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Search, Evaluate, and Read Evidence","\u002Fen\u002Facademic-writing\u002F02-reading-and-literature-matrix","en\u002Facademic-writing\u002F02-reading-and-literature-matrix",{"title":27,"path":28,"stem":29},"3. From Sources to Synthesis and Argument","\u002Fen\u002Facademic-writing\u002F03-arguments-outlines-and-paragraphs","en\u002Facademic-writing\u002F03-arguments-outlines-and-paragraphs",{"title":31,"path":32,"stem":33},"4. Literature Review and a Defensible Gap","\u002Fen\u002Facademic-writing\u002F04-writing-the-literature-review","en\u002Facademic-writing\u002F04-writing-the-literature-review",{"title":35,"path":36,"stem":37},"5. Research Design, Evidence, and Core Sections","\u002Fen\u002Facademic-writing\u002F05-core-sections-and-evidence","en\u002Facademic-writing\u002F05-core-sections-and-evidence",{"title":39,"path":40,"stem":41},"6. Citation, Paraphrasing, Integrity, and AI","\u002Fen\u002Facademic-writing\u002F06-citation-paraphrasing-and-integrity","en\u002Facademic-writing\u002F06-citation-paraphrasing-and-integrity",{"title":43,"path":44,"stem":45},"7. Revision, Review, and Submission","\u002Fen\u002Facademic-writing\u002F07-revision-style-and-submission","en\u002Facademic-writing\u002F07-revision-style-and-submission",{"title":47,"path":48,"stem":49},"8. Research Workbook","\u002Fen\u002Facademic-writing\u002F08-literature-review-checklist-and-template","en\u002Facademic-writing\u002F08-literature-review-checklist-and-template",{"title":51,"path":52,"stem":53},"9. Research Workflow and Tools","\u002Fen\u002Facademic-writing\u002F09-tools-for-academic-writing-and-literature-management","en\u002Facademic-writing\u002F09-tools-for-academic-writing-and-literature-management",{"title":55,"path":56,"stem":57},"10. Worked Project — From Question to Defensible Conclusion","\u002Fen\u002Facademic-writing\u002F10-worked-example-from-block-structure-to-question-chain","en\u002Facademic-writing\u002F10-worked-example-from-block-structure-to-question-chain",{"title":59,"path":60,"stem":61,"children":62,"page":249},"Accounting","\u002Fen\u002Faccounting","en\u002Faccounting",[63,69,87,93,193],{"title":64,"path":65,"stem":66,"children":67},"Accounting — From Evidence to Decisions","\u002Fen\u002Faccounting\u002F00-index","en\u002Faccounting\u002F00-index",[68],{"title":64,"path":65,"stem":66},{"title":70,"path":71,"stem":72,"children":73},"Accounting Appendix","\u002Fen\u002Faccounting\u002Fappendix","en\u002Faccounting\u002Fappendix\u002Findex",[74,75,79,83],{"title":70,"path":71,"stem":72},{"title":76,"path":77,"stem":78},"Worked Examples and Error Diagnosis","\u002Fen\u002Faccounting\u002Fappendix\u002F24-examples-pitfalls","en\u002Faccounting\u002Fappendix\u002F24-examples-pitfalls",{"title":80,"path":81,"stem":82},"Accounting Glossary","\u002Fen\u002Faccounting\u002Fappendix\u002F26-glossary","en\u002Faccounting\u002Fappendix\u002F26-glossary",{"title":84,"path":85,"stem":86},"Reading and Evidence Map","\u002Fen\u002Faccounting\u002Fappendix\u002F27-reading-map","en\u002Faccounting\u002Fappendix\u002F27-reading-map",{"title":88,"path":89,"stem":90,"children":91},"Northstar Record-to-Decision Capstone","\u002Fen\u002Faccounting\u002Fcapstone","en\u002Faccounting\u002Fcapstone\u002Findex",[92],{"title":88,"path":89,"stem":90},{"title":94,"path":95,"stem":96,"children":97},"Financial Accounting","\u002Fen\u002Faccounting\u002Ffinancial-accounting","en\u002Faccounting\u002Ffinancial-accounting\u002Findex",[98,99,117,131,165,179],{"title":94,"path":95,"stem":96},{"title":100,"path":101,"stem":102,"children":103},"1. Foundations","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F01-foundations","en\u002Faccounting\u002Ffinancial-accounting\u002F01-foundations\u002Findex",[104,105,109,113],{"title":100,"path":101,"stem":102},{"title":106,"path":107,"stem":108},"Objectives and Qualitative Characteristics","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F01-foundations\u002F01-objectives-qualitative-characteristics","en\u002Faccounting\u002Ffinancial-accounting\u002F01-foundations\u002F01-objectives-qualitative-characteristics",{"title":110,"path":111,"stem":112},"Equation and Elements","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F01-foundations\u002F02-equation-elements","en\u002Faccounting\u002Ffinancial-accounting\u002F01-foundations\u002F02-equation-elements",{"title":114,"path":115,"stem":116},"Accrual Basis, Estimates and Periods","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F01-foundations\u002F03-accounting-bases-principles","en\u002Faccounting\u002Ffinancial-accounting\u002F01-foundations\u002F03-accounting-bases-principles",{"title":118,"path":119,"stem":120,"children":121},"2. Recording Transactions","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F02-recording-transactions","en\u002Faccounting\u002Ffinancial-accounting\u002F02-recording-transactions\u002Findex",[122,123,127],{"title":118,"path":119,"stem":120},{"title":124,"path":125,"stem":126},"Double-Entry and Debit\u002FCredit","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F02-recording-transactions\u002F04-double-entry-dr-cr","en\u002Faccounting\u002Ffinancial-accounting\u002F02-recording-transactions\u002F04-double-entry-dr-cr",{"title":128,"path":129,"stem":130},"Accounting Cycle","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F02-recording-transactions\u002F05-accounting-cycle","en\u002Faccounting\u002Ffinancial-accounting\u002F02-recording-transactions\u002F05-accounting-cycle",{"title":132,"path":133,"stem":134,"children":135},"3. Measurement and Adjustments","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments","en\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002Findex",[136,137,141,145,149,153,157,161],{"title":132,"path":133,"stem":134},{"title":138,"path":139,"stem":140},"Revenue Recognition","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F07-revenue-recognition","en\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F07-revenue-recognition",{"title":142,"path":143,"stem":144},"Inventory","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F08-inventory","en\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F08-inventory",{"title":146,"path":147,"stem":148},"Receivables and Expected Credit Losses","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F09-receivables","en\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F09-receivables",{"title":150,"path":151,"stem":152},"Property, Plant and Equipment","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F10-ppe","en\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F10-ppe",{"title":154,"path":155,"stem":156},"Intangible Assets","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F11-intangibles","en\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F11-intangibles",{"title":158,"path":159,"stem":160},"Leases","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F12-leases","en\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F12-leases",{"title":162,"path":163,"stem":164},"Current and Deferred Income Tax","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F13-income-tax","en\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F13-income-tax",{"title":166,"path":167,"stem":168,"children":169},"4. Reporting and Cash","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F04-reporting-cash","en\u002Faccounting\u002Ffinancial-accounting\u002F04-reporting-cash\u002Findex",[170,171,175],{"title":166,"path":167,"stem":168},{"title":172,"path":173,"stem":174},"Linked Financial Statements","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F04-reporting-cash\u002F06-financial-statements","en\u002Faccounting\u002Ffinancial-accounting\u002F04-reporting-cash\u002F06-financial-statements",{"title":176,"path":177,"stem":178},"Cash, Reconciliation and Internal Control","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F04-reporting-cash\u002F14-cash-control","en\u002Faccounting\u002Ffinancial-accounting\u002F04-reporting-cash\u002F14-cash-control",{"title":180,"path":181,"stem":182,"children":183},"5. Analysis and Comparison","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F05-analysis-comparison","en\u002Faccounting\u002Ffinancial-accounting\u002F05-analysis-comparison\u002Findex",[184,185,189],{"title":180,"path":181,"stem":182},{"title":186,"path":187,"stem":188},"Ratio