OLS vs Bayesian Decomposition
Overview
MixModeler supports two decomposition types based on your model's estimation method: OLS (Ordinary Least Squares) and Bayesian. Both produce the same chart format but use different coefficient estimates.
Purpose: Choose the appropriate decomposition method based on your model type and analytical needs.
Key Differences
Uses
Point estimates from OLS regression
Posterior means from MCMC samples
Coefficients
Single deterministic value
Average of posterior distribution
Uncertainty
Standard errors
Credible intervals (not shown in chart)
Calculation
Instant
Based on MCMC samples
Priors
None
Can incorporate prior information
Both produce identical chart formats - the difference is which coefficients are used to calculate contributions.
How Each Works
OLS Decomposition
Calculation:
Contribution = β_OLS × Variable Value
Where β_OLS is the coefficient from OLS regressionExample:
TV coefficient from OLS: 2.5
TV spend in Week 1: $10,000
TV contribution: 2.5 × $10,000 = $25,000
Characteristics:
Single point estimate
Deterministic result
Fast calculation
Standard approach
Bayesian Decomposition
Calculation:
Contribution = E[β|Data] × Variable Value
Where E[β|Data] is the posterior mean from Bayesian inferenceExample:
TV posterior mean: 2.3 (average of MCMC samples)
TV spend in Week 1: $10,000
TV contribution: 2.3 × $10,000 = $23,000
Characteristics:
Posterior mean estimate
Based on probability distribution
Incorporates uncertainty
Can use prior information
When to Use OLS Decomposition
Default Choice:
Standard MMM analysis
Most common approach
Well-understood methodology
Best When:
Sufficient data (50+ observations)
Clear relationships in data
No strong prior information
Speed matters
Stakeholders prefer simplicity
Advantages:
Fast and straightforward
Easy to explain
Widely accepted
No need to explain priors
When to Use Bayesian Decomposition
Special Situations:
Limited data available
High noise in data
Want to incorporate prior knowledge
Need uncertainty quantification
Best When:
Sample size is small
Weak signals in data
Have industry benchmarks to use as priors
Hierarchical or regional models
Conservative estimates preferred
Advantages:
Handles small samples better
Can use prior information
Provides uncertainty measures
More stable with limited data
Selecting Decomposition Type
In Decomposition Page:
Toggle Between:
OLS Mode (📊 icon)
Bayesian Mode (🎯 icon)
Indicator Shows:
Current selection
Icon and label
Model type compatibility
Prerequisites:
OLS: Model must be fitted with OLS
Bayesian: Bayesian inference must be run
Comparing Results
Run Both to Compare:
Fit model with both OLS and Bayesian
Run OLS decomposition
Run Bayesian decomposition
Compare contributions
What to Check:
Similar Results (Expected):
With non-informative priors, results should be close
Validates model robustness
Proceed with confidence
Different Results:
Check why (priors, data, model)
Understand which is more appropriate
Consider reporting both
Interpreting Differences
Small Differences (<10%):
Normal variation
Both methods agree
Use either method
Moderate Differences (10-30%):
Priors may be influencing Bayesian
Check if priors are appropriate
Consider reporting range
Large Differences (>30%):
Investigate model specification
Review prior settings
Check data quality
May indicate instability
Impact on Business Decisions
Decision Alignment:
Do both methods rank channels the same?
Would recommendations change?
Which is more credible for your situation?
If Decisions Differ:
Bayesian often more conservative
OLS may show extreme values
Consider business context
Use sensitivity analysis
If Decisions Align:
Robust findings
High confidence
Proceed with either
Technical Notes
Contribution Calculation:
OLS:
For each time period:
Group Contribution = Σ (β_OLS_i × X_i)
Where i = variables in the groupBayesian:
For each time period:
Group Contribution = Σ (E[β_i|Data] × X_i)
Where i = variables in the groupBoth Sum to Predicted:
Total contributions = Predicted KPI
Maintains consistency
Validates calculations
Reporting Considerations
For OLS:
"Decomposition based on OLS regression"
"Point estimate contributions"
Standard and straightforward
For Bayesian:
"Decomposition using Bayesian posterior means"
"Incorporating prior information" (if used)
"Conservative estimates"
Presenting Both:
"Range of estimates"
"Sensitivity analysis"
"OLS and Bayesian comparison"
Common Questions
Q: Which is more accurate?
A: Neither is universally more accurate. OLS is unbiased with sufficient data. Bayesian can be better with limited data or when priors are informative.
Q: Do I need to run both?
A: No. Choose based on your model type. Running both is optional for validation.
Q: Can results be very different?
A: With good data and non-informative priors, results are usually similar. Large differences suggest checking model specification.
Q: Which should I present to stakeholders?
A: OLS is typically simpler to explain. Use Bayesian if you need to explain uncertainty or used strong priors.
Q: Does one give better ROI estimates?
A: ROI calculation is the same (contribution/spend). The contribution values may differ slightly, affecting ROI slightly.
Best Practices
Start with OLS:
Default choice
Establish baseline
Build understanding
Add Bayesian If:
OLS results seem unstable
Want uncertainty quantification
Have reliable priors
Data is limited
Document Choice:
State which method used
Explain why
Note any differences if both run
Validate:
Check if results make business sense
Compare to known campaign effects
Verify against other data sources
Summary
Choose Based On:
Use OLS When:
Standard analysis
Sufficient data
No strong priors
Stakeholder preference
Use Bayesian When:
Limited data
Informative priors available
Uncertainty matters
Hierarchical models
Both Are Valid:
Neither is "better" universally
Context determines appropriateness
Results often similar with good data
Use what fits your situation best
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