Running Decomposition

What Is Decomposition Analysis?

Decomposition analysis breaks down your model's predictions to show how much each variable group contributes to your KPI over time. It answers the fundamental question: "What's driving my business results?"

Purpose: Break down model predictions to show time-series contributions by group (Media, Price, Promotions, etc.) and identify which factors drive KPI performance.

Prerequisites

Before running decomposition:

Required:

  • ✓ Model must be fitted (OLS or Bayesian)

  • ✓ Variables must be organized into contribution groups

  • ✓ Groups must be saved in Contribution Groups page

Recommended:

  • ✓ Colors assigned to each group

  • ✓ Adjustment parameters configured (if needed)

  • ✓ Model diagnostics reviewed and passed

Accessing Decomposition

Navigation:

  1. Click "Decomposition" in the left sidebar

  2. Select your fitted model from dropdown

  3. Choose decomposition type (OLS or Bayesian)

  4. Click "Run Decomposition"

Decomposition Types

OLS Decomposition

Uses: Point estimates from OLS regression

Characteristics:

  • Single value per variable per time period

  • Deterministic contributions

  • Fast calculation

  • Standard approach

When to Use:

  • Default choice for most analyses

  • When using OLS models

  • For clear, simple reporting

  • When speed matters

Bayesian Decomposition

Uses: Posterior mean estimates from Bayesian inference

Characteristics:

  • Based on MCMC samples

  • Reflects parameter uncertainty

  • Point estimates from posterior distribution

  • Same format as OLS in charts

When to Use:

  • When model is Bayesian

  • When uncertainty quantification is important

  • For models with informative priors

  • When Bayesian inference has been run

Note: Both types produce the same chart format - the difference is which coefficients are used in calculation.

The Decomposition Process

How Contributions Are Calculated

For each variable at each time period:

Contribution = Coefficient × Variable Value

For the constant term:

Contribution = Coefficient (same every period)

For each group at each time period:

Group Contribution = Sum of all variable contributions in that group

Total:

Predicted KPI = Sum of all group contributions

Mathematical Example

Model: Sales = 1000 + 2.5×TV + 1.8×Digital + 0.5×Price

Week 1 Values:

  • TV = 100

  • Digital = 50

  • Price = 200

Contributions:

  • Base (constant): 1000

  • TV: 2.5 × 100 = 250

  • Digital: 1.8 × 50 = 90

  • Price: 0.5 × 200 = 100

  • Predicted Sales: 1000 + 250 + 90 + 100 = 1440

If TV and Digital are grouped as "Media":

  • Media contribution = 250 + 90 = 340

Running Main Decomposition

Step 1: Select Model

Model dropdown shows:

  • Model name

  • KPI variable

  • Number of variables

  • Model type (OLS/Bayesian)

Select your desired model for decomposition analysis

Step 2: Choose Decomposition Type

Toggle between:

  • OLS: Uses OLS coefficients (default)

  • Bayesian: Uses Bayesian posterior means

Indicator shows: Current selection with icon

  • 📊 OLS Mode

  • 🎯 Bayesian Mode

Step 3: Click "Run Decomposition"

Button initiates:

  • Retrieval of contribution group settings

  • Calculation of contributions for all time periods

  • Application of any adjustments

  • Generation of charts

Processing:

  • Usually completes in 1-3 seconds

  • Progress indicator shown

  • Charts appear when complete

Step 4: View Results

Two main charts appear:

  1. Actual vs Predicted (Line Chart)

  2. Contribution Breakdown (Stacked Bar Chart)

Main Decomposition Chart

Actual vs Predicted Line Chart

Purpose: Verify model fit and see predictions over time

Chart Elements:

Black Line: Actual KPI values from your data

  • Shows real historical performance

  • Ground truth

Red Dashed Line: Model predicted values

  • Sum of all group contributions

  • Should track actual closely

Good Fit Indicators:

  • Lines track closely together

  • Predicted captures peaks and troughs

  • Small gaps between lines

Poor Fit Indicators:

  • Large persistent gaps

  • Predicted misses major movements

  • Systematic over/under-prediction

Interactive Features:

  • Zoom in/out

  • Pan across time

  • Hover for exact values

  • Reset view

Contribution Breakdown Stacked Bar Chart

Purpose: Show how each group contributes to predicted value over time

Chart Structure:

Stacked Bars:

  • Each bar represents one time period

  • Bar height = Predicted KPI value

  • Each color segment = one group's contribution

  • Segments stack to show total

Colors:

  • Each group has assigned color

  • Consistent across all periods

  • Base usually gray at bottom

  • Marketing groups in distinctive colors

Time Axis (X):

  • Date or time period

  • Chronological order

  • Can zoom to focus on specific periods

Value Axis (Y):

  • KPI units (sales, revenue, etc.)

  • Shows contribution magnitude

  • Starts at zero (or negative if applicable)

Legend:

  • Shows all groups and colors

  • Click to hide/show groups

  • Helps isolate specific contributions

Reading the Chart

Largest Contributors:

  • Tallest segments drive KPI most

  • Usually Base and main marketing groups

Variability:

  • Segments that change height over time

  • Indicate campaign-driven effects

  • Show responsiveness to marketing

Consistency:

  • Steady height segments

  • Represent stable baseline

  • Often Base and seasonality

Timing:

  • When do segments spike?

  • Align with known campaigns?

  • Seasonal patterns visible?