Analysis","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F05-analysis-comparison\u002F15-ratio-analysis","en\u002Faccounting\u002Ffinancial-accounting\u002F05-analysis-comparison\u002F15-ratio-analysis",{"title":190,"path":191,"stem":192},"IFRS versus US GAAP","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F05-analysis-comparison\u002F25-ifrs-gaap","en\u002Faccounting\u002Ffinancial-accounting\u002F05-analysis-comparison\u002F25-ifrs-gaap",{"title":194,"path":195,"stem":196,"children":197},"Management Accounting","\u002Fen\u002Faccounting\u002Fmanagement-accounting","en\u002Faccounting\u002Fmanagement-accounting\u002Findex",[198,199,217,235],{"title":194,"path":195,"stem":196},{"title":200,"path":201,"stem":202,"children":203},"1. Cost Foundations","\u002Fen\u002Faccounting\u002Fmanagement-accounting\u002F01-cost-foundations","en\u002Faccounting\u002Fmanagement-accounting\u002F01-cost-foundations\u002Findex",[204,205,209,213],{"title":200,"path":201,"stem":202},{"title":206,"path":207,"stem":208},"Cost Concepts and Behaviour","\u002Fen\u002Faccounting\u002Fmanagement-accounting\u002F01-cost-foundations\u002F16-cost-concepts","en\u002Faccounting\u002Fmanagement-accounting\u002F01-cost-foundations\u002F16-cost-concepts",{"title":210,"path":211,"stem":212},"Costing Systems","\u002Fen\u002Faccounting\u002Fmanagement-accounting\u002F01-cost-foundations\u002F17-costing-systems","en\u002Faccounting\u002Fmanagement-accounting\u002F01-cost-foundations\u002F17-costing-systems",{"title":214,"path":215,"stem":216},"Variable and Absorption Costing","\u002Fen\u002Faccounting\u002Fmanagement-accounting\u002F01-cost-foundations\u002F19-variable-vs-absorption","en\u002Faccounting\u002Fmanagement-accounting\u002F01-cost-foundations\u002F19-variable-vs-absorption",{"title":218,"path":219,"stem":220,"children":221},"2. Planning and Control","\u002Fen\u002Faccounting\u002Fmanagement-accounting\u002F02-planning-control","en\u002Faccounting\u002Fmanagement-accounting\u002F02-planning-control\u002Findex",[222,223,227,231],{"title":218,"path":219,"stem":220},{"title":224,"path":225,"stem":226},"Cost–Volume–Profit Analysis","\u002Fen\u002Faccounting\u002Fmanagement-accounting\u002F02-planning-control\u002F18-cvp-analysis","en\u002Faccounting\u002Fmanagement-accounting\u002F02-planning-control\u002F18-cvp-analysis",{"title":228,"path":229,"stem":230},"Budgeting and Variance Analysis","\u002Fen\u002Faccounting\u002Fmanagement-accounting\u002F02-planning-control\u002F20-budgeting-variances","en\u002Faccounting\u002Fmanagement-accounting\u002F02-planning-control\u002F20-budgeting-variances",{"title":232,"path":233,"stem":234},"Performance Measurement","\u002Fen\u002Faccounting\u002Fmanagement-accounting\u002F02-planning-control\u002F21-performance-measurement","en\u002Faccounting\u002Fmanagement-accounting\u002F02-planning-control\u002F21-performance-measurement",{"title":236,"path":237,"stem":238,"children":239},"3. Decisions and Investment","\u002Fen\u002Faccounting\u002Fmanagement-accounting\u002F03-decisions-investment","en\u002Faccounting\u002Fmanagement-accounting\u002F03-decisions-investment\u002Findex",[240,241,245],{"title":236,"path":237,"stem":238},{"title":242,"path":243,"stem":244},"Short-Term Decisions","\u002Fen\u002Faccounting\u002Fmanagement-accounting\u002F03-decisions-investment\u002F22-short-term-decisions","en\u002Faccounting\u002Fmanagement-accounting\u002F03-decisions-investment\u002F22-short-term-decisions",{"title":246,"path":247,"stem":248},"Capital Budgeting","\u002Fen\u002Faccounting\u002Fmanagement-accounting\u002F03-decisions-investment\u002F23-capital-budgeting","en\u002Faccounting\u002Fmanagement-accounting\u002F03-decisions-investment\u002F23-capital-budgeting",false,{"title":251,"path":252,"stem":253,"children":254,"page":249},"Business Analytics","\u002Fen\u002Fbusiness-analytics","en\u002Fbusiness-analytics",[255,261,279,305,335,365,383,400],{"title":256,"path":257,"stem":258,"children":259},"Business Analytics — From Data to Defensible Action","\u002Fen\u002Fbusiness-analytics\u002F00-index","en\u002Fbusiness-analytics\u002F00-index",[260],{"title":256,"path":257,"stem":258},{"title":262,"path":263,"stem":264,"children":265},"0. Decision and Data Foundations","\u002Fen\u002Fbusiness-analytics\u002F00-intro","en\u002Fbusiness-analytics\u002F00-intro\u002Findex",[266,267,271,275],{"title":262,"path":263,"stem":264},{"title":268,"path":269,"stem":270},"Decision Framing","\u002Fen\u002Fbusiness-analytics\u002F00-intro\u002F01-decision-framing","en\u002Fbusiness-analytics\u002F00-intro\u002F01-decision-framing",{"title":272,"path":273,"stem":274},"Data Contracts","\u002Fen\u002Fbusiness-analytics\u002F00-intro\u002F02-data-contracts","en\u002Fbusiness-analytics\u002F00-intro\u002F02-data-contracts",{"title":276,"path":277,"stem":278},"Reproducible Analytics Workflow","\u002Fen\u002Fbusiness-analytics\u002F00-intro\u002F03-reproducible-workflow","en\u002Fbusiness-analytics\u002F00-intro\u002F03-reproducible-workflow",{"title":280,"path":281,"stem":282,"children":283},"1. Descriptive Analytics","\u002Fen\u002Fbusiness-analytics\u002F01-descriptive","en\u002Fbusiness-analytics\u002F01-descriptive\u002Findex",[284,285,289,293,297,301],{"title":280,"path":281,"stem":282},{"title":286,"path":287,"stem":288},"Distributions and Exploratory Data Analysis","\u002Fen\u002Fbusiness-analytics\u002F01-descriptive\u002F04-distributions-eda","en\u002Fbusiness-analytics\u002F01-descriptive\u002F04-distributions-eda",{"title":290,"path":291,"stem":292},"KPIs and Denominators","\u002Fen\u002Fbusiness-analytics\u002F01-descriptive\u002F05-kpis-denominators","en\u002Fbusiness-analytics\u002F01-descriptive\u002F05-kpis-denominators",{"title":294,"path":295,"stem":296},"Segments, Cohorts and Funnels","\u002Fen\u002Fbusiness-analytics\u002F01-descriptive\u002F06-segmentation-cohorts-funnels","en\u002Fbusiness-analytics\u002F01-descriptive\u002F06-segmentation-cohorts-funnels",{"title":298,"path":299,"stem":300},"Visual Evidence and Data Stories","\u002Fen\u002Fbusiness-analytics\u002F01-descriptive\u002F07-visualisation-story","en\u002Fbusiness-analytics\u002F01-descriptive\u002F07-visualisation-story",{"title":302,"path":303,"stem":304},"Experiments and Causal Boundaries","\u002Fen\u002Fbusiness-analytics\u002F01-descriptive\u002F08-experiments-causal-boundary","en\u002Fbusiness-analytics\u002F01-descriptive\u002F08-experiments-causal-boundary",{"title":306,"path":307,"stem":308,"children":309},"2. Predictive Analytics","\u002Fen\u002Fbusiness-analytics\u002F02-predictive","en\u002Fbusiness-analytics\u002F02-predictive\u002Findex",[310,311,315,319,323,327,331],{"title":306,"path":307,"stem":308},{"title":312,"path":313,"stem":314},"Validation, Baselines and Leakage","\u002Fen\u002Fbusiness-analytics\u002F02-predictive\u002F09-validation-leakage","en\u002Fbusiness-analytics\u002F02-predictive\u002F09-validation-leakage",{"title":316,"path":317,"stem":318},"Regression and Forecasting","\u002Fen\u002Fbusiness-analytics\u002F02-predictive\u002F10-regression-forecasting","en\u002Fbusiness-analytics\u002F02-predictive\u002F10-regression-forecasting",{"title":320,"path":321,"stem":322},"Classification and Calibration","\u002Fen\u002Fbusiness-analytics\u002F02-predictive\u002F11-classification-calibration","en\u002Fbusiness-analytics\u002F02-predictive\u002F11-classification-calibration",{"title":324,"path":325,"stem":326},"Trees and Ensembles","\u002Fen\u002Fbusiness-analytics\u002F02-predictive\u002F12-trees-ensembles","en\u002Fbusiness-analytics\u002F02-predictive\u002F12-trees-ensembles",{"title":328,"path":329,"stem":330},"Decision Metrics and Thresholds","\u002Fen\u002Fbusiness-analytics\u002F02-predictive\u002F13-decision-metrics-thresholds","en\u002Fbusiness-analytics\u002F02-predictive\u002F13-decision-metrics-thresholds",{"title":332,"path":333,"stem":334},"Explainability, Monitoring and Drift","\u002Fen\u002Fbusiness-analytics\u002F02-predictive\u002F14-explainability-drift","en\u002Fbusiness-analytics\u002F02-predictive\u002F14-explainability-drift",{"title":336,"path":337,"stem":338,"children":339},"3. Prescriptive Analytics","\u002Fen\u002Fbusiness-analytics\u002F03-prescriptive","en\u002Fbusiness-analytics\u002F03-prescriptive\u002Findex",[340,341,345,349,353,357,361],{"title":336,"path":337,"stem":338},{"title":342,"path":343,"stem":344},"Decision-Making under