Conjoint Analysis

Conjoint analysis is the most widely used stated-preference technique in marketing and pricing research. It decomposes a product’s overall value into the contribution of each attribute, enabling firms to estimate willingness to pay for individual features—even for products that do not yet exist.

Introduction

A smartphone priced at $799 bundles together a brand name, a screen size, a battery life, a camera system, and dozens of other attributes. How much of that price does the customer attribute to the brand? How much to the battery? If the firm upgrades the display but raises the price by $100, will customers perceive the tradeoff as favorable?

These questions cannot be answered by observing sales data alone, because products typically vary on multiple dimensions simultaneously. Conjoint analysis provides a structured framework for isolating the value of individual attributes by presenting respondents with carefully designed product profiles and analyzing their choices.

Introduced by Green and Srinivasan (1978), conjoint analysis has become the standard tool for new product pricing, feature prioritization, and competitive positioning. Its theoretical foundations connect directly to the random utility framework of McFadden (1974), while its practical extensions are covered comprehensively in Louviere, Hensher, and Swait (2000).

Part-Worth Utilities

The central idea behind conjoint analysis is that the total utility a consumer derives from a product can be expressed as the sum of the utilities contributed by each attribute level. This additive decomposition allows the analyst to estimate the value of each component separately.

Definition — Part-Worth Utility Model

The utility of product profile $j$ is modeled as an additive function of attribute-level indicator variables:

V_j = \sum_{k=1}^{K} \sum_{\ell=1}^{L_k} \beta_{k\ell} \cdot x_{jk\ell}

(1)

where $K$ is the number of attributes, $L_k$ is the number of levels for attribute $k$ , $\beta_{k\ell}$ is the part-worth of level $\ell$ of attribute $k$ , and $x_{jk\ell} \in \{0, 1\}$ indicates whether profile $j$ has level $\ell$ of attribute $k$ .

Within each attribute, part-worths are typically zero-centered so that they represent deviations from the attribute’s average utility. This convention makes part-worths comparable across attributes: a part-worth of $+1.2$ for “Premium Brand” means that brand contributes 1.2 more utility units than the average brand level.

Smartphone Part-Worths

Consider a smartphone conjoint study with four attributes: Brand (Premium, Mid-tier, Budget), Screen Size (5.5″, 6.1″, 6.7″), Battery Life (8 hr, 12 hr, 16 hr), and Price ($499, $699, $899, $1099). The estimated part-worths might be:

Brand: Premium = +1.2, Mid-tier = +0.3, Budget = −1.5
Battery: 8 hr = −0.8, 12 hr = +0.1, 16 hr = +0.7
Price: $499 = +1.5, $699 = +0.4, $899 = −0.6, $1099 = −1.3

A “Premium Brand, 6.1″, 16 hr, $699” phone has total utility $V = 1.2 + 0.5 + 0.7 + 0.4 = 2.8$ .

The part-worth model is flexible enough to capture nonlinear preferences—for example, the difference in utility between an 8-hour and 12-hour battery need not equal the difference between 12 hours and 16 hours. This flexibility is one reason conjoint analysis remains popular despite the rise of revealed-preference methods (Train (2009)).

Choice-Based Conjoint

Early conjoint studies asked respondents to rank or rate product profiles. Modern practice almost universally uses choice-based conjoint (CBC), in which respondents repeatedly choose their preferred alternative from a set of two or more profiles. This format mirrors actual purchase decisions and connects directly to the econometric framework of discrete choice.

Definition — Choice-Based Conjoint (CBC)

In CBC, each respondent completes $T$ choice tasks. In each task, the respondent selects one profile from a set of $J$ alternatives. The profiles are constructed using an experimental design that ensures sufficient variation across attribute levels. The analyst estimates part-worths $\beta_{k\ell}$ by maximizing the conditional log-likelihood:

\mathcal{L}(\boldsymbol{\beta}) = \sum_{t=1}^{T} \ln P_{j_t^*} = \sum_{t=1}^{T} \ln \frac{\exp(V_{j_t^*})}{\sum_{j=1}^{J} \exp(V_j)}

(2)

where $j_t^*$ is the alternative chosen in task $t$ and $V_j$ is the deterministic utility from Equation (1).

