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| @@ -0,0 +1,127 @@ | ||
| import { getSum } from '../sum.js' | ||
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| import { SIGNIFICANCE_LEVEL } from './groups.js' | ||
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| // The `varianceRatio` tends to increase with lower `groupSize` | ||
| // - It eventually somewhat stabilizes at a specific `groupSize` | ||
| // (the "optimal" size) after reaching a maximum value | ||
| // - That maximum value is the one we want to return | ||
| // However, the population's "optimal" size might differ from the sample's | ||
| // - i.e. it must be estimated with both accuracy and precision | ||
| // We want to ignore groups with a `groupSize` either: | ||
| // - Higher than the "optimal" one since they have lower `varianceRatio` and | ||
| // would return inaccurate results | ||
| // - Lower than the "optimal" one since they are less precise and would make | ||
| // the return value less precise as well | ||
| // - In particular, their lack of precision makes them more likely to | ||
| // contain both very low and high `varianceRatios` | ||
| // - Therefore, the sample's group with the maximum `varianceRatio` might | ||
| // be due to the imprecision of that group | ||
| // We fix this by: | ||
| // - Finding the group with the highest `varianceRatio` | ||
| // - Finding any contiguous lower groups with roughly the same `varianceRatio` | ||
| // - According to chi-squared distribution confidence intervals | ||
| // - We do not look for contiguous higher groups since they do not improve | ||
| // accuracy nor precision | ||
| // - Taking their arithmetic mean | ||
| export const getOptimalVarianceRatio = function (groups) { | ||
| const varianceRatios = groups.map(getGroupVarianceRatio) | ||
| const maxVarianceRatio = Math.max(...varianceRatios) | ||
| const maxIndex = varianceRatios.indexOf(maxVarianceRatio) | ||
| const optionalVarianceRatio = findOptimalVarianceRatio( | ||
| groups, | ||
| varianceRatios, | ||
| maxIndex, | ||
| ) | ||
| return optionalVarianceRatio | ||
| } | ||
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| const getGroupVarianceRatio = function ({ varianceRatio }) { | ||
| return varianceRatio | ||
| } | ||
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| // Look for groups contiguous to the group at `maxIndex` with the same | ||
| // `varianceRatio`, according to confidence intervals, then take their mean. | ||
| // This uses imperative logic for performance reasons. | ||
| // - This includes performing the mean incrementally | ||
| const findOptimalVarianceRatio = function (groups, varianceRatios, maxIndex) { | ||
| const startIndex = 0 | ||
| // eslint-disable-next-line fp/no-let | ||
| let varianceRatioSum = getSum(varianceRatios, startIndex, maxIndex) | ||
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| // eslint-disable-next-line fp/no-loops, fp/no-mutation, fp/no-let | ||
| for (let minIndex = startIndex; minIndex < maxIndex; minIndex += 1) { | ||
| const collLength = maxIndex + 1 - minIndex | ||
| const varianceRatioMean = varianceRatioSum / collLength | ||
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| // eslint-disable-next-line max-depth | ||
| if (areSimilarGroups(groups, varianceRatioMean, maxIndex, minIndex)) { | ||
| return varianceRatioMean | ||
| } | ||
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| // eslint-disable-next-line fp/no-mutation | ||
| varianceRatioSum -= varianceRatios[minIndex] | ||
| } | ||
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| return groups[maxIndex].varianceRatio | ||
| } | ||
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| // Check whether the group has roughly the same `varianceRatio` as the other | ||
| // groups of the collection. | ||
| // We allow a small percentage of groups to not fit (`invalidMax`): | ||
| // - This ensures changing the `CLUSTER_FACTOR` does not change the result too | ||
| // much | ||
| // - However, we require each end of the collection of groups to fit, since | ||
| // having wrong ends does not make sense | ||
| // eslint-disable-next-line max-params | ||
| const areSimilarGroups = function ( | ||
| groups, | ||
| varianceRatioMean, | ||
| maxIndex, | ||
| minIndex, | ||
| ) { | ||
| return ( | ||
| isSimilarGroup(groups[maxIndex], varianceRatioMean) && | ||
| isSimilarGroup(groups[minIndex], varianceRatioMean) && | ||
| areSimilarMidGroups(groups, varianceRatioMean, maxIndex, minIndex) | ||
| ) | ||
| } | ||
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| // eslint-disable-next-line max-params | ||
| const areSimilarMidGroups = function ( | ||
| groups, | ||
| varianceRatioMean, | ||
| maxIndex, | ||
| minIndex, | ||
| ) { | ||
| const collLength = maxIndex + 1 - minIndex | ||
| // eslint-disable-next-line fp/no-let | ||
| let invalidMax = Math.floor(collLength * (1 - SIGNIFICANCE_LEVEL)) | ||
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| // eslint-disable-next-line fp/no-loops, fp/no-mutation, fp/no-let | ||
| for (let collIndex = minIndex + 1; collIndex < maxIndex; collIndex += 1) { | ||
| // eslint-disable-next-line max-depth | ||
| if (!isSimilarGroup(groups[collIndex], varianceRatioMean)) { | ||
| // eslint-disable-next-line fp/no-mutation | ||
| invalidMax -= 1 | ||
| } | ||
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| // eslint-disable-next-line max-depth | ||
| if (invalidMax === -1) { | ||
| return false | ||
| } | ||
| } | ||
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| return true | ||
| } | ||
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| // Check confidence interval of `varianceRatio` against a specific group | ||
| const isSimilarGroup = function ( | ||
| { varianceRatioMin, varianceRatioMax }, | ||
| varianceRatioMean, | ||
| ) { | ||
| return ( | ||
| varianceRatioMean >= varianceRatioMin && | ||
| varianceRatioMean <= varianceRatioMax | ||
| ) | ||
| } |