Multicollinearity (VIF)

What Multicollinearity Tests Check

Multicollinearity tests detect when predictor variables in your model are highly correlated with each other. While multicollinearity doesn't bias coefficient estimates, it inflates standard errors and makes individual coefficients unstable and difficult to interpret.

Purpose: Checks if predictor variables are highly correlated, ensuring coefficient estimates are stable and interpretable.

Why Low Multicollinearity Matters

When predictor variables are not highly correlated:

Coefficients are Stable: Small changes in data don't cause large changes in coefficients

Interpretation is Clear: Each variable's effect can be isolated and understood

Standard Errors are Smaller: More precise estimates and narrower confidence intervals

Statistical Power is Higher: Easier to detect truly significant relationships

High multicollinearity makes it difficult to determine which variables are actually driving the outcome and can lead to counterintuitive or unstable coefficient estimates.

Variance Inflation Factor (VIF)

VIF is the primary metric for measuring multicollinearity:

Formula: VIF = 1 / (1 - R²ᵢ), where R²ᵢ is the R-squared from regressing variable i against all other predictors

Interpretation: VIF measures how much the variance of a coefficient is inflated due to correlation with other predictors

VIF Interpretation Guidelines

VIF Range

Severity

Interpretation

Action

1 - 5

None to Low

No multicollinearity issues

✓ No action needed

5 - 10

Moderate

Some multicollinearity present

Monitor and investigate

> 10

Severe

Serious multicollinearity problem

Take corrective action

Tolerance: The inverse of VIF (1/VIF). Values < 0.1 indicate severe multicollinearity.

Conservative threshold: Some analysts use VIF > 5 as the cutoff for concern

Liberal threshold: VIF > 10 is widely accepted as indicating severe problems

Common Sources in MMM

Marketing Mix Models are particularly prone to multicollinearity:

Correlated Media Channels:

TV and Display often run in parallel
Digital channels coordinated in campaigns
Seasonal promotional calendars align

Time Trends:

Multiple variables growing over time
Seasonal patterns across channels
Economic indicators correlated with marketing

Created Variables:

Adstocked variables correlated with raw spend
Lagged variables correlated with current values
Interaction terms correlated with main effects

Interpreting Test Results

Passed Tests (✓)

What it means: All VIF < 5 (or < 10 depending on threshold)

Implications:

Variables are sufficiently independent
Each coefficient represents a unique contribution
Standard errors are not inflated
Model is stable and interpretable

Action: No action needed - multicollinearity is not a concern

Failed Tests (⚠)

What it means: One or more variables have high VIF (> 10)

Implications:

Affected coefficients have large standard errors
Small data changes cause large coefficient changes
Individual variable effects cannot be isolated
Confidence intervals are very wide

Symptoms:

Coefficients with unexpected signs (negative when should be positive)
Large coefficient swings when adding/removing variables
High R² but few significant coefficients
Coefficients change dramatically with small data changes

What to Do When Tests Fail

If multicollinearity is detected, try these solutions:

1. Remove Highly Correlated Variables (Most Direct)

Identify variables with VIF > 10
Remove one from each pair of highly correlated variables
Keep the variable more theoretically important or easier to measure
Use business logic to decide which to retain

2. Combine Correlated Variables

Create composite indices or aggregate variables
Example: Combine all digital channels into "Digital_Total"
Example: Combine search and social into "Performance_Media"
Sum or average correlated channels

3. Use Principal Component Analysis (PCA)

Create uncorrelated components from correlated variables
First few components explain most variance
Lose interpretability but gain stability

4. Collect More Data

Longer time series can help distinguish effects
More variation in independent variables reduces correlation
Additional observations improve precision

5. Accept Multicollinearity

If focus is on overall model fit rather than individual coefficients
When prediction is the goal (coefficients remain unbiased)
For variables you must keep for business reasons
When VIF is moderate (5-10) rather than severe (>10)

6. Use Regularization Techniques

Ridge regression penalizes large coefficients
Lasso regression performs variable selection
Elastic net combines ridge and lasso
Bayesian methods with informative priors

Practical Guidelines

When to Act:

VIF > 10 (severe multicollinearity)
Coefficients have wrong signs
Model is unstable across specifications
Need to interpret individual coefficients

When Multicollinearity May Be Acceptable:

VIF between 5-10 (moderate multicollinearity)
Primary goal is prediction, not interpretation
All variables are theoretically necessary
Coefficients have expected signs and reasonable magnitudes
Using model for overall attribution, not optimization

Marketing Mix Modeling Considerations:

Total marketing contribution may still be accurate
Overall model fit (R²) not affected
Channel-level ROI calculations become unreliable
Budget optimization requires stable coefficients

Visual Diagnostics

MixModeler provides a correlation matrix showing pairwise correlations between predictors:

Color Coding:

Dark blue: Strong positive correlation (>0.8)
Light blue: Moderate positive correlation (0.5-0.8)
White: Low correlation (-0.5 to 0.5)
Red: Negative correlation

Warning Signs:

Correlations > |0.8| between predictors
Clusters of highly correlated variables
Correlation > 0.9 indicates near-perfect collinearity

Example Interpretation

Scenario 1 - Passed:

All VIF < 3
Highest correlation: 0.62 (TV and Radio)
All coefficients have expected signs

Interpretation: No multicollinearity issues. Each variable's effect can be reliably isolated and interpreted independently.

Scenario 2 - Moderate Multicollinearity:

TV VIF: 6.2
Display VIF: 6.8
Correlation between TV and Display: 0.85

Interpretation: Moderate multicollinearity between TV and Display. Coefficients may be less stable. Consider combining into "Brand_Media" or removing one channel. If both are needed for business reasons, acknowledge limitation when interpreting individual effects.

Scenario 3 - Severe Multicollinearity:

Search VIF: 15.3
Social VIF: 14.7
Correlation: 0.92
Search coefficient is negative (unexpected)

Interpretation: Severe multicollinearity. Search and Social run in tandem, making it impossible to separate their effects. Negative coefficient is likely spurious. Combine into "Digital_Performance" or remove one variable before using model.

Common Mistakes to Avoid

Removing all variables with high VIF:

Only remove one from each correlated pair
Recalculate VIF after each removal
VIF values change when variables are removed

Ignoring business context:

Don't blindly remove variables based on VIF alone
Consider theoretical importance
Maintain necessary control variables

Confusing correlation with causation:

High VIF doesn't mean variables cause each other
It just means they move together in your data

Marketing Mix Modeling Context

Multicollinearity is especially common in MMM because:

Campaign Coordination: Marketing channels often activate together during campaigns

Budget Constraints: When one channel increases, others may increase proportionally

Seasonality: Most channels peak during the same seasons (holidays, summer)

Media Planning: Strategic alignment of channels (TV drives digital search)

Strategies to Reduce Multicollinearity in MMM:

Use longer time series with more varied spend patterns
Include periods with different channel mixes
Test channels independently when possible
Use aggregated channel groups for strategic decisions
Accept moderate multicollinearity for tactical insights

VIF Table Format

MixModeler displays VIF results in an organized table:

Variable

VIF

Tolerance (1/VIF)

Interpretation

TV_Spend

2.3

0.43

Low

Digital_Spend

8.7

0.11

Moderate

Search_Spend

12.4

0.08