Uncertainty","\u002Fen\u002Fbusiness-analytics\u002F03-prescriptive\u002F15-decision-uncertainty","en\u002Fbusiness-analytics\u002F03-prescriptive\u002F15-decision-uncertainty",{"title":346,"path":347,"stem":348},"Linear Optimisation","\u002Fen\u002Fbusiness-analytics\u002F03-prescriptive\u002F16-linear-optimization","en\u002Fbusiness-analytics\u002F03-prescriptive\u002F16-linear-optimization",{"title":350,"path":351,"stem":352},"Inventory and Allocation","\u002Fen\u002Fbusiness-analytics\u002F03-prescriptive\u002F17-inventory-allocation","en\u002Fbusiness-analytics\u002F03-prescriptive\u002F17-inventory-allocation",{"title":354,"path":355,"stem":356},"Queueing and Simulation","\u002Fen\u002Fbusiness-analytics\u002F03-prescriptive\u002F18-queueing-simulation","en\u002Fbusiness-analytics\u002F03-prescriptive\u002F18-queueing-simulation",{"title":358,"path":359,"stem":360},"Pricing and Revenue Management","\u002Fen\u002Fbusiness-analytics\u002F03-prescriptive\u002F19-pricing-experimentation","en\u002Fbusiness-analytics\u002F03-prescriptive\u002F19-pricing-experimentation",{"title":362,"path":363,"stem":364},"Causal Targeting and Policy Learning","\u002Fen\u002Fbusiness-analytics\u002F03-prescriptive\u002F20-causal-targeting","en\u002Fbusiness-analytics\u002F03-prescriptive\u002F20-causal-targeting",{"title":366,"path":367,"stem":368,"children":369},"4. Deployment and Governance","\u002Fen\u002Fbusiness-analytics\u002F04-deployment","en\u002Fbusiness-analytics\u002F04-deployment\u002Findex",[370,371,375,379],{"title":366,"path":367,"stem":368},{"title":372,"path":373,"stem":374},"Data Products and Monitoring","\u002Fen\u002Fbusiness-analytics\u002F04-deployment\u002F21-data-products-monitoring","en\u002Fbusiness-analytics\u002F04-deployment\u002F21-data-products-monitoring",{"title":376,"path":377,"stem":378},"Governance, Fairness and Privacy","\u002Fen\u002Fbusiness-analytics\u002F04-deployment\u002F22-governance-fairness-privacy","en\u002Fbusiness-analytics\u002F04-deployment\u002F22-governance-fairness-privacy",{"title":380,"path":381,"stem":382},"Adoption and Business Value","\u002Fen\u002Fbusiness-analytics\u002F04-deployment\u002F23-adoption-value","en\u002Fbusiness-analytics\u002F04-deployment\u002F23-adoption-value",{"title":384,"path":385,"stem":386,"children":387},"Appendix and Revision Tools","\u002Fen\u002Fbusiness-analytics\u002Fappendix","en\u002Fbusiness-analytics\u002Fappendix\u002Findex",[388,389,393,397],{"title":384,"path":385,"stem":386},{"title":390,"path":391,"stem":392},"Formula and Decision Map","\u002Fen\u002Fbusiness-analytics\u002Fappendix\u002F24-formula-map","en\u002Fbusiness-analytics\u002Fappendix\u002F24-formula-map",{"title":394,"path":395,"stem":396},"Worked Examples and Pitfalls","\u002Fen\u002Fbusiness-analytics\u002Fappendix\u002F25-worked-examples-pitfalls","en\u002Fbusiness-analytics\u002Fappendix\u002F25-worked-examples-pitfalls",{"title":84,"path":398,"stem":399},"\u002Fen\u002Fbusiness-analytics\u002Fappendix\u002F26-reading-map","en\u002Fbusiness-analytics\u002Fappendix\u002F26-reading-map",{"title":401,"path":402,"stem":403,"children":404},"Capstone — The Evening Delivery Promise","\u002Fen\u002Fbusiness-analytics\u002Fcapstone","en\u002Fbusiness-analytics\u002Fcapstone\u002Findex",[405],{"title":401,"path":402,"stem":403},{"title":407,"path":408,"stem":409,"children":410,"page":249},"Financial Economic Time Series","\u002Fen\u002Ffinancial-economic-time-series","en\u002Ffinancial-economic-time-series",[411,417,423,429,435,441,447,453,459,465,471],{"title":412,"path":413,"stem":414,"children":415},"Financial and Economic Time Series — Course Guide","\u002Fen\u002Ffinancial-economic-time-series\u002F00-intro","en\u002Ffinancial-economic-time-series\u002F00-intro\u002Findex",[416],{"title":412,"path":413,"stem":414},{"title":418,"path":419,"stem":420,"children":421},"Three Versions of Time Series","\u002Fen\u002Ffinancial-economic-time-series\u002F01-bridge","en\u002Ffinancial-economic-time-series\u002F01-bridge\u002Findex",[422],{"title":418,"path":419,"stem":420},{"title":424,"path":425,"stem":426,"children":427},"Data, Clocks, and Transformations","\u002Fen\u002Ffinancial-economic-time-series\u002F02-data-transformations","en\u002Ffinancial-economic-time-series\u002F02-data-transformations\u002Findex",[428],{"title":424,"path":425,"stem":426},{"title":430,"path":431,"stem":432,"children":433},"Predictive Regressions and Persistent Predictors","\u002Fen\u002Ffinancial-economic-time-series\u002F03-predictive-regressions","en\u002Ffinancial-economic-time-series\u002F03-predictive-regressions\u002Findex",[434],{"title":430,"path":431,"stem":432},{"title":436,"path":437,"stem":438,"children":439},"Volatility, Tails, and Financial Risk","\u002Fen\u002Ffinancial-economic-time-series\u002F04-volatility-risk","en\u002Ffinancial-economic-time-series\u002F04-volatility-risk\u002Findex",[440],{"title":436,"path":437,"stem":438},{"title":442,"path":443,"stem":444,"children":445},"Unit Roots, Cointegration, and Error Correction","\u002Fen\u002Ffinancial-economic-time-series\u002F05-unit-roots-cointegration","en\u002Ffinancial-economic-time-series\u002F05-unit-roots-cointegration\u002Findex",[446],{"title":442,"path":443,"stem":444},{"title":448,"path":449,"stem":450,"children":451},"VAR, Structural Identification, and Local Projections","\u002Fen\u002Ffinancial-economic-time-series\u002F06-var-identification","en\u002Ffinancial-economic-time-series\u002F06-var-identification\u002Findex",[452],{"title":448,"path":449,"stem":450},{"title":454,"path":455,"stem":456,"children":457},"State Space, Mixed Frequency, and Nowcasting","\u002Fen\u002Ffinancial-economic-time-series\u002F07-state-space-nowcasting","en\u002Ffinancial-economic-time-series\u002F07-state-space-nowcasting\u002Findex",[458],{"title":454,"path":455,"stem":456},{"title":460,"path":461,"stem":462,"children":463},"Forecast Evaluation for Decisions","\u002Fen\u002Ffinancial-economic-time-series\u002F08-forecast-evaluation","en\u002Ffinancial-economic-time-series\u002F08-forecast-evaluation\u002Findex",[464],{"title":460,"path":461,"stem":462},{"title":466,"path":467,"stem":468,"children":469},"Integrated R Laboratory","\u002Fen\u002Ffinancial-economic-time-series\u002F09-r-laboratory","en\u002Ffinancial-economic-time-series\u002F09-r-laboratory\u002Findex",[470],{"title":466,"path":467,"stem":468},{"title":472,"path":473,"stem":474,"children":475},"Capstones, Data, and Reading Ladder","\u002Fen\u002Ffinancial-economic-time-series\u002F10-capstone-readings","en\u002Ffinancial-economic-time-series\u002F10-capstone-readings\u002Findex",[476],{"title":472,"path":473,"stem":474},{"title":478,"path":479,"stem":480,"children":481,"page":249},"Intro To Economics","\u002Fen\u002Fintro-to-economics","en\u002Fintro-to-economics",[482,486,490,494,498,502,506,510,514,518,522,526,530],{"title":483,"path":484,"stem":485},"Introduction to Economics — Decisions, Markets, and the Macroeconomy","\u002Fen\u002Fintro-to-economics\u002F00-intro","en\u002Fintro-to-economics\u002F00-intro",{"title":487,"path":488,"stem":489},"Chapter 1 — Choice, Opportunity Cost, and Trade","\u002Fen\u002Fintro-to-economics\u002F01-foundations","en\u002Fintro-to-economics\u002F01-foundations",{"title":491,"path":492,"stem":493},"Chapter 2 — Demand, Supply, Equilibrium, and Welfare","\u002Fen\u002Fintro-to-economics\u002F02-demand-and-supply","en\u002Fintro-to-economics\u002F02-demand-and-supply",{"title":495,"path":496,"stem":497},"Chapter 3 — Elasticity, Revenue, and Tax Incidence","\u002Fen\u002Fintro-to-economics\u002F03-elasticity","en\u002Fintro-to-economics\u002F03-elasticity",{"title":499,"path":500,"stem":501},"Chapter 4 — Firms, Market Power, and Market Failure","\u002Fen\u002Fintro-to-economics\u002F04-market-structures","en\u002Fintro-to-economics\u002F04-market-structures",{"title":503,"path":504,"stem":505},"Chapter 5 — GDP, Income, Wealth, and Welfare","\u002Fen\u002Fintro-to-economics\u002F05-gdp-and-wealth","en\u002Fintro-to-economics\u002F05-gdp-and-wealth",{"title":507,"path":508,"stem":509},"Chapter 6 — Inflation, Purchasing Power, and Labour Markets","\u002Fen\u002Fintro-to-economics\u002F06-inflation-and-unemployment","en\u002Fintro-to-economics\u002F06-inflation-and-unemployment",{"title":511,"path":512,"stem":513},"Chapter 7 — Productivity, Technology, and Economic