109 lines
3.0 KiB
JSON
109 lines
3.0 KiB
JSON
{
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"model": {
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"name": "Attendance Variance Predictor",
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"version": "1.0.0",
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"author": "Barbara Asbell",
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"location": "Troy, Michigan",
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"date": "2026-07-17",
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"groundedIn": {
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"slug": "predicting-peer-assisted-study-session-attendance",
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"wikidata": "openalex:W2766848659",
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"authors": [
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"Raphael M. Pereira",
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"Kate E. Tonta",
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"Lynne D. Roberts",
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"Peter J. Allen"
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],
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"publication": "Active Learning in Higher Education",
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"year": 2017,
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"citations": 15
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}
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},
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"equation": {
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"formula": "ATTENDANCE(t) = μ_base − σ_hist × Φ⁻¹(P_conf) × S_season × E_event",
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"variables": {
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"μ_base": {
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"description": "mean historical attendance rate",
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"unit": "percent",
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"typicalRange": [88, 96],
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"note": "urban district baseline"
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},
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"σ_hist": {
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"description": "standard deviation of weekly roll data",
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"unit": "percent",
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"measurementPeriod": "12 weeks minimum",
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"typicalRange": [1.5, 5.0]
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},
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"Φ⁻¹": {
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"description": "inverse cumulative normal distribution",
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"implementation": "Abramowitz & Stegun rational approximation",
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"precision": "±0.0001"
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},
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"S_season": {
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"description": "seasonal adjustment factor",
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"values": {
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"neutral_spring_fall": 1.0,
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"winter_flu_season": 1.35,
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"summer_program": 0.85,
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"post_holiday_return": 1.15
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}
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},
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"E_event": {
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"description": "event impact multiplier",
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"values": {
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"no_major_events": 1.0,
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"field_trip_week": 1.25,
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"standardized_testing": 1.4,
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"school_assembly": 0.95
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}
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},
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"t": {
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"description": "prediction horizon",
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"unit": "days",
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"validRange": [1, 14],
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"degradationNote": "reliability drops sharply beyond day 10"
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}
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}
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},
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"workedExample": {
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"inputs": {
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"baseRate": 92.5,
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"stdDev": 3.2,
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"seasonality": 1.35,
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"eventFactor": 1.25,
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"leadDays": 7,
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"confidenceLevel": 95
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},
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"outputs": {
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"expectedDrop": 10.3,
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"peakRiskDay": 4,
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"probabilityOfDrop": 99.2,
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"clusterSize": 6,
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"prepBuffer": 8,
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"confidenceInterval": [82.2, 92.8]
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},
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"cohortSize": 24,
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"interpretation": "Pre-print 8 extra activity packets; expect 4–6 absences on day 4"
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},
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"constraints": {
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"maxHorizon": 14,
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"minStdDev": 0.5,
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"maxStdDev": 15,
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"unmodeledVariables": [
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"family emergencies",
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"weather events",
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"policy changes",
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"transportation disruptions"
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],
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"updateFrequency": "weekly with fresh historical data"
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},
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"validationNotes": {
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"testCase1": {
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"scenario": "Shackleton Crater analog (ΔT=300°C)",
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"adaptation": "thermal drift → attendance drift",
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"reference": "kevin-johnson.4ort.net/thermal-drift.html"
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},
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"designPrinciple": "Every craftsman has instruments; this is ours."
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}
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}
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