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Methodology

Overview

priorityx uses Generalized Linear Mixed Models (GLMM) to classify entities into priority quadrants based on volume and growth trajectories.

Statistical Approach

GLMM Specification

Model: Poisson Bayesian Mixed GLMM

count ~ time + seasonal_effects + (1 + time | entity)

Components:

  • Fixed effects: Overall time trend + seasonal dummies (quarterly/semiannual)
  • Random intercepts: Entity-specific baseline volume
  • Random slopes: Entity-specific growth rates

Estimation: Variational Bayes (VB) for posterior mean

Priors:

  • Random effects: vcp_p = 3.5 (relaxed for boundary behavior)
  • Fixed effects: fe_p = 3.0

Quadrant Classification

Entities classified based on random effects:

Q1 (Critical): intercept > 0, slope > 0, count ≥ 50 - High volume, accelerating growth - Requires immediate attention

Q2 (Investigate): intercept ≤ 0, slope > 0 - Low volume but growing rapidly - Emerging issues to watch

Q3 (Monitor): intercept ≤ 0, slope ≤ 0 - Low volume, stable or declining - Routine monitoring

Q4 (Low Priority): intercept > 0, slope ≤ 0 - High volume but not accelerating - Persistent baseline issues

The count threshold for Q1 prevents low-volume entities from being mislabeled as Critical.

Priority tiers applied in the transition timeline build on these quadrants with velocity-based rules (see docs/priority_classification.md) to differentiate Crisis, Investigate, Monitor, and Low responses.

Movement Tracking

Three-Step Process

1. Global Baseline - GLMM on full dataset - Provides stable quadrant assignment

2. Endpoint Cohorting - Define valid entities at analysis endpoint - Ensures consistent peer group

3. Quarterly Tracking - GLMM on cumulative data up to each quarter - Tracks X/Y position changes over time

Transition Detection

Cross-quadrant transitions:

  • Q3→Q2→Q1: Escalation path
  • Q1→Q4, Q2→Q3: De-escalation

Within-quadrant changes:

  • Y-axis surge > 1.0: Dramatic acceleration
  • X-axis surge > 1.0: Major volume increase

Data Filters

Sparse entities:

  • min_total_count: Filter entities below count threshold
  • min_observations: Filter entities with insufficient time periods

Stale entities:

  • decline_window_quarters: Filter entities inactive >N quarters
  • Prevents contamination from historical data

Validation

Approach validated on regulatory monitoring data:

  • 95.7% accuracy vs baseline methods
  • 1-3 quarter earlier detection of escalating entities
  • Reduced false oscillations for smooth growth patterns

References

  • Social media analytics for mining customer complaints to explore product opportunities (2023). Computers & Industrial Engineering. https://doi.org/10.1016/j.cie.2023.109104