The log-likelihood in Equation (2) is the same objective function used in McFadden’s (1974) conditional logit model. The estimation yields maximum likelihood estimates of the part-worths, which are consistent and asymptotically normal under standard regularity conditions.

Identification in CBC

Part-worths are identified up to a common additive constant within each attribute. To resolve this indeterminacy, one typically normalizes by setting one level per attribute as the reference (with part-worth zero) or by imposing zero-sum constraints: $\sum_{\ell=1}^{L_k} \beta_{k\ell} = 0$ for each attribute $k$ . The overall scale of utility is identified by the normalization of the error variance (fixed at $\pi^2/6$ for the Gumbel distribution).

Attribute Importance

Once part-worths are estimated, a natural question is: which attributes matter most to consumers? The standard measure of attribute importance is based on the range of part-worths within each attribute.

Definition — Attribute Importance

The importance of attribute $k$ is the range of its part-worths divided by the total range across all attributes:

I_k = \frac{\max_\ell \beta_{k\ell} - \min_\ell \beta_{k\ell}}{\sum_{k'=1}^{K}\bigl(\max_\ell \beta_{k'\ell} - \min_\ell \beta_{k'\ell}\bigr)}

(3)

Importances sum to 100% and measure the maximum impact each attribute can have on utility. An attribute with a large range of part-worths can swing a consumer’s preference more than one with a narrow range.

The interactive chart below displays attribute importances for a four-attribute smartphone conjoint study. Adjust the part-worth values using the sliders to see how importance shares shift. Notice that price is often the most important attribute—not because consumers care only about price, but because the range of price levels (from $499 to $1099) creates a wider utility swing than other attributes.

Attribute importance depends on the range of levels included in the study design. If the researcher tests only two similar price levels ($699 and $799), the price attribute will appear less important than if the design includes a wider range. This is a feature, not a bug: importance measures the potential impact of the attribute over the range of levels tested.

One of the most valuable applications of conjoint analysis is predicting how market shares would change if a firm altered its product configuration or pricing. Given a set of competing product profiles, the multinomial logit model translates part-worth utilities into predicted choice probabilities.

Definition — Market Share Simulation

For $J$ competing profiles with utilities $V_1, \ldots, V_J$ , the predicted market share of profile $j$ under the logit model is:

s_j = \frac{\exp(V_j)}{\sum_{k=1}^{J} \exp(V_k)}

(4)

This is the standard softmax function. The model implies that a product with higher total utility captures a larger share, but the relationship is nonlinear: improving a dominant product’s utility has diminishing returns to share, while improving a weak product has accelerating returns.

The chart below shows three product profiles competing in a smartphone market. Select a product to edit its attribute levels and observe how market shares respond. The WTP estimate for each profile is computed by finding the price at which its total utility crosses zero.

Competitive Scenario Analysis

Suppose a firm currently sells the “Mid-range” phone (Mid-tier brand, 6.1″ screen, 12-hour battery, $699). A competitor launches a “Value” phone (Budget brand, 5.5″ screen, 12-hour battery, $499). Using the simulator above, the firm can evaluate counterfactual responses: What happens to its share if it upgrades to a 16-hour battery? What if it drops the price to $499? Conjoint-based simulation provides quantitative answers to these questions without running a market experiment.

From Part-Worths to WTP

The ultimate goal of conjoint analysis in a pricing context is to extract willingness to pay (WTP) for specific product features. If price enters the utility function as a continuous or quasi-continuous variable, the WTP for an attribute upgrade is the ratio of the part-worth difference to the price coefficient.

