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Conjoint Analysis

联合分析（Conjoint Analysis）

Overview

概述

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.
联合分析通过分析消费者在假设产品配置中的选择，估算他们对产品属性的相对价值。基于选择的联合分析（Choice-Based Conjoint, CBC）是最常见的变体。该分析会生成每个属性层级的部分效用值，以及推导得出的支付意愿估算结果。

When to Use

使用场景

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)
触发条件：
  • 确定哪些功能驱动购买决策及其价值
  • 估算特定产品功能的支付意愿
  • 针对目标客群优化产品配置
不适用场景：
  • 仅需确定可接受价格范围时（使用Van Westendorp模型——更简单）
  • 属性无法独立变化时（存在天然约束）

Algorithm

算法

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.
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

阶段1：输入验证

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.
定义：属性（3-7个）、每个属性的层级（2-5个）、设计类型（规模较小时用全因子设计，规模较大时用部分因子/D-最优设计）。至少调研200名受访者。 准入条件： 属性相互独立、层级符合实际、样本量充足。

Phase 2: Core Algorithm

阶段2：核心算法

  1. Generate choice sets using experimental design (D-optimal or balanced overlap)
  2. Present respondents with sets of 3-4 product profiles, ask to choose preferred
  3. Estimate part-worth utilities using multinomial logit (MNL) or hierarchical Bayes (HB)
  4. Compute: attribute importance = range of part-worths within attribute / sum of all ranges
  5. Derive WTP: utility-to-price conversion using the price attribute coefficient
  1. 使用实验设计（D-最优或平衡重叠设计）生成选择集
  2. 向受访者展示3-4个产品配置的组合，要求选择偏好的配置
  3. 使用多项Logit模型（multinomial logit, MNL）或分层贝叶斯模型（hierarchical Bayes, HB）估算部分效用值
  4. 计算：属性重要性 = 属性内部分效用值的范围 / 所有属性范围之和
  5. 推导支付意愿（WTP）：利用价格属性系数进行效用-价格转换

Phase 3: Verification

阶段3：验证

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.
检查：留存任务预测准确率（命中率>60%）、部分效用值的符号是否符合逻辑（价格越高→效用越低）。 准入条件： 留存命中率可接受、效用值方向正确。

Phase 4: Output

阶段4：输出

Return part-worth utilities, attribute importance, and WTP estimates.
返回部分效用值、属性重要性和支付意愿估算结果。

Output Format

输出格式

json
{
  "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}
}
json
{
  "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

示例

Sample I/O

输入输出样例

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.
输入： 笔记本电脑，属性包括：品牌（Apple/Dell/Lenovo）、内存（8/16/32GB）、价格（$800/$1200/$1600） 预期结果： Apple品牌效用最高，32GB内存更受偏好，价格效用为负。Apple品牌溢价的支付意愿约为$200。

Edge Cases

边缘情况

InputExpectedWhy
All attributes equally importantNo clear driverProduct is commodity-like
Price dominates (>60%)Highly price-sensitive marketFeatures don't differentiate enough
One level never chosenExtreme negative utilityThat level is a deal-breaker
输入预期结果原因
所有属性重要性相同无明确驱动因素产品类似大宗商品
价格占主导（>60%）市场对价格高度敏感功能差异化不足
某个层级从未被选择效用极低该层级是决策否决项

Gotchas

注意事项

  • 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.
  • 假设偏差：受访者在假设场景下的选择可能无法反映真实购买行为。采用激励兼容设计（真实选择）效果更好，但成本较高。
  • 属性数量：超过6-7个属性会让受访者不堪重负，导致他们采用简化策略（忽略部分属性）。需保持设计简洁可控。
  • 交互效应：标准分析假设属性相互独立。如果品牌会影响价格敏感度（品牌×价格交互），则需要加入交互项。
  • 客群异质性：平均部分效用值会掩盖偏好相反的客群细分。使用潜在类别模型或HB模型来挖掘细分客群。
  • 设计效率：糟糕的实验设计（不平衡、属性相关）会产生不精确的估算结果。需使用专业的设计软件。

References

参考资料

  • For experimental design generation, see 
    references/experimental-design.md
  • For hierarchical Bayes estimation, see 
    references/hb-estimation.md
  • 实验设计生成相关内容，请查看
    references/experimental-design.md
  • 分层贝叶斯估算相关内容，请查看
    references/hb-estimation.md