Negative Contributions:

  • Segments below zero line

  • Usually price increases or negative coefficients

  • Pull KPI down

Interactive Chart Features

Zoom and Pan

Mouse Wheel Zoom:

  • Scroll to zoom in/out

  • Focus on specific time periods

  • Maintain aspect ratio

Selection Zoom:

  • Click and drag to select area

  • Zooms to selected region

  • Detailed view of period

Pan:

  • Click and drag to move view

  • Navigate across time

  • Explore different periods

Reset:

  • Click reset button

  • Return to full view

  • Restore original zoom level

Toolbar Options

Available tools:

  • 🔍 Zoom

  • ➕ Zoom In

  • ➖ Zoom Out

  • ✋ Pan

  • 🔄 Reset

Location: Top right of chart

Tooltip Information

Hover over any element:

On bars:

  • Time period

  • Group name

  • Contribution value

  • Percentage of total

On lines:

  • Date

  • Actual value

  • Predicted value

  • Difference

Legend Interaction

Click legend items to:

  • Hide/show specific groups

  • Isolate contributions

  • Compare subsets

  • Focus on specific drivers

Use cases:

  • Hide Base to see only marketing

  • Show only Media groups

  • Compare price vs. promotions

Group Decomposition (Drill-Down)

Purpose

Drill into a specific group to see individual variable contributions within that group.

Example: After seeing "Media" is a major contributor, drill down to see TV vs. Digital vs. Radio performance.

Running Group Decomposition

Step 1: Select Group

  • Dropdown shows all groups from main decomposition

  • Choose group to analyze in detail

Step 2: Click "Run Group Decomposition"

  • Calculates individual variable contributions

  • Shows only variables in selected group

Step 3: View Variable-Level Chart

  • Stacked bars show individual variables

  • Black line shows total group contribution

  • Each variable is a different color/shade

Group Decomposition Chart

Structure:

  • Similar to main chart but variable-level

  • Each variable within the group shown separately

  • Total line shows overall group contribution

Insights:

  • Which specific channels drive the group?

  • Are all channels contributing or just one?

  • How do individual channels compare?

Example:

Media Group Drill-Down:
├── TV: $50,000 (largest contributor)
├── Digital: $30,000
├── Radio: $15,000
└── Print: $5,000
Total Media: $100,000

Interpreting Decomposition Results

What to Look For

1. Largest Contributors

  • Which groups have biggest bars?

  • These are your primary drivers

  • Focus optimization efforts here

2. Variability vs. Stability

  • Changing heights = campaign-driven

  • Steady heights = baseline effects

  • Helps identify controllable factors

3. Temporal Patterns

  • When do contributions spike?

  • Align with known activities?

  • Seasonal patterns?

4. Negative Contributions

  • Which factors reduce KPI?

  • Usually price increases

  • Understand trade-offs

5. Model Fit

  • Do actual and predicted align?

  • Large gaps indicate missing factors

  • Overall fit quality

Common Patterns

Pattern 1: Base-Driven

  • Large steady Base contribution

  • Small variable marketing contributions

  • Indicates strong organic baseline

Interpretation: Marketing has modest incremental impact

Pattern 2: Media-Driven

  • Large variable Media contributions

  • Media spikes align with campaigns

  • Base is smaller

Interpretation: Marketing is primary growth driver

Pattern 3: Promotional

  • Spikes in promotion group

  • Regular promotional calendar visible

  • Clear lift during promotions

Interpretation: Promotions create significant lift

Pattern 4: Seasonal

  • Regular cyclical patterns

  • Seasonality group varies predictably

  • Annual rhythm visible

Interpretation: Strong seasonal effects on KPI

Troubleshooting

Charts Don't Appear

Possible causes:

  • Groups not configured

  • Model not fitted

  • Contribution groups not saved

Solutions:

  1. Verify groups are assigned in Contribution Groups

  2. Confirm "Save Groups" was clicked

  3. Re-run model fitting if needed

  4. Check browser console for errors

Contributions Don't Sum to Predicted

This should never happen - if it does:

  • Browser display issue

  • Recalculate decomposition

  • Contact support

Expected: Bar heights should exactly equal predicted line

Colors Are Wrong

If colors don't match expectations:

  • Check color assignment in Contribution Groups

  • Verify "Save Groups" was clicked

  • Refresh page and re-run

Missing Groups

If some groups don't appear:

  • Check that variables are assigned to those groups

  • Verify group names are consistent

  • Ensure coefficients exist for those variables

Negative Total Contributions

Possible in some cases:

  • When many variables have negative coefficients

  • Price increases reduce demand

  • Legitimate model result

Verify: Check if this makes business sense

Best Practices

Start with Main Decomposition:

  • Get overview first

  • Understand major drivers

  • Then drill into specifics

Use Zoom Strategically:

  • Focus on campaign periods

  • Examine anomalies

  • Compare year-over-year

Run Both OLS and Bayesian:

  • Compare point estimates

  • Understand uncertainty impact

  • Use appropriate method for decision

Document Insights:

  • Screenshot key charts

  • Note patterns observed

  • Record business explanations

Share with Stakeholders:

  • Export charts

  • Prepare interpretations

  • Tell the story

Workflow Summary

Complete decomposition workflow:

  1. Verify Setup

    • Model fitted

    • Groups configured

    • Colors assigned

  2. Run Main Decomposition

    • Select model

    • Choose OLS/Bayesian

    • Click Run

  3. Analyze Main Charts

    • Review actual vs. predicted

    • Examine contribution breakdown

    • Identify key patterns

  4. Drill Into Groups

    • Select major contributor groups

    • Run group decomposition

    • Analyze variable-level details

  5. Export and Share

    • Generate reports

    • Share insights

    • Support decisions

Next Steps

After running decomposition:

  • Proceed to Interpreting Results for detailed analysis guidance

  • Calculate ROI by Channel

  • Analyze Seasonal Patterns

  • Export Decomposition Data for further analysis

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