Interpreting MNL model results from a DCE

MNL output tables contain coefficients, t-ratios, and fit statistics - knowing what each means is the difference between a conclusion and a guess.

This article walks through how to read MNL output from SurveyEngine's Apollo integration - what the coefficients mean, how to derive WTP estimates, and how to assess model fit.

Ben White, 07.07.2026

Reading MNL output

You have estimated a multinomial logit model from your DCE data. The output shows a column of coefficients, standard errors, t-ratios, and model fit statistics. What does each number mean? Which coefficients matter? How do you get from these numbers to WTP estimates? And how do you know whether the model is any good?

What the MNL model is doing

The MNL model finds the utility coefficients that best predict respondents' choices across the choice sets. Each coefficient represents the change in utility associated with a one-unit change in that attribute level (for continuous attributes) or the utility of that level relative to the base level (for dummy-coded categorical attributes).

The critical relationship is that the ratio of any two coefficients gives you the trade-off rate between those two attributes. The ratio of an attribute coefficient to the cost coefficient gives the WTP for a unit improvement in that attribute - this is the fundamental output of most DCE analyses.

Model fit is assessed using McFadden's rho-squared: the proportional improvement in log-likelihood over a null model. Values of 0.2–0.4 indicate good fit for DCE data.

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Apollo documentation

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Reading MNL output from Apollo in SurveyEngine

Step 1: Check coefficient signs. Before looking at significance or magnitude, confirm that coefficient signs make sense. A negative sign on cost means higher cost reduces utility - expected. A positive sign on efficacy means higher efficacy increases utility - expected. Unexpected signs indicate either coding errors or genuine preference reversals worth investigating.

Step 2: Assess significance with t-ratios. Each coefficient has a t-ratio: coefficient / standard error. A t-ratio above 1.96 (absolute value) indicates significance at 95% confidence. Below 1.96, the coefficient is not reliably different from zero.

Step 3: Calculate WTP estimates. For a continuous cost attribute: WTP for attribute i = -(beta_i / beta_cost). Include confidence intervals using the delta method or bootstrapping.

Step 4: Assess model fit. McFadden rho-squared = 1 - (LL_model / LL_null). Values 0.2–0.4 indicate good fit. Report LL at convergence, LL of null model, rho-squared, and number of observations.

Step 5: Check for independence of irrelevant alternatives (IIA). The MNL model assumes IIA - that the ratio of choice probabilities for any two alternatives is unaffected by adding a third. Test IIA using the Hausman test or by comparing nested logit results.

Worked example - transport mode choice MNL

A mode choice DCE produces MNL output: time coefficient = -0.042 (t = -8.3), cost coefficient = -0.31 (t = -6.1), reliability_85 = 0.28 (t = 4.2), reliability_95 = 0.51 (t = 7.8). Rho-squared = 0.31.

All coefficients are significant at 99%. Value of travel time = -(−0.042 / −0.31) = £0.136/minute = £8.13/hour. WTP for improving reliability from 70% to 85% = −(0.28 / −0.31) = £0.90/trip. Rho-squared of 0.31 indicates good model fit.