Growth","\u002Fen\u002Fintro-to-economics\u002F07-economic-growth","en\u002Fintro-to-economics\u002F07-economic-growth",{"title":515,"path":516,"stem":517},"Chapter 8 — Money, Credit, and Banking","\u002Fen\u002Fintro-to-economics\u002F08-money-and-banking","en\u002Fintro-to-economics\u002F08-money-and-banking",{"title":519,"path":520,"stem":521},"Chapter 9 — Business Cycles, AD–AS, and Monetary Policy","\u002Fen\u002Fintro-to-economics\u002F09-monetary-policy-and-ad-as","en\u002Fintro-to-economics\u002F09-monetary-policy-and-ad-as",{"title":523,"path":524,"stem":525},"Chapter 10 — Fiscal Policy, Distribution, and Public Debt","\u002Fen\u002Fintro-to-economics\u002F10-fiscal-policy","en\u002Fintro-to-economics\u002F10-fiscal-policy",{"title":527,"path":528,"stem":529},"Chapter 11 — Trade, Capital Flows, and Exchange Rates","\u002Fen\u002Fintro-to-economics\u002F11-open-economy-and-exchange-rates","en\u002Fintro-to-economics\u002F11-open-economy-and-exchange-rates",{"title":531,"path":532,"stem":533},"Chapter 12 — Integrated Economic Analysis Studio","\u002Fen\u002Fintro-to-economics\u002F12-review-and-case-studies","en\u002Fintro-to-economics\u002F12-review-and-case-studies",{"title":535,"path":536,"stem":537,"children":538,"page":249},"Microeconometrics","\u002Fen\u002Fmicroeconometrics","en\u002Fmicroeconometrics",[539,557,563,581,603,629,651,673,691,709],{"title":540,"path":541,"stem":542,"children":543},"0. Causal Questions and Designs","\u002Fen\u002Fmicroeconometrics\u002F00-foundations","en\u002Fmicroeconometrics\u002F00-foundations\u002Findex",[544,545,549,553],{"title":540,"path":541,"stem":542},{"title":546,"path":547,"stem":548},"Causal Questions and Estimands","\u002Fen\u002Fmicroeconometrics\u002F00-foundations\u002F01-causal-question-estimands","en\u002Fmicroeconometrics\u002F00-foundations\u002F01-causal-question-estimands",{"title":550,"path":551,"stem":552},"Potential Outcomes and Experiments","\u002Fen\u002Fmicroeconometrics\u002F00-foundations\u002F02-potential-outcomes-experiments","en\u002Fmicroeconometrics\u002F00-foundations\u002F02-potential-outcomes-experiments",{"title":554,"path":555,"stem":556},"Causal Diagrams and Controls","\u002Fen\u002Fmicroeconometrics\u002F00-foundations\u002F03-dags-controls","en\u002Fmicroeconometrics\u002F00-foundations\u002F03-dags-controls",{"title":558,"path":559,"stem":560,"children":561},"Microeconometrics — Designing Credible Counterfactuals","\u002Fen\u002Fmicroeconometrics\u002F00-index","en\u002Fmicroeconometrics\u002F00-index",[562],{"title":558,"path":559,"stem":560},{"title":564,"path":565,"stem":566,"children":567},"1. Regression and Inference","\u002Fen\u002Fmicroeconometrics\u002F01-regression","en\u002Fmicroeconometrics\u002F01-regression\u002Findex",[568,569,573,577],{"title":564,"path":565,"stem":566},{"title":570,"path":571,"stem":572},"OLS as a Projection","\u002Fen\u002Fmicroeconometrics\u002F01-regression\u002F04-ols-projection","en\u002Fmicroeconometrics\u002F01-regression\u002F04-ols-projection",{"title":574,"path":575,"stem":576},"FWL, Selection and Controls","\u002Fen\u002Fmicroeconometrics\u002F01-regression\u002F05-fwl-selection-controls","en\u002Fmicroeconometrics\u002F01-regression\u002F05-fwl-selection-controls",{"title":578,"path":579,"stem":580},"Inference and Clustering","\u002Fen\u002Fmicroeconometrics\u002F01-regression\u002F06-inference-clustering","en\u002Fmicroeconometrics\u002F01-regression\u002F06-inference-clustering",{"title":582,"path":583,"stem":584,"children":585},"2. Instruments and Panel Data","\u002Fen\u002Fmicroeconometrics\u002F02-iv-panel","en\u002Fmicroeconometrics\u002F02-iv-panel\u002Findex",[586,587,591,595,599],{"title":582,"path":583,"stem":584},{"title":588,"path":589,"stem":590},"Instrumental Variables","\u002Fen\u002Fmicroeconometrics\u002F02-iv-panel\u002F07-iv-identification","en\u002Fmicroeconometrics\u002F02-iv-panel\u002F07-iv-identification",{"title":592,"path":593,"stem":594},"Weak Instruments and LATE","\u002Fen\u002Fmicroeconometrics\u002F02-iv-panel\u002F08-weak-iv-late","en\u002Fmicroeconometrics\u002F02-iv-panel\u002F08-weak-iv-late",{"title":596,"path":597,"stem":598},"Panel Fixed Effects","\u002Fen\u002Fmicroeconometrics\u002F02-iv-panel\u002F09-panel-fixed-effects","en\u002Fmicroeconometrics\u002F02-iv-panel\u002F09-panel-fixed-effects",{"title":600,"path":601,"stem":602},"Dynamic Panels and Limits","\u002Fen\u002Fmicroeconometrics\u002F02-iv-panel\u002F10-dynamic-panel","en\u002Fmicroeconometrics\u002F02-iv-panel\u002F10-dynamic-panel",{"title":604,"path":605,"stem":606,"children":607},"3. Policy Evaluation Designs","\u002Fen\u002Fmicroeconometrics\u002F03-policy-designs","en\u002Fmicroeconometrics\u002F03-policy-designs\u002Findex",[608,609,613,617,621,625],{"title":604,"path":605,"stem":606},{"title":610,"path":611,"stem":612},"Difference-in-Differences","\u002Fen\u002Fmicroeconometrics\u002F03-policy-designs\u002F11-did-core","en\u002Fmicroeconometrics\u002F03-policy-designs\u002F11-did-core",{"title":614,"path":615,"stem":616},"Staggered DID and Event Studies","\u002Fen\u002Fmicroeconometrics\u002F03-policy-designs\u002F12-staggered-event-studies","en\u002Fmicroeconometrics\u002F03-policy-designs\u002F12-staggered-event-studies",{"title":618,"path":619,"stem":620},"Regression Discontinuity","\u002Fen\u002Fmicroeconometrics\u002F03-policy-designs\u002F13-rdd","en\u002Fmicroeconometrics\u002F03-policy-designs\u002F13-rdd",{"title":622,"path":623,"stem":624},"Matching, Weighting and Overlap","\u002Fen\u002Fmicroeconometrics\u002F03-policy-designs\u002F14-matching-weighting","en\u002Fmicroeconometrics\u002F03-policy-designs\u002F14-matching-weighting",{"title":626,"path":627,"stem":628},"Synthetic Control","\u002Fen\u002Fmicroeconometrics\u002F03-policy-designs\u002F15-synthetic-control","en\u002Fmicroeconometrics\u002F03-policy-designs\u002F15-synthetic-control",{"title":630,"path":631,"stem":632,"children":633},"Module 4 — Choice and Limited Outcomes","\u002Fen\u002Fmicroeconometrics\u002F04-outcomes-choice","en\u002Fmicroeconometrics\u002F04-outcomes-choice\u002Findex",[634,635,639,643,647],{"title":630,"path":631,"stem":632},{"title":636,"path":637,"stem":638},"Binary Choice","\u002Fen\u002Fmicroeconometrics\u002F04-outcomes-choice\u002F16-binary-choice","en\u002Fmicroeconometrics\u002F04-outcomes-choice\u002F16-binary-choice",{"title":640,"path":641,"stem":642},"Multinomial and Ordered Choice","\u002Fen\u002Fmicroeconometrics\u002F04-outcomes-choice\u002F17-multinomial-choice","en\u002Fmicroeconometrics\u002F04-outcomes-choice\u002F17-multinomial-choice",{"title":644,"path":645,"stem":646},"Count Outcomes","\u002Fen\u002Fmicroeconometrics\u002F04-outcomes-choice\u002F18-count-outcomes","en\u002Fmicroeconometrics\u002F04-outcomes-choice\u002F18-count-outcomes",{"title":648,"path":649,"stem":650},"Censoring, Truncation and Selection","\u002Fen\u002Fmicroeconometrics\u002F04-outcomes-choice\u002F19-censoring-selection","en\u002Fmicroeconometrics\u002F04-outcomes-choice\u002F19-censoring-selection",{"title":652,"path":653,"stem":654,"children":655},"Module 5 — Modern Causal Analysis","\u002Fen\u002Fmicroeconometrics\u002F05-modern-causal","en\u002Fmicroeconometrics\u002F05-modern-causal\u002Findex",[656,657,661,665,669],{"title":652,"path":653,"stem":654},{"title":658,"path":659,"stem":660},"Double Machine Learning","\u002Fen\u002Fmicroeconometrics\u002F05-modern-causal\u002F20-dml","en\u002Fmicroeconometrics\u002F05-modern-causal\u002F20-dml",{"title":662,"path":663,"stem":664},"Heterogeneity and Policy Learning","\u002Fen\u002Fmicroeconometrics\u002F05-modern-causal\u002F21-heterogeneity-policy","en\u002Fmicroeconometrics\u002F05-modern-causal\u002F21-heterogeneity-policy",{"title":666,"path":667,"stem":668},"Sensitivity and Partial Identification","\u002Fen\u002Fmicroeconometrics\u002F05-modern-causal\u002F22-sensitivity-partial-id","en\u002Fmicroeconometrics\u002F05-modern-causal\u002F22-sensitivity-partial-id",{"title":670,"path":671,"stem":672},"External Validity and Transport","\u002Fen\u002Fmicroeconometrics\u002F05-modern-causal\u002F23-external-validity","en\u002Fmicroeconometrics\u002F05-modern-causal\u002F23-external-validity",{"title":674,"path":675,"stem":676,"children":677},"Module 6 — From Data to Auditable Evidence","\u002Fen\u002Fmicroeconometrics\u002F06-workflow","en\u002Fmicroeconometrics\u002F06-workflow\u002Findex",[678,679,683,687],{"title":674,"path":675,"stem":676},{"title":680,"path":681,"stem":682},"Data