Theoretical basis of choice modelling

ence technique in this area, techniques such as choice modelling CM, also referred to as the choice experiment, are increasingly being favoured. Whilst applications of the discrete choice CVM require respondents to choose between a base option and a single alternative, respondents to CM exercises are typically presented with six to ten choice sets, each containing a base option and two or three alternatives. They are required to indicate which option they prefer in each choice set. The levels of the attributes characterising the different choice set options are varied according to an experimental design, permitting estimates of the relative importance of the attributes describ- ing the options to be obtained. Rather ‘than being questioned about a single event in detail, as in CVM analysis, subjects are questioned about a sample of events drawn from the universe of possible events of that type’ Boxall et al., 1996, p. 244. A fundamental question that arises in the appli- cation of CM is whether to present the choice sets in a generic or labelled form. The generic form involves assigning generic labels to each alterna- tive in the choice set, such as ‘alternative A’, ‘alternative B’ etc. The labelled form involves assigning labels that communicate, directly or in- directly, information regarding the tangible and or intangible qualities of the alternatives. In marketing applications, labels tend to consist of brand names and logos, which consumers have learnt to associate with different product charac- teristics and feelings. In the context of environ- mental policy, labels tend to refer to sites, locations, policy names or other descriptors. An advantage of assigning issue-relevant and alternative-specific labels is that responses will better reflect the emotional context in which pref- erences are ultimately revealed. For example, a respondent may have a predisposition toward vis- iting a particular recreation site because he or she has fond memories from a past visit. This factor may not be reflected in the results of a CM exercise that describes sites purely in terms of tangible attributes involving recreation opportuni- ties, camping facilities, proximity and cost. Often, the most plausible way of including such informa- tion is in the form of a label. This information not only increases predictive validity, but may also make the exercise less cognitively demanding. Offsetting this potential advantage of labelled choice set configurations is the likelihood that generic configurations may encourage more dis- cerning and discriminating responses. Instead of respondents being able to base their responses wholly or largely on the alternative with the most superficially attractive label or descriptor, respon- dents are required to consider differences in policy options as described by the attributes listed in the choice sets Blamey et al., 1997; Morrison et al., 1997. The resultant more informed and deliber- ated preferences may be desirable from a non- market valuation perspective Mitchell and Carson, 1989. In this paper, the effects of employing labelled rather than generic choice-set configurations are considered. A split sample approach is used. Two statistically equivalent samples of the Brisbane population were presented with the same basic CM questionnaire, with the exception that one employed a generic approach and the other a labelled approach. This enables a direct compari- son of the two sets of results with a view to assessing the degree of convergent validity. These issues are considered in the context of a CM study of remnant vegetation values in the Desert Up- lands of Central Queensland, Australia. The paper is structured as follows. The theoret- ical basis of CM is briefly reviewed in Sections 2 and 3, and the case study is introduced in Section 4. Methods are then presented in Sections 5 – 7, and the results are presented in Section 8. Some conclusions are finally drawn.

