WTP space vs preference space estimation

Estimating WTP from the ratio of coefficients produces unreliable confidence intervals. WTP space models estimate WTP directly and give better inference.

This article explains the difference between preference space and WTP space DCE model estimation, the statistical advantages of WTP space, and how to implement it in Apollo.

Ben White, 07.07.2026

The problem with ratio-based WTP estimates

In preference space models (standard MNL or mixed logit), WTP is calculated as the ratio of an attribute coefficient to the cost coefficient. This ratio is well-defined at the point estimate level but has problematic statistical properties - the distribution of the ratio of two normally distributed variables has heavy tails and sometimes undefined moments.

This means confidence intervals for WTP from preference space models may be unreliable, particularly when the cost coefficient estimate has a large standard error. In mixed logit models, combining distributions of the attribute coefficient and the cost coefficient through a ratio is even more complex.

How WTP space models solve the problem

WTP space models reparametrize the utility function to estimate WTP directly rather than as a ratio of other parameters. The utility function is expressed in terms of WTP values rather than preference weights, and the cost coefficient is implicitly normalised to -1.

The advantages are: WTP parameters are directly estimated with standard errors that can be used for inference; the WTP distribution is estimated directly as a distribution rather than derived from a ratio of distributions; and WTP estimates from different models are directly comparable without transformation.

The disadvantage is that WTP space models can be more difficult to specify and interpret, and may have worse convergence properties than preference space models for complex designs. Apollo supports both estimation approaches.

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Implementing WTP space models in Apollo

Step 1: Export your DCE data from SurveyEngine in the standard format. WTP space models use the same data as preference space models.

Step 2: Reparametrize the utility function. In preference space, utility = beta_time × time + beta_cost × cost. In WTP space, utility = lambda × (WTP_time × time - cost) where lambda is the cost coefficient (estimated as a positive scale parameter) and WTP_time is the WTP directly.

Step 3: Specify distributions for WTP parameters. In a mixed logit WTP space model, each WTP parameter has a specified distribution. Normal distributions are typical for continuous WTP parameters; lognormal for parameters that should always be positive.

Step 4: Estimate and compare with preference space. Estimate both preference space and WTP space models and compare WTP estimates and confidence intervals. If they agree, the choice of specification is unimportant. If they disagree, investigate whether the preference space confidence intervals are reliable.

Step 5: Report WTP space results for regulatory submissions. For FDA patient preference submissions and NICE submissions, WTP space estimates with proper confidence intervals are preferred over ratio-based estimates from preference space models.

Worked example - comparing preference and WTP space

A health preference DCE is estimated in both preference space and WTP space. In preference space, WTP for a 10% reduction in nausea probability is €82/month with a 95% CI of €54–€147 (derived using the delta method). In WTP space, the same WTP parameter has point estimate €79/month with CI of €61–€97.

The WTP space CI is narrower and more symmetric. The preference space CI is wider because it propagates uncertainty in both the nausea and cost coefficients through the ratio calculation. For the regulatory submission, the WTP space estimates are reported as primary.