Provenance","\u002Fen\u002Fmicroeconometrics\u002F06-workflow\u002F24-data-provenance","en\u002Fmicroeconometrics\u002F06-workflow\u002F24-data-provenance",{"title":684,"path":685,"stem":686},"Reproducibility and Reporting","\u002Fen\u002Fmicroeconometrics\u002F06-workflow\u002F25-reproducibility-reporting","en\u002Fmicroeconometrics\u002F06-workflow\u002F25-reproducibility-reporting",{"title":688,"path":689,"stem":690},"Paper and Evidence Audit","\u002Fen\u002Fmicroeconometrics\u002F06-workflow\u002F26-paper-audit","en\u002Fmicroeconometrics\u002F06-workflow\u002F26-paper-audit",{"title":692,"path":693,"stem":694,"children":695},"Appendix — Revision and Evidence Map","\u002Fen\u002Fmicroeconometrics\u002Fappendix","en\u002Fmicroeconometrics\u002Fappendix\u002Findex",[696,697,701,705],{"title":692,"path":693,"stem":694},{"title":698,"path":699,"stem":700},"Formula and Design Map","\u002Fen\u002Fmicroeconometrics\u002Fappendix\u002F27-formula-design-map","en\u002Fmicroeconometrics\u002Fappendix\u002F27-formula-design-map",{"title":702,"path":703,"stem":704},"Ten Worked Microeconometric Pitfalls","\u002Fen\u002Fmicroeconometrics\u002Fappendix\u002F28-worked-pitfalls","en\u002Fmicroeconometrics\u002Fappendix\u002F28-worked-pitfalls",{"title":706,"path":707,"stem":708},"Reading and Software Map","\u002Fen\u002Fmicroeconometrics\u002Fappendix\u002F29-reading-software-map","en\u002Fmicroeconometrics\u002Fappendix\u002F29-reading-software-map",{"title":710,"path":711,"stem":712,"children":713},"Capstone — Should Northbridge Expand Pathways?","\u002Fen\u002Fmicroeconometrics\u002Fcapstone","en\u002Fmicroeconometrics\u002Fcapstone\u002Findex",[714],{"title":710,"path":711,"stem":712},{"title":716,"path":717,"stem":718,"children":719,"page":249},"Microeconomics","\u002Fen\u002Fmicroeconomics","en\u002Fmicroeconomics",[720,726,732,738,744,750,756,762,768,774,780,786,792],{"title":721,"path":722,"stem":723,"children":724},"Advanced Microeconomics — Course Guide","\u002Fen\u002Fmicroeconomics\u002F00-intro","en\u002Fmicroeconomics\u002F00-intro\u002Findex",[725],{"title":721,"path":722,"stem":723},{"title":727,"path":728,"stem":729,"children":730},"Module 1 — Choice, Duality, and Revealed Preference","\u002Fen\u002Fmicroeconomics\u002F01-fundations","en\u002Fmicroeconomics\u002F01-fundations\u002Findex",[731],{"title":727,"path":728,"stem":729},{"title":733,"path":734,"stem":735,"children":736},"Module 2 — Comparative Statics and Welfare Measurement","\u002Fen\u002Fmicroeconomics\u002F02-comparative-statics","en\u002Fmicroeconomics\u002F02-comparative-statics\u002Findex",[737],{"title":733,"path":734,"stem":735},{"title":739,"path":740,"stem":741,"children":742},"Module 3 — Choice under Risk and Insurance","\u002Fen\u002Fmicroeconomics\u002F03-uncertainty","en\u002Fmicroeconomics\u002F03-uncertainty\u002Findex",[743],{"title":739,"path":740,"stem":741},{"title":745,"path":746,"stem":747,"children":748},"Module 4 — General Equilibrium and Welfare","\u002Fen\u002Fmicroeconomics\u002F04-general-equilibrium","en\u002Fmicroeconomics\u002F04-general-equilibrium\u002Findex",[749],{"title":745,"path":746,"stem":747},{"title":751,"path":752,"stem":753,"children":754},"Module 5 — Static, Dynamic, and Repeated Games","\u002Fen\u002Fmicroeconomics\u002F05-game-theory","en\u002Fmicroeconomics\u002F05-game-theory\u002Findex",[755],{"title":751,"path":752,"stem":753},{"title":757,"path":758,"stem":759,"children":760},"Module 6 — Oligopoly, Entry, and Algorithmic Pricing","\u002Fen\u002Fmicroeconomics\u002F06-oligopoly","en\u002Fmicroeconomics\u002F06-oligopoly\u002Findex",[761],{"title":757,"path":758,"stem":759},{"title":763,"path":764,"stem":765,"children":766},"Module 7 — Information Economics and Contracts","\u002Fen\u002Fmicroeconomics\u002F07-information-economics","en\u002Fmicroeconomics\u002F07-information-economics\u002Findex",[767],{"title":763,"path":764,"stem":765},{"title":769,"path":770,"stem":771,"children":772},"Module 8 — Mechanism Design and Auctions","\u002Fen\u002Fmicroeconomics\u002F08-mechanism-design","en\u002Fmicroeconomics\u002F08-mechanism-design\u002Findex",[773],{"title":769,"path":770,"stem":771},{"title":775,"path":776,"stem":777,"children":778},"Module 9 — Behavioural and Experimental Microeconomics","\u002Fen\u002Fmicroeconomics\u002F09-behavioural-economics","en\u002Fmicroeconomics\u002F09-behavioural-economics\u002Findex",[779],{"title":775,"path":776,"stem":777},{"title":781,"path":782,"stem":783,"children":784},"Module 10 — Externalities, Public Goods, and Collective Action","\u002Fen\u002Fmicroeconomics\u002F10-externalities-public-goods","en\u002Fmicroeconomics\u002F10-externalities-public-goods\u002Findex",[785],{"title":781,"path":782,"stem":783},{"title":787,"path":788,"stem":789,"children":790},"Module 11 — Matching and Market Design","\u002Fen\u002Fmicroeconomics\u002F11-market-design","en\u002Fmicroeconomics\u002F11-market-design\u002Findex",[791],{"title":787,"path":788,"stem":789},{"title":793,"path":794,"stem":795,"children":796},"Module 12 — Integrated Microeconomic Design Studio","\u002Fen\u002Fmicroeconomics\u002F12-review","en\u002Fmicroeconomics\u002F12-review\u002Findex",[797],{"title":793,"path":794,"stem":795},{"title":799,"path":800,"stem":801,"children":802},"Playground","\u002Fen\u002Fplayground","en\u002Fplayground\u002Findex",[803,804,808,812,816,820],{"title":799,"path":800,"stem":801},{"title":805,"path":806,"stem":807},"Typst Plugin Playground","\u002Fen\u002Fplayground\u002F01-typstex","en\u002Fplayground\u002F01-typstex",{"title":809,"path":810,"stem":811},"Citation Plugin Test","\u002Fen\u002Fplayground\u002F02-citation","en\u002Fplayground\u002F02-citation",{"title":813,"path":814,"stem":815},"Pyodide Playground","\u002Fen\u002Fplayground\u002F03-pyodide","en\u002Fplayground\u002F03-pyodide",{"title":817,"path":818,"stem":819},"WebR Playground","\u002Fen\u002Fplayground\u002F04-webr","en\u002Fplayground\u002F04-webr",{"title":821,"path":822,"stem":823},"Chart.js 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文献综述的构建与写作","\u002Fzh\u002Facademic-writing\u002F04-writing-the-literature-review","zh\u002Facademic-writing\u002F04-writing-the-literature-review",{"title":1056,"path":1057,"stem":1058},"8. 文献综述清单与模板","\u002Fzh\u002Facademic-writing\u002F08-literature-review-checklist-and-template","zh\u002Facademic-writing\u002F08-literature-review-checklist-and-template",{"title":1060,"path":1061,"stem":1062},"10. 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mean degree completion. The policy question may be",[1802,1881,1884],{"className":1882},[1883],"katex-display",[1802,1885,1887,1976],{"className":1886},[1805],[1802,1888,1890],{"className":1889},[1809],[1811,1891,1893],{"xmlns":1813,"display":1892},"block",[1815,1894,1895,1973],{},[1818,1896,1897,1900,1904,1906,1909,1911,1914,1917,1919,1921,1924,1926,1929,1931,1934,1936,1938,1940,1942,1944,1946,1948,1950,1952,1954,1956,1958,1960,1962,1964,1966,1968,1970],{},[1821,1898,1899],{},"E",[1825,1901,1903],{"stretchy":1902},"false","[",[1821,1905,1823],{},[1825,1907,1908],{"stretchy":1902},"(",[1829,1910,1831],{},[1825,1912,1913],{"stretchy":1902},")",[1825,1915,1916],{},"−",[1821,1918,1823],{},[1825,1920,1908],{"stretchy":1902},[1829,1922,1923],{},"0",[1825,1925,1913],{"stretchy":1902},[1825,1927,1928],{"stretchy":1902},"]",[1825,1930,1827],{},[1821,1932,1933],{},"P",[1825,1935,1908],{"stretchy":1902},[1821,1937,1823],{},[1825,1939,1908],{"stretchy":1902},[1829,1941,1831],{},[1825,1943,1913],{"stretchy":1902},[1825,1945,1827],{},[1829,1947,1831],{},[1825,1949,1913],{"stretchy":1902},[1825,1951,1916],{},[1821,1953,1933],{},[1825,1955,1908],{"stretchy":1902},[1821,1957,1823],{},[1825,1959,1908],{"stretchy":1902},[1829,1961,1923],{},[1825,1963,1913],{"stretchy":1902},[1825,1965,1827],{},[1829,1967,1831],{},[1825,1969,1913],{"stretchy":1902},[1825,1971,1972],{"separator":1841},",",[1833,1974,1975],{"encoding":1835},"E[Y(1)-Y(0)]=P(Y(1)=1)-P(Y(0)=1),",[1802,1977,1979,2017,2045,2079,2100,2133],{"className":1978,"ariaHidden":1841},[1840],[1802,1980,1982,1986,1990,1994,1997,2000,2003,2007,2010,2014],{"className":1981},[1845],[1802,1983],{"className":1984,"style":1985},[1849],"height:1em;vertical-align:-0.25em;",[1802,1987,1899],{"className":1988,"style":1989},[1854,1855],"margin-right:0.0576em;",[1