | ||
| * It should be valid for at least up to the 3PL model, probably others too | ||
| TODO: citation | ||
| """ | ||
| # irθ_prime = ForwardDiff.derivative(ir, θ) | ||
| irθ_prime = ForwardDiff.derivative(x -> resp(ir, x), θ) | ||
| irθ = resp(ir, θ) | ||
| if irθ_prime == 0.0 | ||
| return 0.0 | ||
| else | ||
| return (irθ_prime * irθ_prime) / (irθ * (1 - irθ)) | ||
| end | ||
| end | ||
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| function alt_expected_mirt_item_information(ir::ItemResponse, θ) | ||
| """ | ||
| This is a special case of the expected_item_information function for | ||
| * Multidimensional | ||
| * Dichotomous items | ||
| * It should be valid for at least up to the 3PL model, probably others too | ||
| TODO: citation | ||
| """ | ||
| irθ_prime = ForwardDiff.gradient(x -> resp(ir, x), θ) | ||
| pθ = resp(ir, θ) | ||
| qθ = 1 - pθ | ||
| (irθ_prime * irθ_prime') / (pθ * qθ) | ||
| end | ||
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| function alt_expected_mirt_3pl_item_information(ir::ItemResponse, θ) | ||
| """ | ||
| This is a special case of the expected_item_information function for | ||
| * Multidimensional | ||
| * Dichotomous items | ||
| * 3PL model only | ||
| Mulder J, van der Linden WJ. | ||
| Multidimensional Adaptive Testing with Optimal Design Criteria for Item Selection. | ||
| Psychometrika. 2009 Jun;74(2):273-296. doi: 10.1007/s11336-008-9097-5. | ||
| Equation 4 | ||
| """ | ||
| # XXX: Should avoid using item_params | ||
| params = item_params(ir.item_bank.discriminations, ir.index) | ||
| pθ = resp(ir, θ) | ||
| qθ = 1 - pθ | ||
| a = params.discrimination | ||
| c = params.guess | ||
| common_factor = (qθ * (pθ - c)^2) / (pθ * (1 - c)^2) | ||
| common_factor * (a * a') | ||
| end |
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,128 @@ | ||
| abstract type MatrixScalarizer end | ||
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| struct DeterminantScalarizer <: MatrixScalarizer end | ||
| (::DeterminantScalarizer)(mat) = det(mat) | ||
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| struct TraceScalarizer <: MatrixScalarizer end | ||
| (::TraceScalarizer)(mat) = tr(mat) | ||
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| abstract type StateCriteria end | ||
| abstract type ItemCriteria end | ||
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| struct AbilityCovarianceStateCriteria{ | ||
| DistEstT <: DistributionAbilityEstimator, | ||
| IntegratorT <: AbilityIntegrator | ||
| } <: StateCriteria | ||
| dist_est::DistEstT | ||
| integrator::IntegratorT | ||
| skip_zero::Bool | ||
| end | ||
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| function AbilityCovarianceStateCriteria(bits...) | ||
| skip_zero = false | ||
| @requiresome (dist_est, integrator) = _get_dist_est_and_integrator(bits...) | ||
| return AbilityCovarianceStateCriteria(dist_est, integrator, skip_zero) | ||
| end | ||
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| # XXX: Should be at type level | ||
| should_minimize(::AbilityCovarianceStateCriteria) = true | ||
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| function (criteria::AbilityCovarianceStateCriteria)( | ||
| tracked_responses::TrackedResponses, | ||
| denom = normdenom(criteria.integrator, | ||
| criteria.dist_est, | ||
| tracked_responses) | ||
| ) | ||
| if denom == 0.0 && criteria.skip_zero | ||
| return Inf | ||
| end | ||
| covariance_matrix( | ||
| criteria.integrator, | ||
| criteria.dist_est, | ||
| tracked_responses, | ||
| denom | ||
| ) | ||
| end | ||
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| struct ScalarizedStateCriteron{ | ||
| StateCriteriaT <: StateCriteria, | ||
| MatrixScalarizerT <: MatrixScalarizer | ||
| } <: StateCriterion | ||
| criteria::StateCriteriaT | ||
| scalarizer::MatrixScalarizerT | ||
| end | ||
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| function (ssc::ScalarizedStateCriteron)(tracked_responses) | ||
| res = ssc.criteria(tracked_responses) |> ssc.scalarizer | ||
| if !should_minimize(ssc.criteria) | ||
| res = -res | ||
| end | ||
| res | ||
| end | ||
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| struct InformationMatrixCriteria{AbilityEstimatorT <: AbilityEstimator, F} <: ItemCriteria | ||
| ability_estimator::AbilityEstimatorT | ||
| expected_item_information::F | ||
| end | ||
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| function InformationMatrixCriteria(ability_estimator) | ||
| InformationMatrixCriteria(ability_estimator, expected_item_information) | ||
| end | ||
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| function init_thread(item_criterion::InformationMatrixCriteria, | ||
| responses::TrackedResponses) | ||
| # TODO: No need to do this one per thread. It just need to be done once per | ||
| # θ update. | ||
| # TODO: Update this to use track!(...) mechanism | ||
| ability = maybe_tracked_ability_estimate(responses, item_criterion.ability_estimator) | ||
| responses_information(responses.item_bank, responses.responses, ability) | ||
| end | ||
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| function (item_criterion::InformationMatrixCriteria)(acc_info::Matrix{Float64}, | ||
| tracked_responses::TrackedResponses, | ||
| item_idx) | ||
| # TODO: Add in information from the prior | ||
| ability = maybe_tracked_ability_estimate( | ||
| tracked_responses, item_criterion.ability_estimator) | ||
| return acc_info .+ | ||
| item_criterion.expected_item_information( | ||
| ItemResponse(tracked_responses.item_bank, item_idx), ability) | ||
| end | ||
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| should_minimize(::InformationMatrixCriteria) = false | ||
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| struct ScalarizedItemCriteron{ | ||
| ItemCriteriaT <: ItemCriteria, | ||
| MatrixScalarizerT <: MatrixScalarizer | ||
| } <: ItemCriterion | ||
| criteria::ItemCriteriaT | ||
| scalarizer::MatrixScalarizerT | ||
| end | ||
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| function (ssc::ScalarizedItemCriteron)(tracked_responses, item_idx) | ||
| res = ssc.criteria( | ||
| init_thread(ssc.criteria, tracked_responses), tracked_responses, item_idx) |> | ||
| ssc.scalarizer | ||
| if !should_minimize(ssc.criteria) | ||
| res = -res | ||
| end | ||
| res | ||
| end | ||
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| struct WeightedStateCriteria{InnerT <: StateCriteria} <: StateCriteria | ||
| weights::Vector{Float64} | ||
| criteria::InnerT | ||
| end | ||
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| function (wsc::WeightedStateCriteria)(tracked_responses, item_idx) | ||
| wsc.weights' * wsc.criteria(tracked_responses, item_idx) * wsc.weights | ||
| end | ||
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| struct WeightedItemCriteria{InnerT <: ItemCriteria} <: ItemCriteria | ||
| weights::Vector{Float64} | ||
| criteria::InnerT | ||
| end | ||
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| function (wsc::WeightedItemCriteria)(tracked_responses, item_idx) | ||
| wsc.weights' * wsc.criteria(tracked_responses, item_idx) * wsc.weights | ||
| end |
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