2. Theoretical basis of choice modelling

Choice modelling has its origin in conjoint analysis, information integration theory in psy- chology and discrete choice theory in economics econometrics Louviere, 1988. Conjoint analysis has been widely used in market research, and involves the use of individual evaluations of a designed set of multiattribute alternatives to ob- tain a decomposition of the total utility of any one or more alternatives into the utility associated with the individual attributes of those alternatives Louviere, 1988. As such, these approaches have foundations in Lancaster’s 1966, 1991 modern consumer theory. 1 Environmental applications of CM include Adamowicz et al. 1994, Boxall et al. 1996, Rolfe and Bennett 1996, Adamowicz et al. 1998, Hanley et al. 1998a,b, Morrison et al. 1999 and Blamey et al. 1999. Boxall et al. 1996 observe that CM is attractive for environ- mental valuation because it relies on the same model structures as referendum CVM models and discrete choice travel cost models p. 244 – 5. Both CM and the dichotomous-choice CVM have their theoretical bases in random utility the- ory RUT. According to RUT, the ith respon- dent is assumed to obtain utility U ij from the jth alternative in choice set C. U ij is held to be a function of both the attributes of the alternatives X jk representing the kth attribute value of the jth alternative and characteristics of the individual, S i . U ij is assumed to comprise a systematic com- ponent V ij and a random component e ij . Whilst V ij relates to the measurable component of utility, e ij captures the effect of omitted or unobserved vari- ables. We thus have U ij = V ij X ij , S i + e ij 1 Respondent i will choose alternative h in prefer- ence to j if U ih \ U ij . Hence, the probability of i choosing h is: P ih = ProbU ih \ U ij for all j in C, j h = ProbV ih − V ij \ e ij − e ih , for all j in C, j h 2 The e ij for all j in C are typically assumed to be independently and identically distributed IID and in accordance with the extreme value Gum- bell distribution. This gives rise to the multino- mial logit model, commonly employed in discrete choice modelling, of which the binary logit used in CVM studies is a special case: P ih = exp[lV ih ] j C exp[lV ij ] 3 where l is a scale parameter, which is inversely proportional to the variance of the error term, and commonly normalised to 1 for any one data set Ben-Akiva and Lerman, 1985. An estimated linear-in-parameters utility function for the jth alternative often takes the following form: V j = ASC j + b 1 X 1 + b 2 X 2 + b 3 X 3 + …b k X k + …b n X n + g 1 S 1 ASC j + … + g m S m ASC j 4 where there are n attributes with generic coeffi- cients across alternatives, and m individual-spe- cific variables multiplied by an alternative- specific-constant ASC. The ASCs capture the mean effect of the unobserved factors in the error terms for each alternative. This provides a zero mean for the error terms and causes the average probability of selecting each alternative over the sample to equal the proportion of respondents actually choosing the alternative. Socioeconomic and attitudinal variables can be included by inter- acting them with the alternative-specific constants as shown in Eq. 4 andor the attributes not shown. ASCs should be included regardless of whether generic or alternative-specific labels are employed. The inclusion of alternative-specific la- bels simply alters the interpretation of the esti- mated ASCs. The inclusion of ASCs helps mitigate inaccura- cies due to violations in the assumption of inde- pendence of irrelevant alternatives IIA Train, 1986. This assumption, which arises from the above-mentioned IID assumption, implies that the ratio of the choice probabilities for any two alternatives be unaffected by the addition or re- moval of alternatives. This is equivalent to assum- ing that the random error components of utility are uncorrelated between choices and have the same variance Carson et al., 1994. Violations of the IIA assumption render the MNL model inappropriate. 1 Several different conjoint paradigms exist, differing in terms of the response modes employed, methods of analysis and interpretation of results Louviere, 1988. Morrison et al. 1996 discuss the different paradigms in detail. One way of circumventing the IIA property is to allow for correlations among the error terms within different subsets or classes of alternatives by estimating a nested logit model McFadden, 1978; Daganzo and Kusnic, 1993. In a two-level nested logit model, the probability of an individ- ual choosing the hth alternative in the rth branch P hr is represented as: P hr = PhrPr 5 where Phr is the probability of an individual choosing the hth alternative conditional on choos- ing the rth class of outcome, located in the rth branch of the tree. Pr is the probability that the individual chooses the rth branch. Following Kling and Thomson 1996: Phr = exp[V hr a r ] exp[I r ] 6 P = exp[a r I r ] R k = 1 exp[a k I k ] 7 where I r = log H r i = 1 expV ir a r n 8 is referred to as the inclusive value. This is a measure of the expected maximum utility from the alternatives associated with the rth class of alternatives. H r is the number of alternatives in branch r, and V hr is the utility of the hth alterna- tive in the rth branch. The coefficient of the inclusive value, a r , measures substitutability across alternatives. When substitutability is greater within rather than between alternatives, 0 B a r B 1. In this case, respondents will shift to other alternatives in the branch more readily than they will shift to other branches Train et al., 1987. The popularity of the nested logit model is in part due to the way in which nested decision structures lend themselves to behavioural interpretations. Welfare estimates are obtained in CM studies using the following general formula described by Hanemann 1984: W = − 1 m ln i C e V i 0 − ln i C e V i 1 n 9 where m is the marginal utility of income, V i0 and V i1 represent the indirect observable utility before and after the change under consideration, and C is the choice set. In CM, the absolute value of the coefficient of the monetary attribute in the choice model is taken as an estimate of m. Changes in V i0 or V i1 can arise from changes in the attributes of alternatives or the removal or addition of alter- natives altogether. For example, in recreational site studies where alternatives are substitutes in consumption, the removal of an alternative from the choice set might correspond to a site closure, which one would expect to result in a welfare loss. When alternatives are substitutes in ‘production’, such as when a single solution has to be chosen from a set of feasible solutions, the removal of alternatives can be used to estimate selection probabilities and welfare implications based on different choice sets. When the choice set includes a single before and after policy option, Eq. 9 reduces to: W = − 1 m [lne V i 0 − lne V i 1 ] = − 1 m [V i0 − V i1 ] 10 In the case of changes in a single attribute, this further reduces to − b j m when a linear in parameters utility function is employed. This is equivalent to calculating the ratio of marginal utilities for the attribute in question and the mon- etary attribute, or the marginal rate of substitu- tion MRS Hensher and Johnson, 1981. Kling and Thomson 1996, Herriges and Kling 1997, Choi and Moon 1997 consider the application of Eq. 9 in the nested logit case.

3. Labels and choice