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