Algo Price Conjoint

Conjoint Analysis

Overview

Conjoint analysis estimates the relative value consumers place on product attributes by analyzing their choices among hypothetical product profiles. Choice-Based Conjoint (CBC) is the most common variant. Produces part-worth utilities per attribute level and derived willingness-to-pay estimates.

When to Use

Trigger conditions:

• Determining which features drive purchase decisions and how much they're worth
• Estimating willingness to pay for specific product features
• Optimizing product configuration for a target segment

When NOT to use:

• When you only need an acceptable price range (use Van Westendorp — simpler)
• When attributes can't be varied independently (natural constraints)

Algorithm

IRON LAW: Conjoint Results Are Valid ONLY for Tested Attribute Levels
Extrapolating beyond tested ranges is unreliable. If you tested
prices $10-$50, you cannot predict preference at $100. The utility
function is only defined within the experimental design space.

Phase 1: Input Validation

Define: attributes (3-7), levels per attribute (2-5 each), design type (full factorial if small, fractional/D-optimal if large). Survey 200+ respondents minimum.

Gate: Attributes independent, levels realistic, sample size sufficient.

Phase 2: Core Algorithm

• Generate choice sets using experimental design (D-optimal or balanced overlap)
• Present respondents with sets of 3-4 product profiles, ask to choose preferred
• Estimate part-worth utilities using multinomial logit (MNL) or hierarchical Bayes (HB)
• Compute: attribute importance = range of part-worths within attribute / sum of all ranges
• Derive WTP: utility-to-price conversion using the price attribute coefficient

Phase 3: Verification

Check: holdout task prediction accuracy (hit rate > 60%), signs of part-worths are logical (higher price → lower utility).

Gate: Holdout hit rate acceptable, utilities directionally correct.

Phase 4: Output

Return part-worth utilities, attribute importance, and WTP estimates.

Output Format

{
  "attribute_importance": [{"attribute": "price", "importance_pct": 35}, {"attribute": "brand", "importance_pct": 28}],
  "part_worths": {"price": {"$10": 2.1, "$30": 0.5, "$50": -1.8}},
  "wtp": {"feature_x": 12.50, "brand_premium": 8.00},
  "metadata": {"respondents": 300, "model": "hierarchical_bayes", "holdout_hit_rate": 0.72}
}

Examples

Sample I/O

Input: Laptop with attributes: Brand(Apple/Dell/Lenovo), RAM(8/16/32GB), Price($800/$1200/$1600)

Expected: Apple has highest brand utility, 32GB RAM preferred, price negative utility. WTP for Apple brand premium ≈ $200.

Edge Cases

| Input | Expected | Why |

|-------|----------|-----|

| All attributes equally important | No clear driver | Product is commodity-like |

| Price dominates (>60%) | Highly price-sensitive market | Features don't differentiate enough |

| One level never chosen | Extreme negative utility | That level is a deal-breaker |

Gotchas

• Hypothetical bias: Respondents making hypothetical choices may not reflect real purchase behavior. Incentive-compatible designs (real choices) are better but expensive.
• Number of attributes: More than 6-7 attributes overwhelms respondents, leading to simplification strategies (ignore some attributes). Keep designs manageable.
• Interaction effects: Standard analysis assumes attributes are independent. If brand affects price sensitivity (brand×price interaction), you need interaction terms.
• Segment heterogeneity: Average part-worths mask segments with opposite preferences. Use latent class or HB models to uncover segments.
• Design efficiency: Poor experimental designs (unbalanced, correlated attributes) produce imprecise estimates. Use proper design software.

References

• For experimental design generation, see references/experimental-design.md
• For hierarchical Bayes estimation, see references/hb-estimation.md