802,1991,1903],{"className":1992},[1993],"mopen",[1802,1995,1823],{"className":1996,"style":1856},[1854,1855],[1802,1998,1908],{"className":1999},[1993],[1802,2001,1831],{"className":2002},[1854],[1802,2004,1913],{"className":2005},[2006],"mclose",[1802,2008],{"className":2009,"style":1856},[1860],[1802,2011,1916],{"className":2012},[2013],"mbin",[1802,2015],{"className":2016,"style":1856},[1860],[1802,2018,2020,2023,2026,2029,2032,2036,2039,2042],{"className":2019},[1845],[1802,2021],{"className":2022,"style":1985},[1849],[1802,2024,1823],{"className":2025,"style":1856},[1854,1855],[1802,2027,1908],{"className":2028},[1993],[1802,2030,1923],{"className":2031},[1854],[1802,2033,2035],{"className":2034},[2006],")]",[1802,2037],{"className":2038,"style":1861},[1860],[1802,2040,1827],{"className":2041},[1865],[1802,2043],{"className":2044,"style":1861},[1860],[1802,2046,2048,2051,2055,2058,2061,2064,2067,2070,2073,2076],{"className":2047},[1845],[1802,2049],{"className":2050,"style":1985},[1849],[1802,2052,1933],{"className":2053,"style":2054},[1854,1855],"margin-right:0.1389em;",[1802,2056,1908],{"className":2057},[1993],[1802,2059,1823],{"className":2060,"style":1856},[1854,1855],[1802,2062,1908],{"className":2063},[1993],[1802,2065,1831],{"className":2066},[1854],[1802,2068,1913],{"className":2069},[2006],[1802,2071],{"className":2072,"style":1861},[1860],[1802,2074,1827],{"className":2075},[1865],[1802,2077],{"className":2078,"style":1861},[1860],[1802,2080,2082,2085,2088,2091,2094,2097],{"className":2081},[1845],[1802,2083],{"className":2084,"style":1985},[1849],[1802,2086,1831],{"className":2087},[1854],[1802,2089,1913],{"className":2090},[2006],[1802,2092],{"className":2093,"style":1856},[1860],[1802,2095,1916],{"className":2096},[2013],[1802,2098],{"className":2099,"style":1856},[1860],[1802,2101,2103,2106,2109,2112,2115,2118,2121,2124,2127,2130],{"className":2102},[1845],[1802,2104],{"className":2105,"style":1985},[1849],[1802,2107,1933],{"className":2108,"style":2054},[1854,1855],[1802,2110,1908],{"className":2111},[1993],[1802,2113,1823],{"className":2114,"style":1856},[1854,1855],[1802,2116,1908],{"className":2117},[1993],[1802,2119,1923],{"className":2120},[1854],[1802,2122,1913],{"className":2123},[2006],[1802,2125],{"className":2126,"style":1861},[1860],[1802,2128,1827],{"className":2129},[1865],[1802,2131],{"className":2132,"style":1861},[1860],[1802,2134,2136,2139,2142,2145],{"className":2135},[1845],[1802,2137],{"className":2138,"style":1985},[1849],[1802,2140,1831],{"className":2141},[1854],[1802,2143,1913],{"className":2144},[2006],[1802,2146,1972],{"className":2147},[2148],"mpunct",[1798,2150,2151,2152,2156],{},"an average ",[2153,2154,2155],"strong",{},"risk difference",". A logit coefficient is a change in log-odds, not this quantity.",[1793,2158,2160],{"id":2159},"three-models-three-conveniences","Three models, three conveniences",[2162,2163,2164,2183],"table",{},[2165,2166,2167],"thead",{},[2168,2169,2170,2174,2177,2180],"tr",{},[2171,2172,2173],"th",{},"Model",[2171,2175,2176],{},"Conditional mean",[2171,2178,2179],{},"Main advantage",[2171,2181,2182],{},"Main caution",[2184,2185,2186,2342,2468],"tbody",{},[2168,2187,2188,2192,2282,2285],{},[2189,2190,2191],"td",{},"linear probability",[2189,2193,2194],{},[1802,2195,2197,2223],{"className":2196},[1805],[1802,2198,2200],{"className":2199},[1809],[1811,2201,2202],{"xmlns":1813},[1815,2203,2204,2220],{},[1818,2205,2206,2217],{},[2207,2208,2209,2212],"msup",{},[1821,2210,2211],{},"X",[1825,2213,2216],{"mathvariant":2214,"lspace":2215,"rspace":2215},"normal","0em","′",[1821,2218,2219],{},"β",[1833,2221,2222],{"encoding":1835},"X'\\beta",[1802,2224,2226],{"className":2225,"ariaHidden":1841},[1840],[1802,2227,2229,2233,2278],{"className":2228},[1845],[1802,2230],{"className":2231,"style":2232},[1849],"height:0.9463em;vertical-align:-0.1944em;",[1802,2234,2236,2240],{"className":2235},[1854],[1802,2237,2211],{"className":2238,"style":2239},[1854,1855],"margin-right:0.0785em;",[1802,2241,2244],{"className":2242},[2243],"msupsub",[1802,2245,2248],{"className":2246},[2247],"vlist-t",[1802,2249,2252],{"className":2250},[2251],"vlist-r",[1802,2253,2257],{"className":2254,"style":2256},[2255],"vlist","height:0.7519em;",[1802,2258,2260,2265],{"style":2259},"top:-3.063em;margin-right:0.05em;",[1802,2261],{"className":2262,"style":2264},[2263],"pstrut","height:2.7em;",[1802,2266,2272],{"className":2267},[2268,2269,2270,2271],"sizing","reset-size6","size3","mtight",[1802,2273,2275],{"className":2274},[1854,2271],[1802,2276,2216],{"className":2277},[1854,2271],[1802,2279,2219],{"className":2280,"style":2281},[1854,1855],"margin-right:0.0528em;",[2189,2283,2284],{},"coefficients are probability-point changes",[2189,2286,2287,2288,2341],{},"predictions can leave ",[1802,2289,2291,2313],{"className":2290},[1805],[1802,2292,2294],{"className":2293},[1809],[1811,2295,2296],{"xmlns":1813},[1815,2297,2298,2310],{},[1818,2299,2300,2302,2304,2306,2308],{},[1825,2301,1903],{"stretchy":1902},[1829,2303,1923],{},[1825,2305,1972],{"separator":1841},[1829,2307,1831],{},[1825,2309,1928],{"stretchy":1902},[1833,2311,2312],{"encoding":1835},"[0,1]",[1802,2314,2316],{"className":2315,"ariaHidden":1841},[1840],[1802,2317,2319,2322,2325,2328,2331,2335,2338],{"className":2318},[1845],[1802,2320],{"className":2321,"style":1985},[1849],[1802,2323,1903],{"className":2324},[1993],[1802,2326,1923],{"className":2327},[1854],[1802,2329,1972],{"className":2330},[2148],[1802,2332],{"className":2333,"style":2334},[1860],"margin-right:0.1667em;",[1802,2336,1831],{"className":2337},[1854],[1802,2339,1928],{"className":2340},[2006],"; heteroskedastic errors",[2168,2343,2344,2347,2433,2436],{},[2189,2345,2346],{},"logit",[2189,2348,2349],{},[1802,2350,2352,2379],{"className":2351},[1805],[1802,2353,2355],{"className":2354},[1809],[1811,2356,2357],{"xmlns":1813},[1815,2358,2359,2376],{},[1818,2360,2361,2364,2366,2372,2374],{},[1821,2362,2363],{"mathvariant":2214},"Λ",[1825,2365,1908],{"stretchy":1902},[2207,2367,2368,2370],{},[1821,2369,2211],{},[1825,2371,2216],{"mathvariant":2214,"lspace":2215,"rspace":2215},[1821,2373,2219],{},[1825,2375,1913],{"stretchy":1902},[1833,2377,2378],{"encoding":1835},"\\Lambda(X'\\beta)",[1802,2380,2382],{"className":2381,"ariaHidden":1841},[1840],[1802,2383,2385,2389,2392,2395,2427,2430],{"className":2384},[1845],[1802,2386],{"className":2387,"style":2388},[1849],"height:1.0019em;vertical-align:-0.25em;",[1802,2390,2363],{"className":2391},[1854],[1802,2393,1908],{"className":2394},[1993],[1802,2396,2398,2401],{"className":2397},[1854],[1802,2399,2211],{"className":2400,"style":2239},[1854,1855],[1802,2402,2404],{"className":2403},[2243],[1802,2405,2407],{"className":2406},[2247],[1802,2408,2410],{"className":2409},[2251],[1802,2411,2413],{"className":2412,"style":2256},[2255],[1802,2414,2415,2418],{"style":2259},[1802,2416],{"className":2417,"style":2264},[2263],[1802,2419,2421],{"className":2420},[2268,2269,2270,2271],[1802,2422,2424],{"className":2423},[1854,2271],[1802,2425,2216],{"className":2426},[1854,2271],[1802,2428,2219],{"className":2429,"style":2281},[1854,1855],[1802,2431,1913],{"className":2432},[2006],[2189,2434,2435],{},"valid probabilities; odds interpretation",[2189,2437,2438,2439,2467],{},"effects depend on ",[1802,2440,2442,2455],{"className":2441},[1805],[1802,2443,2445],{"className":2444},[1809],[1811,2446,2447],{"xmlns":1813},[1815,2448,2449,2453],{},[1818,2450,2451],{},[1821,2452,2211],{},[1833,2454,2211],{"encoding":1835},[1802,2456,2458],{"className":2457,"ariaHidden":1841},[1840],[1802,2459,2461,2464],{"className":2460},[1845],[1802,2462],{"className":2463,"style":1850},[1849],[1802,2465,2211],{"className":2466,"style":2239},[1854,1855]," and baseline