Modelling protest responses in environmental DCE analysis

How you model protest responses matters as much as how you detect them. Simple exclusion biases WTP upward; ignoring them biases it downward. Spike models offer a middle path.

This article explains the statistical approaches to modelling protest responses in environmental DCE analysis, from simple exclusion to spike models and double-hurdle specifications.

Ben White, 07.07.2026

The modelling challenge of protest responses

Protest responses produce zero or very low WTP estimates in the choice data, but for reasons that are not related to genuine preference. Including them in the analysis biases WTP downward (attenuating the estimate toward zero). Excluding them biases WTP upward (removing respondents whose choices would pull the estimate down).

The correct approach depends on the research question. If the study aims to estimate the WTP of the full affected population, protest responses should be modelled appropriately rather than simply excluded. If the study aims to estimate the WTP of respondents who engage genuinely with the payment vehicle, exclusion may be defensible.

Statistical approaches to protest responses

The simplest approach is exclusion with sensitivity analysis: exclude identified protesters from the main analysis and compare WTP estimates with and without them. This is transparent and widely accepted, but leaves the question of how to interpret the difference unanswered.

Spike models explicitly model a mass of probability at zero WTP - the 'spike' - alongside a continuous WTP distribution for positive values. The spike accommodates both genuine zero-WTP and protest respondents without requiring them to be identified individually.

Double-hurdle models use a two-stage process: the first hurdle determines whether the respondent has positive WTP (crossing zero); the second hurdle estimates the level of WTP conditional on it being positive. This cleanly separates participation decisions from level decisions and can accommodate both genuine zeros and protests.

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Implementing protest modelling in R and Apollo

Step 1: Identify protest respondents using debriefing questions. Create a binary protest indicator variable using the debriefing question taxonomy described in the protest responses article.

Step 2: Estimate the baseline model including all respondents. This is your lower bound WTP estimate.

Step 3: Estimate the model excluding identified protesters. This is your upper bound WTP estimate. The difference between the two estimates is the protest-induced WTP gap.

Step 4: Estimate a spike model as the preferred specification. In R (using the support.CEs package or similar), specify a spike model that allows a mass of probability at zero. The spike model produces WTP estimates that are between the inclusion and exclusion estimates.

Step 5: Report all three estimates. Present main analysis (all respondents), sensitivity analysis (excluding protesters), and spike model estimate. Discuss the implications of the range for the policy decision.

Worked example - biodiversity offset WTP protest modelling

A biodiversity offset valuation study identifies 24% of respondents as protest respondents using debriefing questions. Three WTP estimates are reported for improving the biodiversity index by 20 points: (1) full-sample MNL: WTP = £31/year; (2) excluding protesters: WTP = £52/year; (3) spike model: WTP = £41/year.

The spike model estimate of £41/year is presented as the primary estimate because it models the protest response explicitly rather than arbitrarily including or excluding protesters. The range £31–£52 is reported as the uncertainty bound attributable to protest responses and is presented to the policy client as a range within which the true WTP lies.