INFRAIMPACT — Methodology Note (v1.0)

Authoritative reference for the scoring engine implemented in assets/js/scoring.js and assets/js/aggregation.js.

1. Conceptual Framework

INFRAIMPACT decomposes the performance of a sanitation asset into two orthogonal blocks:

Blok CAUSE / Origin Stage — prasyarat sebelum/saat aset dibangun.
- Institusi (C-I*): status hukum UPTD/BUMD, struktur organisasi, SDM, koordinasi lintas sektor.
- Regulasi (C-R*): Perda ALD, SOP LLTT, mandatory connection, konsistensi RISPALD–RPJMD.
- Finansial (C-F*): earmark APBD O&M, rasio terhadap kebutuhan normatif, cost-recovery, subsidi silang.
Blok IMPACT / Runtime Stage — kinerja pasca-konstruksi.
- Layanan/Proses (I-S*): idle capacity ratio, LLTT coverage, off-taker activity, service continuity, response time.
- Fisik/Teknis (I-T*): structural integrity, MTBF, effluent compliance, sludge compliance, energy efficiency.

Output utama bukan satu skor tunggal, melainkan pasangan (S_CAUSE, S_IMPACT) yang ditempatkan di matriks 2×2:

	IMPACT < 0.5	IMPACT ≥ 0.5
CAUSE ≥ 0.5	Operational Decay	Resilient Asset
CAUSE < 0.5	Investment-in-Failure	Compensated Failure

2. Normalization

For each indicator $i$ with raw value $v$:

\[x_i = \begin{cases} (v - v_{\min}) / (v_{\max} - v_{\min}) & \text{min-max} \\ \mathrm{map}[v] & \text{categorical ordinal} \\ [v=\text{true}] & \text{boolean} \end{cases}\]

Then clip $x_i$ to $[0, 1]$, and if indicator orientation is negative (e.g., idle capacity ratio), invert: $x_i \leftarrow 1 - x_i$.

3. Aggregation

Dimension score (weighted arithmetic mean within available indicators):

\[S_d = \frac{\sum_{i \in d} w_i \cdot x_i}{\sum_{i \in d} w_i}\]

Block score (weighted geometric mean — non-compensatory partial):

\[S_b = \exp\!\left(\frac{\sum_{d \in b} w_d \cdot \ln S_d}{\sum_{d \in b} w_d}\right)\]

The geometric mean penalises any dimension that collapses to zero, preventing institusi-strong/finansial-zero assets from looking healthy on arithmetic mean.

4. Bobot (Best-Worst Method)

Weights derive from a three-tier BWM (Rezaei, 2015, 2016):

Block weights (CAUSE vs IMPACT) — MVP default 0.5 / 0.5.
Dimension weights within block.
Indicator weights within dimension.

The MVP 1 weights in weights.json are placeholders (panel PANEL-SIM-A). The consistency ratio (CR) of the placeholder panel is 0.18, marginally acceptable (< 0.25). For publication, the panel must be replaced with a documented expert elicitation.

5. Quadrant Classification

function classifyQuadrant(sCause, sImpact, threshold = 0.5) {
  if (sCause >= threshold && sImpact >= threshold) return 'resilient';
  if (sCause >= threshold && sImpact <  threshold) return 'operational_decay';
  if (sCause <  threshold && sImpact >= threshold) return 'compensated_failure';
  return 'investment_in_failure';
}

6. Risk Zone (with absolute override)

The composite zone uses the average of the block scores:

Composite < 0.33 → red
0.33 ≤ Composite < 0.66 → yellow
Composite ≥ 0.66 → green

Absolute compliance override: if effluent_compliance_rate < 0.50 (proxy for pelanggaran baku mutu), the zone is forced to red regardless of composite. This avoids the situation where institusi-strong assets mask serious environmental non-compliance.

7. Trajectory Classification

Given a series of yearly observations for one asset, the trajectory class is:

recovered: zone[start] = red ∧ zone[end] ≠ red.
relapse: zone[start] ≠ red ∧ zone[end] = red.
volatile: stddev of composite > 0.15 across the series.
improving: mean OLS slope (cause, impact) > +0.015 / year.
declining: mean OLS slope < −0.015 / year.
stagnant: otherwise.

8. Treatment of Missing Data and Left-Censoring

An asset with construction_year > selected_year is rendered as not_yet_constructed (hatch pattern) and excluded from idle/failed metrics for that year.
An observation with data_quality_flag = "missing" is excluded from all aggregations; it is not imputed as zero.
If a series has fewer than 2 observations, trajectory class defaults to stagnant.

9. Aggregation Across Assets (Spatial)

Province/district aggregation uses median + IQR for $(S_{CAUSE}, S_{IMPACT})$ to be robust against outlier assets. Dominant quadrant is computed by majority count. Tooltips display dispersion to mitigate ecological fallacy (Robinson, 1950).

10. Sensitivity Considerations (advisory for MVP 2)

BWM weights are uncertain. Future versions should support perturbation ±20% with on-the-fly reclassification.
The threshold 0.5 is conventional; consider quantile-based thresholds when working with the empirical distribution rather than the normative.

11. Versioning

Every observation carries:

scoring_method_version (e.g., v1.0)
data_quality_flag (observed | estimated | imputed | missing)
data_source
last_updated

When weights.json or the aggregation rule changes, bump the version and add an entry to scoring_versions.json. Do not silently overwrite scores from older versions.

12. References

Rezaei, J. (2015). Best-worst multi-criteria decision-making method. Omega, 53, 49–57.
Rezaei, J. (2016). Best-worst multi-criteria decision-making method: Some properties and a linear model. Omega, 64, 126–130.
Robinson, W. S. (1950). Ecological correlations and the behavior of individuals. American Sociological Review, 15(3), 351–357.
Hart, O., Shleifer, A., & Vishny, R. W. (1997). The proper scope of government: Theory and an application to prisons. Quarterly Journal of Economics, 112(4), 1127–1161.
Williamson, O. E. (2000). The new institutional economics. Journal of Economic Literature, 38(3), 595–613.

Reza Prama Arviandi