CUADRO CLÍNICO

The choice dataset used in this chapter was obtained from a DCE conducted in Scotland in 2016. Details regarding the DCE design and data collection procedures can be found in chapter 3. The analysis of the present chapter uses the choices of a representative sample of 589 individuals (see table 3-4) to estimate society’s WTP for improving flood control, recreation and biodiversity in the Clyde, Forth and Tay catchment areas. The summary of the descriptive statistics of the sample and the process for testing its representativeness can be revisited in section 3.5 of the previous chapter.

The analysis presented below has four main sections. The first two sections (4.3.1 and 4.3.2) explore whether there is preference heterogeneity around the mean utility weights, as well as whether individuals with different socioeconomic characteristics have similar preferences for improvements in estuarine ES. The third section (4.3.3), narrows the exploration of preference heterogeneity to focus on two variables i) the study area and ii) the user type. First, we assessed if these characteristics are a significant source of preference heterogeneity for opting out of the status quo (using interactions with the ASC). Second, we test whether these characteristics influence preferences for the estuarine ES improvements (using interactions with the attributes). The fourth and final section (4.3.4) analysing the choice data explores whether there is heterogeneity in the WTP estimates for the different ES, among user types and across study cases.

Several specification forms were tested for the following models. We found that the better-fitted models define the utility as a linear function of the attributes of that scenario and the ASC. Table 4-1 describes the coding used in the models. All models were coded and estimated in R software (version 3.3.2). They were estimated with the pooled dataset, as well as with the site-specific datasets and accounted for both, the systematic and

stochastic component of preference heterogeneity. Please note that the model output tables have been moved to the end of this chapter for ease of reading.

Table 4-1 Explanation of variable abbreviations and coding Variable Explanation

ASC Constant term (0 = Option1: NO new policy, 1 = Option 2 or 3)

F1 Change in flood control from “increase in flood risk” to “slight reduction in flood risk” (1 = yes, 0 = no)

F2 Change in flood control from “increase in flood risk” to “large reduction in flood risk” (1 = yes, 0 = no)

B1 Change in biodiversity from “decrease in biodiversity” to “slight increase in biodiversity” (1 = yes, 0 = no)

B2 Change in biodiversity from “decrease in biodiversity” to “large increase in biodiversity” (1 = yes, 0 = no)

R1 Change in recreation from “decrease in recreation” to “slight increase in recreation” (1 = yes, 0 = no)

R2 Change in recreation from “decrease in recreation” to “large increase in recreation” (1 = yes, 0 = no)

Cost Additional council tax payment

Resident Whether respondent resides in the catchment area (1 = yes, 0 = no)

Visitor Whether respondent visited the area for outdoor recreational activities in the last 12 months (1 = yes, 0 = no)

Female Respondent's gender (1 = Female, 0 = Male)

Age Respondent's age is above the average (1 = yes, 0 = no)

Graduate Whether respondent has undergraduate and/or postgraduate education (1 = yes, 0 = no) Income Respondent's income is above the average for the sample (1 = yes, 0 = no)

4.2.1. Choice modelling

The basis for the analysis of the discrete choice data is the RUM model (McFadden, 1973). According to this model, the total indirect utility 𝑈_𝑖𝑛𝑡 that an individual derive

from alternative 𝑖 is the sum of its deterministic and random part. The utility of respondent

𝑛 choosing alternative 𝑖 in the choice occasion 𝑡 is given by:

𝑈𝑖𝑛𝑡 = 𝑉𝑖𝑛𝑡+ 𝜀𝑖𝑛𝑡 4-1

where 𝑈_𝑖𝑛𝑡 is indirect utility, 𝜀_𝑖𝑛𝑡 captures the factors that affect utility but are not

observed by the modeller and therefore not included in 𝑉_𝑖𝑛𝑡. The deterministic component

