29:null 2a:["$","title",null,{"children":"Correlated Traits | Mike Stringer | Observable"}] 2f:[] 2d:{"id":"dfd750adfee9320e","slug":"correlated-traits","title":"Correlated Traits","thumbnail":"ea9401800fa6de85bb892cfeaff5f6597102854e7354f0386755093217a37a43","access_level":"public","create_time":"$D2025-01-22T19:47:01.626Z","update_time":"$D2025-01-23T00:05:52.903Z","view_time":null,"first_public_time":"$D2025-01-22T21:31:50.061Z","has_unpublished_edits":null,"fork":false,"stars":0,"starred":false,"owner":{"type":"team","id":"03c047a4f7c01c7d","login":"stringertheory","name":"Mike Stringer","avatar_url":"https://avatars-next.observableusercontent.com/22750d026c52fd24881cb2eb265d03d5cafee7d9b9c7640bc14c1c591e53852f","tier":"starter_2024"},"version":236,"publish_version":null,"role":null,"authored":false,"authors":[{"type":"individual","id":"845474becb001208","login":"stringertheory","name":"Mike Stringer","avatar_url":"https://avatars-next.observableusercontent.com/22750d026c52fd24881cb2eb265d03d5cafee7d9b9c7640bc14c1c591e53852f","tier":null}],"members":[{"type":"team","id":"03c047a4f7c01c7d","login":"stringertheory","name":"Mike Stringer","avatar_url":"https://avatars-next.observableusercontent.com/22750d026c52fd24881cb2eb265d03d5cafee7d9b9c7640bc14c1c591e53852f","tier":"starter_2024","role":"editor"},{"type":"individual","id":"845474becb001208","login":"stringertheory","name":"Mike Stringer","avatar_url":"https://avatars-next.observableusercontent.com/22750d026c52fd24881cb2eb265d03d5cafee7d9b9c7640bc14c1c591e53852f","tier":null,"role":"editor"}],"comments":[],"custom_thumbnail":false,"trashed":false,"lapsed":null,"subscribed":null,"forks":0,"collection":null,"type":"notebook","body":{"title":"Correlated Traits","cells":[{"id":0,"value":"# Correlated Traits","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":170,"value":"viewof button = Inputs.button(\"New Sample\")","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":48,"value":"viewof threshold = Inputs.form({\n a: Inputs.range([-4, 4], { step: 0.1, value: 0, label: \"Intelligence\" }),\n b: Inputs.range([-4, 4], { step: 0.1, value: 0, label: \"Conscientiousness\" }),\n c: Inputs.range([-4, 4], {\n step: 0.1,\n value: 0,\n label: \"Emotional Stability\"\n })\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":87,"value":"

${d3.format(\",\")(subset.length)} people out of a million (${d3.format(\"0.2f\")(100*subset.length/sample.length)}%) have ${formatTrait(\"Intelligence\", threshold.a)}, ${formatTrait(\"Conscientiousness\", threshold.b)}, _and_ ${formatTrait(\"Emotional Stability\", threshold.c)}.

","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":128,"value":"Plot.plot({\n inset: 8,\n width: 440,\n height: 400,\n grid: true,\n color: {\n legend: true,\n label: \"Emotional Stability\",\n scheme: \"Spectral\",\n domain: [-4, 4],\n ticks: 10\n },\n x: {\n label: \"Intelligence\",\n domain: [-4, 4],\n ticks: 10\n },\n y: {\n label: \"Conscientiousness\",\n domain: [-4, 4]\n },\n marks: [\n Plot.dot(plotSample, {\n x: (d) => d[0],\n y: (d) => d[1],\n fill: (d) => d[2],\n r: 3\n }),\n Plot.dot(plotSubset, {\n x: (d) => d[0],\n y: (d) => d[1],\n r: 3.5,\n stroke: \"black\"\n })\n ]\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":121,"value":"
\n\n---\n\n
","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":208,"value":"Reproducing the result of [this paper](https://www.sciencedirect.com/science/article/pii/S019188692400415X), via [Joe Brown](https://www.linkedin.com/in/hijoebrown/).","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":112,"value":"function formatTrait(traitName, value) {\n if (value === 0) {\n return `at least average ${traitName}`;\n } else if (value > 0) {\n return `${traitName} higher than ${value} SD above average`;\n } else {\n return `${traitName} higher than ${value} SD below average`;\n }\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":224,"value":"plotSample = _.sampleSize(sample, 1_000)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":226,"value":"plotSubset = plotSample.filter(\n ([a, b, c]) => a >= threshold.a && b >= threshold.b && c >= threshold.c\n)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":45,"value":"subset = sample.filter(\n ([a, b, c]) => a >= threshold.a && b >= threshold.b && c >= threshold.c\n)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":5,"value":"sample = {\n button;\n return trivariateNorm(\n 1_000_000,\n correlation.ab,\n correlation.ac,\n correlation.bc\n );\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":68,"value":"viewof correlation = Inputs.form({\n ab: Inputs.range([-1, 1], {\n step: 0.01,\n value: -0.03,\n label: \"Intelligence - Conscientiousness\",\n disabled: true\n }),\n ac: Inputs.range([-1, 1], {\n step: 0.01,\n value: 0.07,\n label: \"Intelligence - Emotional Stability\",\n disabled: true\n }),\n bc: Inputs.range([-1, 1], {\n step: 0.01,\n value: 0.42,\n label: \"Conscientiousness - Emotional Stability\",\n disabled: true\n })\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":14,"value":"function trivariateNorm(n, rhoAB, rhoAC, rhoBC) {\n const correlations = [rhoAB, rhoAC, rhoBC];\n\n const correlationMatrix = [\n [1, rhoAB, rhoAC],\n [rhoAB, 1, rhoBC],\n [rhoAC, rhoBC, 1]\n ];\n\n const determinant =\n 1 -\n rhoBC * rhoBC -\n rhoAB * (rhoAB - rhoBC * rhoAC) +\n rhoAC * (rhoAB * rhoBC - rhoAC);\n\n if (determinant <= 0) {\n throw new Error(\n \"Invalid correlation coefficients (correlation matrix must be positive definite)\"\n );\n }\n\n const L = choleskyDecomposition(correlationMatrix);\n\n const samples = [];\n const standardNormal = d3.randomNormal();\n for (let i = 0; i < n; i++) {\n const z = Array(3)\n .fill()\n .map(() => standardNormal());\n\n const sample = [\n L[0][0] * z[0],\n L[1][0] * z[0] + L[1][1] * z[1],\n L[2][0] * z[0] + L[2][1] * z[1] + L[2][2] * z[2]\n ];\n\n samples.push(sample);\n }\n\n return samples;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":11,"value":"function choleskyDecomposition(matrix) {\n const n = matrix.length;\n const L = Array(n)\n .fill()\n .map(() => Array(n).fill(0));\n\n for (let i = 0; i < n; i++) {\n for (let j = 0; j <= i; j++) {\n let sum = 0;\n\n if (j === i) {\n for (let k = 0; k < j; k++) {\n sum += L[j][k] * L[j][k];\n }\n L[j][j] = Math.sqrt(matrix[j][j] - sum);\n } else {\n for (let k = 0; k < j; k++) {\n sum += L[i][k] * L[j][k];\n }\n L[i][j] = (matrix[i][j] - sum) / L[j][j];\n }\n }\n }\n\n return L;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"}],"files":"$W2f","stdlib":"1","titling":"auto"}} 2e:"$2d:body"