Creating Curve Variables

How to Generate and Use Saturation-Transformed Variables

Overview

Creating curve variables transforms your original marketing spend data using saturation curves, generating new variables that capture diminishing returns and threshold effects. These transformed variables replace or supplement original variables in your models.

Two Methods for Creating Curves

Method 1: Via Curve Testing Interface

Path: Variable Workshop → Curve Testing

Process:

1. Test multiple curve configurations

2. Review statistical results

3. Select winning curves

4. Click "Add to Model" or "Create Variables"

5. Variables automatically created and added to model

Advantages:

• Data-driven selection based on statistical fit

• See all options before committing

• Visual comparison of curve shapes

• Automatically finds optimal parameters

Method 2: Manual Creation

Path: Variable Workshop → Create Curve Variables

Process:

1. Manually specify curve parameters

2. Choose specific Alpha and Power values

3. Create curve without testing

Use when:

• You already know optimal parameters

• Replicating curves from previous models

• Following established guidelines for a channel

Creating Curves from Test Results

Step 1: Run Curve Tests

1. Navigate to Curve Testing

2. Select model to test against

3. Choose formula (ATAN recommended)

4. Select curve type (ICP or ADBUG)

5. Select variable to transform

6. Click "Test Curves"

Step 2: Review Results

Results table shows all tested combinations with:

• R² Increase: How much curve improves model fit

• P-Value: Statistical significance

• Coefficient: Regression coefficient value

• Alpha & Power: Parameter values tested

Sort by R² Increase to see best-fitting curves first

Step 3: Visualize Top Candidates

1. Select curves to compare (checkboxes)

2. Click "Generate Chart"

3. Review curve shapes visually

4. Verify shapes align with business expectations

What to verify:

• Saturation level makes sense for channel

• Inflection point aligns with spend levels

• No unexpected curve behavior

Step 4: Select Winners

Selection Criteria:

✅ Statistical Fit:

• High R² increase (> 0.01 meaningful)

• P-value < 0.05 (preferably < 0.01)

• Positive coefficient (more spend → more sales)

✅ Business Logic:

• Parameters align with channel behavior

• Curve shape matches expectations

• Saturation point is reasonable

Checkbox Selection:

• Select 1-3 top candidates per variable

• Can create multiple curve versions for comparison

Step 5: Add to Model

1. Click "Add to Model" or "Create Variables" button

2. Confirmation message shows variables created

3. Variables now available in Model Builder

What happens:

• New columns added to your dataset

• Variables registered in data loader

• Transformation parameters stored for Excel export

• Variables appear in Model Builder variable list

Variable Naming Convention

ATAN Curve Variables

Format: OriginalVariable|CurveType_ATAN aX.X_powerY.Y

Components:

• Base variable: Your original variable name

• Pipe separator: | divides base from transformation

• Curve type: ICP (S-shape) or ADBUG (concave)

• Formula: ATAN

• Alpha value: a + value (e.g., a0.5)

• Power value: power + value (e.g., power1.8)

Examples:

• TV_Spend|ICP_ATAN a0.5_power1.8

• Search_Spend|ADBUG_ATAN a0.3_power1.0

• Display_Impressions|ICP_ATAN a0.7_power2.0

Combined with Adstock

If your original variable already has adstock:

Format: OriginalVariable_adstock_XX|CurveType_ATAN aX.X_powerY.Y

Example: TV_Spend_adstock_70|ICP_ATAN a0.6_power1.9

Transformation order:

1. Original variable

2. Adstock applied (carryover effects)

3. Curve applied (saturation effects)

This is the correct order - always apply adstock first, then saturation.

Using Curve Variables in Models

Adding to Model Builder

1. Navigate to Model Builder

2. Select your model

3. Open variable selection interface

4. Find your curve variable (search or scroll)

5. Click to add to model

Replacing vs. Supplementing Original Variables

Option 1: Replace (Recommended)

Remove original variable, add curve version:

• TV_Spend → removed

• TV_Spend|ICP_ATAN a0.6_power1.8 → added

Advantage: Avoids multicollinearity (original and curved are highly correlated)

Option 2: Keep Both

Include both original and curved:

• TV_Spend → kept

• TV_Spend|ICP_ATAN a0.6_power1.8 → added

Risk: Multicollinearity issues (high VIF), coefficient instability

Best Practice: Replace original with curve version in final models

Running Models with Curves

After adding curve variables:

1. Remove original variable (if kept)

2. Run regression (OLS or Bayesian)

3. Check diagnostics:

   • VIF < 10 for all variables

   • Residuals normally distributed

   • No autocorrelation

4. Review coefficients:

   • Positive sign for media variables

   • Statistically significant (p < 0.05)

   • Magnitude makes business sense

Creating Multiple Curve Versions

Why Create Multiple Versions?

Testing alternative specifications:

• Compare ICP vs. ADBUG for same variable

• Test different alpha values

• Evaluate sensitivity to power parameter

Model comparison:

• Build Model A with ICP curves

• Build Model B with ADBUG curves

• Compare overall model performance

Managing Multiple Curves

Naming helps differentiate:

• TV_Spend|ICP_ATAN a0.6_power1.8

• TV_Spend|ICP_ATAN a0.7_power1.9

• TV_Spend|ADBUG_ATAN a0.4_power1.0

Best Practice: Only keep 1-2 versions per variable in final model to avoid clutter

Curve Variables in Excel Export

When you export models to Excel, curve transformations are included in the "All Transformations" sheet:

Information stored:

• Original variable name

• Curve type (ICP/ADBUG)

• Formula (ATAN)

• Alpha parameter

• Power parameter

• Adstock rate (if applicable)

Reimport capability: When you reimport the Excel file, MixModeler automatically recreates all curve variables with exact parameters.

