Weighted Variables (WGTD)

Combining Multiple Variables with Custom Coefficients

Weighted Variables (WGTD) allow you to combine multiple related variables into a single composite variable using custom coefficients as weights. This is particularly useful for consolidating multiple channels or campaigns into one variable while maintaining the flexibility to adjust their relative importance.

What Are Weighted Variables?

Combining Multiple Channels

Instead of including multiple related variables separately in your model, you can combine them into one weighted variable.

Example - Multiple Digital Channels:

Separate variables:
- PPC_Spend
- Meta_Spend  
- Instagram_Spend
- LinkedIn_Spend
- Display_Spend

Combined as:
Digital_Mix|WGTD

Why: Reduces model complexity, prevents multicollinearity, creates meaningful composites

How It Works

Step 1: Test Variables

MixModeler first tests all selected variables to get their OLS coefficients.

Example Test Results:

PPC_Spend:       Coefficient = 0.8,  t-stat = 3.2
Meta_Spend:      Coefficient = 0.5,  t-stat = 2.1
Instagram_Spend: Coefficient = 0.4,  t-stat = 1.9
LinkedIn_Spend:  Coefficient = 0.3,  t-stat = 1.5
Display_Spend:   Coefficient = 0.6,  t-stat = 2.4

Step 2: Review and Adjust Weights

The interface shows you the coefficients and lets you modify them based on:

  • Statistical significance (t-stats)

  • Business knowledge

  • Channel priorities

  • Budget allocation strategies

You can:

  • Accept the OLS coefficients as weights

  • Manually adjust weights based on business logic

  • Set some weights to zero (exclude channels)

Step 3: Create Weighted Variable

Formula:

Weighted_Var = w₁×Var₁ + w₂×Var₂ + w₃×Var₃ + ...

Example:

Digital_Mix = 0.8×PPC + 0.5×Meta + 0.4×Instagram + 0.3×LinkedIn + 0.6×Display

Result: Single variable representing combined digital effect

Common Use Cases

Use Case 1: Consolidating Similar Channels

Problem: You have 5 different digital channels that are highly correlated

Solution:

Create: Digital_Mix|WGTD
Components: PPC, Meta, Instagram, LinkedIn, Display
Weights: Based on OLS coefficients or business priorities

Benefit: One variable instead of five, reduced multicollinearity

Use Case 2: Multiple TV Campaigns

Problem: Running 3 TV campaigns simultaneously (Campaign1, Campaign2, Campaign3)

Solution:

Create: TV_Total|WGTD
Components: TV_Campaign1, TV_Campaign2, TV_Campaign3
Weights: Adjust based on creative quality or reach

Example Weights:

Campaign1: 1.2 (best creative)
Campaign2: 1.0 (standard)
Campaign3: 0.8 (lower quality)

Use Case 3: Regional Media Mix

Problem: Different regional spends that should be combined

Solution:

Create: TV_National|WGTD
Components: TV_Northeast, TV_Southeast, TV_West, TV_Midwest
Weights: Based on market size or importance

Use Case 4: Channel with Sub-Channels

Problem: Social media has multiple platforms

Solution:

Create: Social_Media_Total|WGTD
Components: Facebook_Ads, Instagram_Ads, Twitter_Ads, TikTok_Ads
Weights: OLS coefficients or strategic priorities

Creating Weighted Variables in MixModeler

Step-by-Step Process

Step 1: Select Variables

  • Navigate to Variable Workshop

  • Select multiple related variables (hold Ctrl/Cmd for multi-select)

  • Click "Create Weighted Variable"

Step 2: Test Variables

  • MixModeler runs OLS to get coefficients

  • Results table shows:

    • Variable name

    • OLS Coefficient

    • T-statistic (significance)

    • Editable "Model Coefficient" field

Step 3: Adjust Weights

  • Review OLS coefficients

  • Modify "Model Coefficient" column as needed

  • Enter custom weights based on:

    • Statistical significance (higher t-stat = more reliable)

    • Business priorities

    • Budget allocation

    • Channel importance

Step 4: Name and Create

  • Enter base name (e.g., "Digital_Mix")

  • MixModeler creates: Digital_Mix|WGTD

  • New variable appears in Variable Library

Weight Selection Strategies

Strategy 1: Use OLS Coefficients (Data-Driven)

When: You trust the statistical relationships How: Accept default weights from test results Example:

PPC: 0.8 (highest coefficient)
Meta: 0.5
Display: 0.6

Strategy 2: Normalize by Significance (Conservative)

When: Want to weight by statistical confidence How: Use coefficient × (t-stat/2) as weight Example:

PPC: 0.8 × (3.2/2) = 1.28
Meta: 0.5 × (2.1/2) = 0.525
Display: 0.6 × (2.4/2) = 0.72

Strategy 3: Equal Weights (Simplest)

When: All channels equally important How: Set all weights to 1.0 Example:

PPC: 1.0
Meta: 1.0  
Display: 1.0

Result: Simple sum of all channels

Strategy 4: Business-Driven Weights

When: You have strategic priorities How: Set weights based on business importance Example:

PPC: 1.5 (priority channel)
Meta: 1.0 (standard)
Display: 0.7 (experimental)

Interpreting Weighted Variables

In Model Results

Model:

Sales = β₀ + β₁×Digital_Mix|WGTD + ...

If β₁ = 0.4:

  • A 1-unit increase in weighted digital spending → $0.40 increase in sales

  • The "unit" is the weighted combination of all component channels

Component Contributions

When you export to Excel:

  • Weighted variable contribution is automatically decomposed

  • Each component gets proportional credit based on its weight

  • Example: If Digital_Mix contributes $100K total:

    • PPC contribution: proportional to its weight

    • Meta contribution: proportional to its weight

    • etc.

Best Practices

✅ Do's

Group Related Variables Combine channels that serve similar purpose or are highly correlated

Use Meaningful Names Name weighted variables descriptively: Digital_Performance|WGTD, TV_Campaigns|WGTD

Document Weight Rationale Record why you chose specific weights (statistical, business logic, both)

Test Impact on Model Compare model R² with weighted vs. separate variables

Start with OLS Coefficients Use statistical weights as starting point, then adjust if needed

Adjust for Known Differences If Campaign A has 2× better creative than Campaign B, adjust weight accordingly

❌ Don'ts

Don't Combine Unrelated Channels Don't mix TV and Email just to reduce variables - they behave differently

Don't Use Arbitrary Weights Every weight should have a justification (statistical or business)

Don't Ignore Multicollinearity Purpose of weighted variables is often to address high VIF - verify it helps

Don't Over-Combine Keep some separation for actionable insights - don't combine everything into one variable

Don't Forget to Update If channel mix changes significantly, recreate weighted variable with new data

Advantages of Weighted Variables

Reduces Model Complexity 10 digital channels → 1 weighted variable

Addresses Multicollinearity Highly correlated channels combined, reducing VIF

Maintains Flexibility Weights adjustable based on business knowledge

Simplifies Interpretation One coefficient for "total digital" easier to communicate

Enables Fair Comparison Channels weighted by effectiveness, not just raw spend

When NOT to Use Weighted Variables

Don't Combine If:

❌ Channels behave very differently TV (brand) and Search (performance) should stay separate

❌ You need channel-specific insights If stakeholders want individual channel ROI, keep separate

❌ Channels not correlated If VIF is low (<3), no need to combine

❌ Strategic importance differs drastically If one channel is 10× more important, maybe keep separate

Example Workflow

Consolidating Digital Channels

Starting Variables:

- PPC_Spend (coef: 0.8, t-stat: 3.2)
- Meta_Spend (coef: 0.5, t-stat: 2.1)
- Display_Spend (coef: 0.6, t-stat: 2.4)
- LinkedIn_Spend (coef: 0.3, t-stat: 1.5)

Step 1: Select all four variables

Step 2: Create weighted variable, review OLS results

Step 3: Adjust weights:

PPC: 0.8 (keep - high significance)
Meta: 0.5 (keep - moderate significance)
Display: 0.6 (keep - moderate significance)
LinkedIn: 0.4 (increase from 0.3 - strategic priority)

Step 4: Name: Digital_Performance

Step 5: Created: Digital_Performance|WGTD

Result in Model:

Sales = β₀ + β₁×Digital_Performance|WGTD + β₂×TV + ...

Instead of:
Sales = β₀ + β₁×PPC + β₂×Meta + β₃×Display + β₄×LinkedIn + β₅×TV + ...

Benefit: 4 fewer variables, cleaner model, same insights

Summary

Key Takeaways:

⚖️ WGTD = Weighted combination of multiple variables with custom coefficients

📊 Uses OLS coefficients as starting weights - data-driven default

✏️ Fully adjustable - modify weights based on business logic

🎯 Reduces model complexity - many variables → one composite

📉 Addresses multicollinearity - combines correlated channels

💼 Business flexibility - weight channels by strategic importance

🔧 Common uses - digital channels, TV campaigns, regional media

Weighted variables are powerful for creating meaningful composites while maintaining statistical rigor and business relevance!

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