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
Understanding x_score and y_score
The priority matrix axes represent entity-specific deviations from population trends:
| Score | GLMM Component | Interpretation |
|---|---|---|
| x_score | Random intercept | Entity’s baseline volume relative to peers |
| y_score | Random slope | Entity’s growth trajectory relative to peers |
Scale interpretation:
- Poisson models (count-based): Scores are on log-scale. A value of 0.5 means ~65% higher than average (exp(0.5) ≈ 1.65).
- Gaussian/Gamma models (metric-based): Scores are z-standardized for comparability across metrics.
Quadrant Classification
Entities classified based on random effects:
Q1 (Critical): x_score > 0, y_score > 0, count ≥ 50
- High volume, accelerating growth
- Requires immediate attention
Q2 (Investigate): x_score ≤ 0, y_score > 0
- Low volume but growing rapidly
- Emerging issues to watch
Q3 (Monitor): x_score ≤ 0, y_score ≤ 0
- Low volume, stable or declining
- Routine monitoring
Q4 (Low Priority): x_score > 0, y_score ≤ 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