risk",[2168,2469,2470,2473,2558,2561],{},[2189,2471,2472],{},"probit",[2189,2474,2475],{},[1802,2476,2478,2505],{"className":2477},[1805],[1802,2479,2481],{"className":2480},[1809],[1811,2482,2483],{"xmlns":1813},[1815,2484,2485,2502],{},[1818,2486,2487,2490,2492,2498,2500],{},[1821,2488,2489],{"mathvariant":2214},"Φ",[1825,2491,1908],{"stretchy":1902},[2207,2493,2494,2496],{},[1821,2495,2211],{},[1825,2497,2216],{"mathvariant":2214,"lspace":2215,"rspace":2215},[1821,2499,2219],{},[1825,2501,1913],{"stretchy":1902},[1833,2503,2504],{"encoding":1835},"\\Phi(X'\\beta)",[1802,2506,2508],{"className":2507,"ariaHidden":1841},[1840],[1802,2509,2511,2514,2517,2520,2552,2555],{"className":2510},[1845],[1802,2512],{"className":2513,"style":2388},[1849],[1802,2515,2489],{"className":2516},[1854],[1802,2518,1908],{"className":2519},[1993],[1802,2521,2523,2526],{"className":2522},[1854],[1802,2524,2211],{"className":2525,"style":2239},[1854,1855],[1802,2527,2529],{"className":2528},[2243],[1802,2530,2532],{"className":2531},[2247],[1802,2533,2535],{"className":2534},[2251],[1802,2536,2538],{"className":2537,"style":2256},[2255],[1802,2539,2540,2543],{"style":2259},[1802,2541],{"className":2542,"style":2264},[2263],[1802,2544,2546],{"className":2545},[2268,2269,2270,2271],[1802,2547,2549],{"className":2548},[1854,2271],[1802,2550,2216],{"className":2551},[1854,2271],[1802,2553,2219],{"className":2554,"style":2281},[1854,1855],[1802,2556,1913],{"className":2557},[2006],[2189,2559,2560],{},"latent-normal formulation",[2189,2562,2563],{},"scale is not directly substantive",[1798,2565,2566],{},"For causal work, all three still require a credible treatment-assignment argument. Robust standard errors address heteroskedasticity in an LPM; they do not repair confounding.",[1793,2568,2570],{"id":2569},"odds-are-not-risks","Odds are not risks",[1798,2572,2573],{},"Suppose completion rises from 0.20 to 0.30:",[2575,2576,2577,2659,2720],"ul",{},[2578,2579,2580,2581,2658],"li",{},"risk difference: ",[1802,2582,2584,2609],{"className":2583},[1805],[1802,2585,2587],{"className":2586},[1809],[1811,2588,2589],{"xmlns":1813},[1815,2590,2591,2606],{},[1818,2592,2593,2596,2598,2601,2603],{},[1829,2594,2595],{},"0.30",[1825,2597,1916],{},[1829,2599,2600],{},"0.20",[1825,2602,1827],{},[1829,2604,2605],{},"0.10",[1833,2607,2608],{"encoding":1835},"0.30-0.20=0.10",[1802,2610,2612,2631,2649],{"className":2611,"ariaHidden":1841},[1840],[1802,2613,2615,2619,2622,2625,2628],{"className":2614},[1845],[1802,2616],{"className":2617,"style":2618},[1849],"height:0.7278em;vertical-align:-0.0833em;",[1802,2620,2595],{"className":2621},[1854],[1802,2623],{"className":2624,"style":1856},[1860],[1802,2626,1916],{"className":2627},[2013],[1802,2629],{"className":2630,"style":1856},[1860],[1802,2632,2634,2637,2640,2643,2646],{"className":2633},[1845],[1802,2635],{"className":2636,"style":1875},[1849],[1802,2638,2600],{"className":2639},[1854],[1802,2641],{"className":2642,"style":1861},[1860],[1802,2644,1827],{"className":2645},[1865],[1802,2647],{"className":2648,"style":1861},[1860],[1802,2650,2652,2655],{"className":2651},[1845],[1802,2653],{"className":2654,"style":1875},[1849],[1802,2656,2605],{"className":2657},[1854],";",[2578,2660,2661,2662,2658],{},"risk ratio: ",[1802,2663,2665,2689],{"className":2664},[1805],[1802,2666,2668],{"className":2667},[1809],[1811,2669,2670],{"xmlns":1813},[1815,2671,2672,2686],{},[1818,2673,2674,2676,2679,2681,2683],{},[1829,2675,2595],{},[1821,2677,2678],{"mathvariant":2214},"\u002F",[1829,2680,2600],{},[1825,2682,1827],{},[1829,2684,2685],{},"1.50",[1833,2687,2688],{"encoding":1835},"0.30\u002F0.20=1.50",[1802,2690,2692,2711],{"className":2691,"ariaHidden":1841},[1840],[1802,2693,2695,2698,2702,2705,2708],{"className":2694},[1845],[1802,2696],{"className":2697,"style":1985},[1849],[1802,2699,2701],{"className":2700},[1854],"0.30\u002F0.20",[1802,2703],{"className":2704,"style":1861},[1860],[1802,2706,1827],{"className":2707},[1865],[1802,2709],{"className":2710,"style":1861},[1860],[1802,2712,2714,2717],{"className":2713},[1845],[1802,2715],{"className":2716,"style":1875},[1849],[1802,2718,2685],{"className":2719},[1854],[2578,2721,2722,2723,2817],{},"odds ratio: ",[1802,2724,2726,2767],{"className":2725},[1805],[1802,2727,2729],{"className":2728},[1809],[1811,2730,2731],{"xmlns":1813},[1815,2732,2733,2764],{},[1818,2734,2735,2737,2739,2741,2744,2746,2748,2750,2752,2754,2757,2759,2761],{},[1825,2736,1908],{"stretchy":1902},[1829,2738,2595],{},[1821,2740,2678],{"mathvariant":2214},[1829,2742,2743],{},"0.70",[1825,2745,1913],{"stretchy":1902},[1821,2747,2678],{"mathvariant":2214},[1825,2749,1908],{"stretchy":1902},[1829,2751,2600],{},[1821,2753,2678],{"mathvariant":2214},[1829,2755,2756],{},"0.80",[1825,2758,1913],{"stretchy":1902},[1825,2760,1827],{},[1829,2762,2763],{},"1.71",[1833,2765,2766],{"encoding":1835},"(0.30\u002F0.70)\u002F(0.20\u002F0.80)=1.71",[1802,2768,2770,2808],{"className":2769,"ariaHidden":1841},[1840],[1802,2771,2773,2776,2779,2783,2786,2789,2792,2796,2799,2802,2805],{"className":2772},[1845],[1802,2774],{"className":2775,"style":1985},[1849],[1802,2777,1908],{"className":2778},[1993],[1802,2780,2782],{"className":2781},[1854],"0.30\u002F0.70",[1802,2784,1913],{"className":2785},[2006],[1802,2787,2678],{"className":2788},[1854],[1802,2790,1908],{"className":2791},[1993],[1802,2793,2795],{"className":2794},[1854],"0.20\u002F0.80",[1802,2797,1913],{"className":2798},[2006],[1802,2800],{"className":2801,"style":1861},[1860],[1802,2803,1827],{"className":2804},[1865],[1802,2806],{"className":2807,"style":1861},[1860],[1802,2809,2811,2814],{"className":2810},[1845],[1802,2812],{"className":2813,"style":1875},[1849],[1802,2815,2763],{"className":2816},[1854],".",[1798,2819,2820],{},"“A 71% increase” would misdescribe the risk. State the scale.",[1793,2822,2824],{"id":2823},"convert-nonlinear-coefficients-into-quantities-people-can-read","Convert nonlinear coefficients into quantities people can read",[1798,2826,2827,2828,3010,3011,1972],{},"For a logit model 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the derivative is 0.20 at ",[1802,3590,3592,3611],{"className":3591},[1805],[1802,3593,3595],{"className":3594},[1809],[1811,3596,3597],{"xmlns":1813},[1815,3598,3599,3608],{},[1818,3600,3601,3603,3605],{},[1821,3602,1798],{},[1825,3604,1827],{},[1829,3606,3607],{},"0.5",[1833,3609,3610],{"encoding":1835},"p=0.5",[1802,3612,3614,3632],{"className":3613,"ariaHidden":1841},[1840],[1802,3615,3617,3620,3623,3626,3629],{"className":3616},[1845],[1802,3618],{"className":3619,"style":2879},[1849],[1802,3621,1798],{"className":3622},[1854,1855],[1802,3624],{"className":3625,"style":1861},[1860],[1802,3627,1827],{"className":3628},[1865],[1802,3630],{"className":3631,"style":1861},[1860],[1802,3633,3635,3638],{"className":3634},[1845],[1802,3636],{"className":3637,"style":1875},[1849],[1802,3639,3607],{"className":3640},[1854]," but only 0.072 at ",[1802,3643,3645,3663],{"className":3644},[1805],[1802,3646,3648],{"className":3647},[1809],[1811,3649,3650],{"xmlns":1813},[1815,3651,3652,3660],{},[1818,3653,3654,3656,3658],{},[1821,3655,1798],{},[1825,3657,1827],{},[1829,3659,2605],{},[1833,3661,3662],{"encoding":1835},"p=0.10",[1802,3664,3666,3684],{"className":3665,"ariaHidden":1841},[1840],[1802,3667,3669,3672,3675,3678,3681],{"className":3668},[1845],[1802,3670],{"className":3671,"style":2879},[1849],[1802,3673,1798],{"className":3674},[1854,1855],[1802,3676],{"className":3677,"style":1861},[1860],[1802,3679,1827],{"className":3680},[1865],[1802,3682],{"className":3683,"style":1861},[1860],[1802,3685,3687,3690],{"className":3686},[1845],[1802,3688],{"className":3689,"style":1875},[1849],[1802,3691,2605],{"className":3692},[1854],". A single coefficient does not imply a constant probability change.",[1798,3695,3696],{},"For a binary scholarship offer, prefer a discrete change:",[1802,3698,3700],{"className":3699},[1883],[1802,3701,3703,3807],{"className":3702},[1805],[1802,3704,3706],{"className":3705},[1809],[1811,3707,3708],{"xmlns":1813,"display":1892},[1815,3709,3710,3804],{},[1818,3711,3712,3728,3730,3737,3745,3802],{},[3713,3714,3715,3725],"mover",{"accent":1841},[1818,3716,3717,3720,3723],{},[1821,3718,3719],{},"A",[1821,3721,3722],{},"M",[1821,3724,1899],{},[1825,3726,3727],{"stretchy":1841},"^",[1825,3729,1827],{},[3102,3731,3732,3734],{},[1829,3733,1831],{},[1821,3735,3736],{},"n",[3738,3739,3740,3743],"munder",{},[1825,3741,3742],{},"∑",[1821,3744,2847],{},[1818,3746,3747,3749,3755,3757,3760,3762,3764,3766,3772,3774,3776,3782,3784,3786,3788,3790,3792,3798,3800],{},[1825,3748,1903],{"fence":1841},[3713,3750,3751,3753],{"accent":1841},[1821,3752,1798],{},[1825,3754,3727],{},[1825,3756,1908],{"stretchy":1902},[1821,3758,3759],{},"D",[1825,3761,1827],{},[1829,3763,1831],{},[1825,3765,1972],{"separator":1841},[2841,3767,3768,3770],{},[1821,3769,2211],{},[1821,3771,2847],{},[1825,3773,1913],{"stretchy":1902},[1825,3775,1916],{},[3713,3777,3778,3780],{"accent":1841},[1821,3779,1798],{},[1825,3781,3727],{},[1825,3783,1908],{"stretchy":1902},[1821,3785,3759],{},[1825,3787,1827],{},[1829,3789,1923],{},[1825,3791,1972],{"separator":1841},[2841,3793,3794,3796],{},[1821,3795,2211],{},[1821,3797,2847],{},[1825,3799,1913],{"stretchy":1902},[1825,3801,1928],{"fence":1841},[1821,3803,2817],{"mathvariant":2214},[1833,3805,3806],{"encoding":1835},"\\widehat{AME}=\\frac{1}{n}\\sum_i\n\\left[\\hat 