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:
Copy 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
Step 1: Test Variables
MixModeler first tests all selected variables to get their OLS coefficients.
Example Test Results:
Step 2: Review and Adjust Weights
The interface shows you the coefficients and lets you modify them based on:
Statistical significance (t-stats)
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:
Example:
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:
Benefit: One variable instead of five, reduced multicollinearity
Use Case 2: Multiple TV Campaigns
Problem: Running 3 TV campaigns simultaneously (Campaign1, Campaign2, Campaign3)
Solution:
Example Weights:
Problem: Different regional spends that should be combined
Solution:
Use Case 4: Channel with Sub-Channels
Problem: Social media has multiple platforms
Solution:
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:
T-statistic (significance)
Editable "Model Coefficient" field
Step 3: Adjust Weights
Modify "Model Coefficient" column as needed
Enter custom weights based on:
Statistical significance (higher t-stat = more reliable)
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:
Strategy 2: Normalize by Significance (Conservative)
When: Want to weight by statistical confidence How: Use coefficient × (t-stat/2) as weight Example:
Strategy 3: Equal Weights (Simplest)
When: All channels equally important How: Set all weights to 1.0 Example:
Result: Simple sum of all channels
Strategy 4: Business-Driven Weights
When: You have strategic priorities How: Set weights based on business importance Example:
Interpreting Weighted Variables
In Model Results
Model:
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
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'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:
Step 1: Select all four variables
Step 2: Create weighted variable, review OLS results
Step 3: Adjust weights:
Step 4: Name: Digital_Performance
Step 5: Created: Digital_Performance|WGTD
Result in Model:
Benefit: 4 fewer variables, cleaner model, same insights
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!