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title: "Choice-Level Analysis"
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  Why choice-level analysis offers deeper insights compared to standard profile-level analysis.
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  %\VignetteIndexEntry{Choice-Level Analysis}
  %\VignetteEngine{knitr::rmarkdown}
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## **Why Choice-Level Analysis?**

💡 **Choice-level analysis is simpler, easier, and more powerful than profile-level analysis.**

- 🧠 Conjoint designs began in market research and psychology, where respondents **rated** two profiles (e.g., products). Each rating was treated as an **independent observation**, creating the **profile-level design** with `2 × n` rows for `n` respondents. 
- 🔍 Social scientists later used conjoint designs for **choices** instead of ratings but kept the same structure with a **single binary outcome**. This shift introduced **statistical and conceptual issues**.

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### ⚠️ **Problems with Profile-Level Analysis**

🚫 Profile-level analysis forces researchers to correct a dependence that they created themselves.

- 🔁 **Redundant structure:** Each choice task generates **two rows** per task for each respondent even though there is only **one independent choice**.  
- 🔗 **Mechanical dependence:** Selecting one profile **necessarily implies rejecting the other**, violating the independence assumption.  
- 🧩 **Artificial complexity:** Analysts must correct for this dependence using **complicated statistical adjustments**, even though it arises solely from how the data were organized—not from respondents’ behavior.


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### ✅ **Advantages of Choice-Level Analysis**

In contrast, **choice-level analysis** organizes data by respondent *decisions* rather than profiles.

- 📋 Each unit of observation represents **a choice** for a given task per respondent.  
- ⚡ The outcome variable reflects **which profile was chosen** in that task.  
- 🧠 This data structure allows researchers to model the choice **conditional on the full comparison**.

🎯 **Choice-level analysis** directly models the respondent’s decision between two (or more) alternatives,  
capturing the true structure of the conjoint task.

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## **Key Issues and Applications**

- Profile-level estimands like **AMCEs** assume that each profile is generated independently and ignores how respondents evaluate one profile *relative* to another.  This limits the types of questions researchers can ask.

- Choice-level analysis allows researchers to explore questions that **explicitly depend on the comparison between profiles**, such as:

<details>
<summary><strong>Examples of Choice-Level Research Questions</strong></summary>

- 🗳️ Do voters choose a **white** candidate over a **non-white** candidate?  
  (The levels—white vs. Asian, Black, Hispanic—always differ between profiles.)

- 🌐 Do **Asian Democrat respondents** prefer an **Asian Republican** over a **white Democrat**?  
  (Profiles are intentionally designed with multiple correlated attributes.)

- 📊 Do voters care about **electability**?  
  (The two percentages representing win probability must sum to 100.)

- ⚖️ Do voters prefer the **status quo** over a **policy proposal**?  
  (One profile is fixed while the other varies across tasks.)

- 🧭 How much do voters prefer **extreme left-leaning** or **extreme right-leaning** policies?  
  (Attributes are consistently positioned on the ideological spectrum.)

</details>

Furthermore, when individuals compare profiles side-by-side, their evaluations are often **psychologically influenced by the alternative**, such as through **assimilation or contrast effects**  
(see *Horiuchi and Johnson 2025*).

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## **Why Move to Choice-Level Analysis?**

🔍 **Choice-level analysis models the decision *between* two profiles, not the evaluation of a single profile.**

This structure more closely mirrors:

- 🧠 **Real-world decision-making**, where people choose among competing alternatives.  
- 🔄 **Comparative cognition**, where evaluations depend on the context of available options.  
- 🎛️ **Tradeoff reasoning**, where respondents weigh attribute combinations jointly.

Hence, rather than estimating the probability of selecting an isolated profile, choice-level analysis estimates the **probability of choosing one profile over another**, conditional on all attributes involved.

✅ Mirrors real-world behavior  
✅ Captures comparative judgment and psychological context  
✅ Reveals authentic tradeoffs and priorities  

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## **Summary**

| Profile-Level Analysis | Choice-Level Analysis |
|:-----------------------|:----------------------|
| Treats profiles as independent | Models the decision *between* profiles |
| Ignores comparative context | Captures mutual influence of options |
| May blur or bias tradeoffs | Highlights actual tradeoffs |
| Can misstate uncertainty | Produces more interpretable estimates |
| Requires complex correction methods | Works with simple and transparent models |

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## **Key Takeaway**

🚀 If your conjoint design presents respondents with **two or more profiles for comparison**,  
then **choice-level analysis is essential for valid, interpretable, and psychologically realistic inference**.

It provides:

- **Deeper insights into human decision-making**  
- **Cleaner estimation procedures**  
- **Closer correspondence to real-world behavior**

---

## 📚 **References**

- **Clayton, Horiuchi, Kaufman, King, & Komisarchik (Forthcoming).**  
  *Correcting Measurement Error Bias in Conjoint Survey Experiments.*  
  _Forthcoming, American Journal of Political Science._  
  [Preprint available](https://gking.harvard.edu/conjointE)

- **Horiuchi & Johnson (2025).**  
  *Advancing Conjoint Analysis: Delving Further into Profile Comparisons.*  
  _Work in progress._