Mixed logit - accounting for preference heterogeneity

The MNL model assumes everyone values attributes the same way. Mixed logit relaxes this assumption - and typically produces much more realistic and insightful results.

This article explains mixed logit (random parameters logit) models for DCE analysis, how to specify them in Apollo, and how to interpret the output including mean and standard deviation of random parameters.

Ben White, 07.07.2026

Why MNL is not enough

The multinomial logit model assumes that all respondents have identical preference parameters - that everyone values a reduction in side effects, a faster journey, or cleaner water by the same amount. This is almost never true. Preference heterogeneity - variation in preferences across individuals - is ubiquitous in DCE data.

Ignoring heterogeneity produces parameter estimates that represent the 'average' preference but cannot describe the distribution of preferences in the population. For policy analysis and benefit transfer, knowing that the average WTP is £50/year is less useful than knowing that 30% of the population has WTP above £100 and 20% has WTP below £20.

How mixed logit accounts for heterogeneity

The mixed logit model (also called random parameters logit or RPL) extends the MNL by allowing parameters to vary across respondents according to specified distributions - typically normal, lognormal, or triangular. The model estimates the mean and standard deviation of each random parameter's distribution.

A significant standard deviation indicates that preferences for that attribute vary substantially across respondents. A large standard deviation relative to the mean for the cost parameter implies that some respondents are relatively insensitive to cost - a finding with important implications for pricing and market segmentation.

Mixed logit is estimated by simulation - the likelihood function is approximated using Halton draws or other quasi-random sequences. Apollo handles the simulation automatically; you specify the number of draws and the distribution for each parameter.

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Estimating mixed logit in Apollo via SurveyEngine

Step 1: Export your DCE data from SurveyEngine. The data export includes one row per choice observation with the attribute levels each respondent saw and their chosen alternative.

Step 2: Specify the model in Apollo. In your Apollo model code, specify which parameters are random (varying across respondents) and which are fixed. Typically all attribute parameters are random; the cost parameter may be fixed or lognormal to ensure the correct sign.

Step 3: Choose the distribution for each random parameter. Normal distributions allow both positive and negative values - appropriate for attributes where some respondents may have negative preference (e.g. side effects some patients tolerate well). Lognormal enforces a single sign - appropriate for cost coefficients.

Step 4: Set the number of draws. More draws give a more accurate approximation of the simulated likelihood but require more computation time. 500–1000 Halton draws is a reasonable starting point.

Step 5: Interpret mean and standard deviation. The mean parameter is the average preference in the population. The standard deviation describes the spread of preferences. Report both with confidence intervals. Calculate WTP distributions from the ratio of attribute and cost parameters.

Worked example - mixed logit for health preference study

An oncology patient preference DCE is estimated with mixed logit. The nausea probability coefficient has mean -0.032 (t = -5.2) and standard deviation 0.018 (t = 3.1), indicating significant heterogeneity in how much patients dislike nausea risk. The cost coefficient is fixed at -0.28 (t = -7.4).

WTP for reducing nausea probability by 10 percentage points has mean £114/month and standard deviation £64/month - a wide distribution suggesting some patients are very sensitive to nausea risk while others are less so. This heterogeneity informs the benefit-risk framework and market segmentation strategy.