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averages the same treatment contrast over the observed covariate distribution.",[4266,4267],"pyodide",{"code64":4268,"layout":4269,"locale":7,"title":4270},"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","vertical","From a log-odds coefficient to risk changes",[1798,4272,4273,4274,4361],{},"The odds ratio 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is constant, while the probability change is not.",[1793,4363,4365],{"id":4364},"interactions-are-contrasts-of-predictions","Interactions are contrasts of predictions",[1798,4367,4368,4369,4423],{},"In a nonlinear model, the coefficient on ",[1802,4370,4372,4392],{"className":4371},[1805],[1802,4373,4375],{"className":4374},[1809],[1811,4376,4377],{"xmlns":1813},[1815,4378,4379,4389],{},[1818,4380,4381,4383,4386],{},[1821,4382,3759],{},[1825,4384,4385],{},"×",[1821,4387,4388],{},"G",[1833,4390,4391],{"encoding":1835},"D\\times G",[1802,4393,4395,4414],{"className":4394,"ariaHidden":1841},[1840],[1802,4396,4398,4402,4405,4408,4411],{"className":4397},[1845],[1802,4399],{"className":4400,"style":4401},[1849],"height:0.7667em;vertical-align:-0.0833em;",[1802,4403,3759],{"className":4404,"style":4072},[1854,1855],[1802,4406],{"className":4407,"style":1856},[1860],[1802,4409,4385],{"className":4410},[2013],[1802,4412],{"className":4413,"style":1856},[1860],[1802,4415,4417,4420],{"className":4416},[1845],[1802,4418],{"className":4419,"style":1850},[1849],[1802,4421,4388],{"className":4422},[1854,1855]," is generally not the interaction effect on probability. Compute four predictions:",[1802,4425,4427],{"className":4426},[1883],[1802,4428,4430,4506],{"className":4429},[1805],[1802,4431,4433],{"className":4432},[1809],[1811,4434,4435],{"xmlns":1813,"display":1892},[1815,4436,4437,4503],{},[1818,4438,4439,4441,4443,4445,4447,4449,4451,4453,4455,4457,4459,4461,4463,4465,4467,4469,4471,4473,4475,4477,4479,4481,4483,4485,4487,4489,4491,4493,4495,4497,4499,4501],{},[1825,4440,1903],{"stretchy":1902},[1821,4442,1798],{},[1825,4444,1908],{"stretchy":1902},[1829,4446,1831],{},[1825,4448,1972],{"separator":1841},[1829,4450,1831],{},[1825,4452,1913],{"stretchy":1902},[1825,4454,1916],{},[1821,4456,1798],{},[1825,4458,1908],{"stretchy":1902},[1829,4460,1923],{},[1825,4462,1972],{"separator":1841},[1829,4464,1831],{},[1825,4466,1913],{"stretchy":1902},[1825,4468,1928],{"stretchy":1902},[1825,4470,1916],{},[1825,4472,1903],{"stretchy":1902},[1821,4474,1798],{},[1825,4476,1908],{"stretchy":1902},[1829,4478,1831],{},[1825,4480,1972],{"separator":1841},[1829,4482,1923],{},[1825,4484,1913],{"stretchy":1902},[1825,4486,1916],{},[1821,4488,1798],{},[1825,4490,1908],{"stretchy":1902},[1829,4492,1923],{},[1825,4494,1972],{"separator":1841},[1829,4496,1923],{},[1825,4498,1913],{"stretchy":1902},[1825,4500,1928],{"stretchy":1902},[1821,4502,2817],{"mathvariant":2214},[1833,4504,4505],{"encoding":1835},"[p(1,1)-p(0,1)]-[p(1,0)-p(0,0)].",[1802,4507,4509,4548,4584,4623],{"className":4508,"ariaHidden":1841},[1840],[1802,4510,4512,4515,4518,4521,4524,4527,4530,4533,4536,4539,4542,4545],{"className":4511},[1845],[1802,4513],{"className":4514,"style":1985},[1849],[1802,4516,1903],{"className":4517},[1993],[1802,4519,1798],{"className":4520},[1854,1855],[1802,4522,1908],{"className":4523},[1993],[1802,4525,1831],{"className":4526},[1854],[1802,4528,1972],{"className":4529},[2148],[1802,4531],{"className":4532,"style":2334},[1860],[1802,4534,1831],{"className":4535},[1854],[1802,4537,1913],{"className":4538},[2006],[1802,4540],{"className":4541,"style":1856},[1860],[1802,4543,1916],{"className":4544},[2013],[1802,4546],{"className":4547,"style":1856},[1860],[1802,4549,4551,4554,4557,4560,4563,4566,4569,4572,4575,4578,4581],{"className":4550},[1845],[1802,4552],{"className":4553,"style":1985},[1849],[1802,4555,1798],{"className":4556},[1854,1855],[1802,4558,1908],{"className":4559},[1993],[1802,4561,1923],{"className":4562},[1854],[1802,4564,1972],{"className":4565},[2148],[1802,4567],{"className":4568,"style":2334},[1860],[1802,4570,1831],{"className":4571},[1854],[1802,4573,2035],{"className":4574},[2006],[1802,4576],{"className":4577,"style":1856},[1860],[1802,4579,1916],{"className":4580},[2013],[1802,4582],{"className":4583,"style":1856},[1860],[1802,4585,4587,4590,4593,4596,4599,4602,4605,4608,4611,4614,4617,4620],{"className":4586},[1845],[1802,4588],{"className":4589,"style":1985},[1849],[1802,4591,1903],{"className":4592},[1993],[1802,4594,1798],{"className":4595},[1854,1855],[1802,4597,1908],{"className":4598},[1993],[1802,4600,1831],{"className":4601},[1854],[1802,4603,1972],{"className":4604},[2148],[1802,4606],{"className":4607,"style":2334},[1860],[1802,4609,1923],{"className":4610},[1854],[1802,4612,1913],{"className":4613},[2006],[1802,4615],{"className":4616,"style":1856},[1860],[1802,4618,1916],{"className":4619},[2013],[1802,4621],{"className":4622,"style":1856},[1860],[1802,4624,4626,4629,4632,4635,4638,4641,4644,4647,4650],{"className":4625},[1845],[1802,4627],{"className":4628,"style":1985},[1849],[1802,4630,1798],{"className":4631},[1854,1855],[1802,4633,1908],{"className":4634},[1993],[1802,4636,1923],{"className":4637},[1854],[1802,4639,1972],{"className":4640},[2148],[1802,4642],{"className":4643,"style":2334},[1860],[1802,4645,1923],{"className":4646},[1854],[1802,4648,2035],{"className":4649},[2006],[1802,4651,2817],{"className":4652},[1854],[1798,4654,4655],{},"Report uncertainty for this contrast, preferably through the model’s delta method or resampling scheme aligned with the design.",[1793,4657,4659],{"id":4658},"fit-is-not-only-discrimination","Fit is not only discrimination",[2162,4661,4662,4672],{},[2165,4663,4664],{},[2168,4665,4666,4669],{},[2171,4667,4668],{},"Diagnostic",[2171,4670,4671],{},"Question",[2184,4673,4674,4682,4690,4698],{},[2168,4675,4676,4679],{},[2189,4677,4678],{},"calibration plot",[2189,4680,4681],{},"do predicted 0.30 risks occur about 30% of the time?",[2168,4683,4684,4687],{},[2189,4685,4686],{},"Brier\u002Flog loss",[2189,4688,4689],{},"are probabilistic predictions accurate?",[2168,4691,4692,4695],{},[2189,4693,4694],{},"ROC\u002FAUC",[2189,4696,4697],{},"can the model rank cases?",[2168,4699,4700,4703],{},[2189,4701,4702],{},"time or site validation",[2189,4704,4705],{},"does performance survive the intended deployment setting?",[1798,4707,4708],{},"AUC can be high while probabilities are poorly calibrated. For a causal effect, neither calibration nor AUC proves exchangeability.",[1793,4710,4712],{"id":4711},"quick-check","Quick check",[1798,4714,4715],{},"The estimated odds ratio is 1.5 in both a low-risk and high-risk group. Are the risk differences equal?",[4717,4718,4720],"legacy-details",{"title":4719},"Answer","No. The same odds ratio implies different probability changes at different baseline risks. Compute group-specific counterfactual predictions and average the relevant contrasts.",[1798,4722,4723],{},[4724,4725,4727],"a",{"href":4726},".\u002F17-multinomial-choice","Next: Multinomial Choice",{"title":10,"searchDepth":4729,"depth":4729,"links":4730},2,[4731,4732,4733,4734,4735,4736,4737],{"id":1795,"depth":4729,"text":1796},{"id":2159,"depth":4729,"text":2160},{"id":2569,"depth":4729,"text":2570},{"id":2823,"depth":4729,"text":2824},{"id":4364,"depth":4729,"text":4365},{"id":4658,"depth":4729,"text":4659},{"id":4711,"depth":4729,"text":4712},"Interpret linear probability, logit and probit models through risks, marginal effects and policy contrasts","md",{},true,{"title":636,"description":4738},"aN1oX9LB-Mn21wRTqZWuymU-DVfHZKiCXivg3zOJxaE",[4745,4747],{"title":630,"path":631,"stem":632,"description":4746,"children":-1},"Model probabilities, alternatives, event counts, censoring and selection without losing the substantive estimand",{"title":640,"path":641,"stem":642,"description":4748,"children":-1},"Match unordered, ordered and alternative-specific decisions to interpretable probability contrasts",1785754729155]