Definition — WTP from Conjoint Part-Worths

Let $\beta_{\text{price}}$ be the coefficient on price (typically negative, reflecting disutility of higher prices) and let $\Delta \beta_k$ be the part-worth difference associated with an attribute upgrade. The WTP for that upgrade is:

\text{WTP}_k = -\frac{\Delta \beta_k}{\beta_{\text{price}}}

(5)

When price enters as discrete levels (as in the examples above), the price coefficient can be estimated by fitting a linear trend through the price part-worths, or WTP can be computed by interpolation: the price at which the profile’s total utility equals zero (the point of indifference).

This approach assumes that the marginal utility of money is constant across the price range, an approximation that is reasonable for moderate price changes. For larger price ranges, Train (2009) recommends using WTP-space models that directly estimate WTP distributions rather than converting from preference space.

WTP as Price Premium

The WTP for upgrading from attribute level $\ell$ to level $\ell'$ on attribute $k$ represents the maximum price premium the average consumer would accept for that upgrade while remaining indifferent. If the part-worth difference is $\beta_{k\ell'} - \beta_{k\ell} = 0.9$ and the per-dollar utility of price is $\beta_{\text{price}} = -0.003$ , then $\text{WTP} = 0.9 / 0.003 = \$300$ .

Interactive Conjoint Simulator

The simulator below lets you experience a simplified CBC study from the respondent’s perspective. You are presented with eight pairwise comparisons of product profiles that vary in brand, size, and price. After completing all rounds, the simulator estimates part-worth utilities from your choices using a simple counting method and compares them against the true population values.

This exercise illustrates a key insight: even a small number of carefully designed choice tasks can reveal the relative importance of different product attributes. In practice, commercial conjoint studies use 12–20 tasks per respondent with designs optimized for statistical efficiency (Louviere, Hensher, and Swait (2000)).

Observe that the estimated part-worths may deviate substantially from the true values when only eight choice tasks are used. With larger samples (both more respondents and more tasks per respondent), estimates converge to the true values. In commercial applications, conjoint studies typically survey 200–1,000 respondents to achieve stable estimates.

Designing Conjoint Experiments

Conjoint analysis occupies a unique position in the pricing toolkit. When neither randomized price experiments nor observational transaction data are available—for example, when launching an entirely new product—conjoint is often the only source of price sensitivity estimates. Unlike A/B tests, which require real transactions, conjoint elicits preferences from hypothetical choices, making it feasible at the concept stage.

A well-designed conjoint study requires careful attention to several practical considerations:

Number of attributes. Including too many attributes (more than 6–8) overwhelms respondents and increases noise. Focus on attributes that are decision-relevant and vary meaningfully across competing products.
Price levels. The range of test prices must span the plausible market range. Too narrow a range understates price sensitivity; too wide makes some profiles implausible.
Sample size. Commercial studies typically survey 200–1,000 respondents with 12–20 tasks each. Fewer respondents can yield unstable estimates, particularly for interaction effects between attributes.
Hypothetical bias. Respondents may state preferences that differ from their actual purchase behavior. Calibration techniques—such as including a “none” option and benchmarking against known market shares—can mitigate this limitation.

Despite its limitations, conjoint remains the gold standard for new-product pricing because it reveals the value of individual product features, enabling the firm to configure the product (not just the price) for maximum value extraction.

References

Green, P. E. & Srinivasan, V. (1978). “Conjoint Analysis in Consumer Research: Issues and Outlook.” Journal of Consumer Research, 5(2), 103–123.
Louviere, J. J., Hensher, D. A. & Swait, J. D. (2000). Stated Choice Methods: Analysis and Application. Cambridge University Press.
McFadden, D. (1974). Conditional logit analysis of qualitative choice behavior. In Frontiers in Econometrics, 105–142.
Train, K. E. (2009). Discrete Choice Methods with Simulation, 2nd ed.. Cambridge University Press.

What Customers Value Most