𝑉𝑖𝑛𝑡 = 𝑓(𝛽, 𝑥𝑖𝑛𝑡, 𝑧𝑛) 4-2

where 𝛽_𝑛 is a vector of utility weights of respondent 𝑛, 𝑥_𝑖𝑛𝑡 is a vector of attributes of

alternative 𝑖 in choice occasion t, 𝑧𝑛 is a vector of measured attributes of respondent 𝑛

and 𝜀𝑖,𝑛,𝑡 is a random term which is assumed to be independent and identically distributed

(IID). Further assuming that a respondent chooses the alternative that maximises their utility, the probability of individual 𝑛 of choosing alternative 𝑖 is:

𝑃_𝑖𝑛𝑡 = Pr(𝑦_𝑛𝑡_{| ∙) =} 𝑒𝑉𝑖𝑛𝑡 ∑𝐽_𝑗=1𝑒𝑉𝑗𝑛𝑡

4-3

The equation can be estimated using the MNL model. This model follows the independence of irrelevant alternatives (IIA) assumption which states that the ratio of choice probabilities between any two alternatives in a choice card is not affected by the introduction of removal of additional alternatives (Louviere et al., 2000). Moreover, the MNL assumes homogenous preferences across respondents since it estimates a single (mean) attribute parameter for each choice attribute. Notably, the previously described characteristics of the MNL have been considered relevant limitations and have led to the development of other models.

In this chapter, we also used the RPL13, which is a model that account for preference heterogeneity by incorporating preference deviation around the attribute means. The utility specification of the RPL model is an extension of equation 4-1 but includes coefficients varying in the population. The equation is rewritten as:

𝑈_𝑖𝑛𝑡 = (𝛽 + 𝑧_𝑛) 𝑥_𝑖𝑛𝑡+ 𝜀_𝑖𝑛𝑡 4-4 The general RPL form is as follows:

𝑉𝑖𝑛𝑡 = 𝐴𝑆𝐶 + ∑ 𝛽𝑘∙ 𝜉k+ ∑ 𝛽𝑚∙ 𝑍m 4-5

Where the ASC captures the effect of unobserved attributes on the choice, 𝑘 is the number

of attributes and m the number of socioeconomic factors included in the model, if any.

In the RPL model, the attribute parameters are assumed to be random, following a specific distribution. Our RPL uses a fixed cost parameter and assumes normally distributed

parameters for the ES attributes and the ASC, with mean 𝛽 and standard deviation σ. The

fixed cost coefficient was used to avoid convergence issues and to facilitate the calculation of the implicit prices for the ES attributes (Revelt and Train, 1998; Wielgus

et al., 2009). Hence, the conditional choice probability for respondent 𝑛 choosing

alternative 𝑖 is given by:

𝑃𝑖𝑛𝑡 = Pr(𝑦𝑛𝑡| ∙) = ∫ ∏ 𝑒 𝑉𝑖𝑛𝑡 ∑𝐽_𝑗=1𝑒𝑉𝑖𝑗𝑡 𝑇𝑛 𝑡=1 𝛽 𝑓(𝛽|θ)𝑑𝛽, 4-6

Finally, the model is estimated by maximum likelihood. The log-likelihood (LL) function for the model is given by 𝐿𝐿(θ) = ∑𝑁_𝑛=1ln 𝑃_𝑖𝑛𝑡. This expression cannot be solved

analytically and simulation-based estimation of the model is used to evaluate 𝑃_𝑛 at a large

number of draws from 𝛽, in our case 1,000 Sobol draws. We used this type of draws as

they have been found to outperform Halton, modified Latin hypercube sampling, and pseudo-random draws (Czajkowski and Budzinksi, 2017).

The simulated log likelihood of the RPL model is given by:

𝐿𝐿(θ) = ∑ ln [_𝑅1∑𝑅 𝑃_𝑛(𝛽𝑖𝑛/θ₎

𝑟=1 ]

𝑁

𝑛=1 4-7

where 𝑅 is the number of draws, 𝛽𝑖𝑛/θ is a vector of 𝛽s obtained in the r-th draw from

the distribution 𝑓(𝛽|θ) for individual 𝑛.

In the RPL model, the parameters of 𝛽 distribution (θ) are estimated, rather than a vector

of 𝛽 point values as is done in the MNL model.