Common Workflows

Workflow 1: Single Variable Optimization

1. Test curves for one variable (e.g., TV_Spend)

2. Select best curve based on R² and business logic

3. Create variable

4. Add to model, remove original

5. Run model and validate

Workflow 2: Full Media Mix Saturation

1. List all media variables

2. Test curves for each individually:

   • TV_Spend → ICP curve

   • Digital_Spend → ADBUG curve

   • Radio_Spend → ICP curve

3. Create all winning curves

4. Build comprehensive model with all curves

5. Run diagnostics and validate

Workflow 3: Adstock + Curve Combination

For media with carryover effects:

1. First: Create adstock variable TV_Spend → TV_Spend_adstock_70

2. Then: Test curves on adstock variable Test TV_Spend_adstock_70

3. Create curve: TV_Spend_adstock_70|ICP_ATAN a0.6_power1.8

4. Use in model: Final variable captures both carryover AND saturation

Important: Always adstock first, then curve. Never curve first, then adstock.

Best Practices

Parameter Selection

Don't guess - test systematically:

• Use Curve Testing interface to find optimal parameters

• Review statistical metrics (R², p-value)

• Validate with business logic

• Visualize curve shapes before creating

Variable Management

Keep it organized:

• Use consistent naming conventions

• Document which curves you selected and why

• Delete experimental curves you don't use

• Keep 1-2 final versions per variable maximum

Model Integration

Replace, don't supplement:

• Remove original variable when adding curve version

• Avoid including both in same model (multicollinearity)

• Check VIF after adding curves

Quality Checks

After creating curves:

• Verify variable appears in Model Builder

• Check transformation is stored in data loader

• Confirm parameters match what you selected

• Test in a model to ensure it works

Troubleshooting

Curve Variable Not Appearing in Model Builder

Possible causes:

• Variable creation failed silently

• Model cache not refreshed

• Data loader not updated

Solutions:

• Refresh browser page

• Re-select model in Model Builder

• Recreate variable through Curve Testing

Multicollinearity Issues After Adding Curves

Symptoms:

• VIF > 10 for curve variables

• Unstable coefficients

• Large standard errors

Solutions:

• Remove original variable (keep only curve version)

• Check if multiple curve versions of same variable are included

• Review for other correlated variables

Negative Coefficients on Curve Variables

Possible causes:

• Wrong curve type selected (ICP vs. ADBUG)

• Multicollinearity with other variables

• Variable doesn't have saturation pattern

Solutions:

• Try opposite curve type

• Remove correlated variables

• Consider if curve is appropriate for this variable

Curve Doesn't Improve Model Fit

Possible causes:

• Variable has linear relationship (no saturation)

• Variable is control factor, not marketing spend

• Insufficient data variation

Solutions:

• Check if saturation is expected for this channel

• Review variable min/max/variance statistics

• Consider keeping original variable without curve

Advanced: Manual Curve Creation

For advanced users who want to specify exact parameters without testing:

When to Use Manual Creation

• Replicating curves from previous models

• Applying standard parameters for a channel type

• Creating curves based on external research

• Batch creating similar curves for multiple variables

Process

1. Navigate to Variable Workshop

2. Select manual curve creation option

3. Choose base variable

4. Select formula (ATAN)

5. Select curve type (ICP or ADBUG)

6. Enter specific Alpha value (e.g., 0.6)

7. Enter specific Power value (e.g., 1.8)

8. Click "Create"

Caution: Manual creation bypasses statistical validation. Only use if you're confident in parameter choices.

Curve Variables in Bayesian Models

Curve variables work identically in Bayesian models:

Priors: You'll set priors on the curve variable coefficient (not the original)

Example:

Sales ~ Normal(μ, σ)
μ = β₀ + β₁ × TV_Spend|ICP_ATAN_a0.6_power1.8 + ...
β₁ ~ Normal(500, 200)  # Prior on curve coefficient

Interpretation: The prior is on the effect per unit of transformed (saturated) spend, not raw spend.

Model Comparison with Curves

Comparing Models With vs. Without Curves

Model A (No curves):

• Variables: TV_Spend, Digital_Spend, Radio_Spend

• R²: 0.75

• Assumption: Linear relationships (constant ROI)

Model B (With curves):

• Variables: TV_Spend|ICP_ATAN, Digital_Spend|ADBUG_ATAN, Radio_Spend|ICP_ATAN

• R²: 0.82

• Assumption: Saturating relationships (diminishing ROI)

Comparison:

• R² improvement: 0.07 (significant)

• Model B captures realistic saturation

• Model B enables optimization (know where to cut/invest)

Best Practice: Always compare curved vs. non-curved models to quantify improvement.

Key Takeaways

• Create curve variables via Curve Testing for data-driven selection

• Use ATAN formula (2 parameters) for most channels

• Variable naming follows pattern: Variable|Type_ATAN aX.X_powerY.Y

• Replace original variables with curve versions in models

• Combine with adstock: adstock first, then curve

• Verify curves improve model fit and make business sense

• Keep variable library organized (delete experimental versions)

• Curves enable optimization by capturing varying ROI at different spend levels