The Initial Full Model

Understandably, it is important not to overlook any variables that may significantly influence respondents’ answers to the WTP question. Thus it is reasonable to build an initial full model that includes all the potentially important explanatory variables at the outset of the modelling procedure. Generally, explanatory variables in Contingent Valuations studies include respondents’ environmental awareness, knowledge and attitudes, their experiences/behaviours related to the valued ecosystem services and their demographic characteristics (Spash et al. 2009; Vasquez et al. 2009; Ramajo-Hernandez and del Saz-Salazar 2012; Wang et al. 2013b). Accordingly, a total of 21 potential explanatory variables were considered for the initial full model of this study (Table 3.2).

Table 3.2 Potential Explanatory Variables in the Initial Full Model Variable Description and Coding

Perceive- shortage

Perception of the water shortage in the city: 1 to 3 (from Abundant to Scarce) a

Opinion-service Opinions about the current tap water service: 1 to 3 (from Satisfactory to Dissatisfactory) b Know-bill Know their water bills: No = 0; Yes = 1

Know-price Know the current water price: No = 0; Yes = 1

Heard-SNWTP Have heard about the South-to-North Water Transfer Project (SNWTP): No= 1 c; Yes = 0

Know-benefits Know the potential benefits of the SNWTP: 0 to 4 d Heard-mid-route Have heard the specific Middle Route of the SNWTP:

No = 0; Yes = 1

Know-reservoir Know the Danjingkou Reservoir as the water supply area of the middle route project: No = 0; Yes = 1

Heard-EC Have heard about Ecological Compensation (EC): No = 0; Yes = 1

Understand-EC e Can correctly describe the general idea of EC: No = 0; Yes = 1

Opinion-EC Opinion about the general idea of EC f

: 1 to 5 (from Highly agree to Highly disagree) Price-increase The proposed increase in water price in the WTP

question: 0.1; 0.2; 0.5; 0.8; 1.0; 1.5 (yuan/m3) Household-size Number of family members living with the

respondents

Gender Female = 0; Male = 1

Age 30 and below = 1; 31 to 40 = 2; 41 to 50 = 3; 51 to 60 = 4; Above 60 = 5

Education College or higher = 1; High school = 2; Middle, primary school or below = 3 g Income Monthly gross income (in Chinese Yuan)

h :

Below 2500 = 1; 2500 to 4000 = 2; Above 4000 = 3

Job

Public Sector (government departments, state-owned companies and institutes) = 1; Private Sector (private companies, businessmen, freelancer) = 2; Retired = 3; Unemployed = 4;

Residence Length of stay in the city (in years) i

:

Over 20 = 1; 10 to 20 = 2; 5 to 10 = 3; Below 5 = 4 Visit Visited the water supply areas before: No = 0; Yes =1 Relatives Have relatives or close friends living in the water

supply areas: No = 0; Yes =1

a

The original options of “Very abundant” and “Abundant” were merged into

“Abundant”, “Very scarce” and “Scarce” were merged into “Scarce” in order to assure that there are enough number of answers in each category for the regression modelling.

b

Similarly, the original options of “Very satisfactory” and “Satisfactory” were merged into “Satisfied”, “Very dissatisfactory” and “Dissatisfactory” were merged into “Dissatisfied”.

c _{Since most respondents have heard of the project before, the no answer was}

coded as 1, and the yes answer was coded as 0 (the reference level). For regression analysis with categorical variable, it is better to take the category that has a fairly large number of observations as the reference level.

d _{A multiple-option question including four major benefits of the water transfer}

project and an “I Don’t know” option was asked to the respondents. Choosing each benefit scored 1 and choosing “I Don’t know” scored 0.

e _{This variable is different from the preceding one (Heard-EC) as respondents who}

have heard about EC did not necessarily understand its idea correctly.

f _{A brief description of the general idea of EC was given to the respondents before}

asking their opinions (but after the preceding question about whether they understand the general idea of EC).

g _{Primary and middle schooling are legally compulsory and free in China. A fairly}

large number of respondents have received college or higher education, so this category is coded with the smallest number as the reference level.

h _{The starting income level of the personal income tax in China was 2000}

Some original income ranges in the questionnaire (see Appendix 1) were merged into these three ranges so that each range contains enough number of observations for the modelling analysis.

i _{The longest residence was coded with the smallest number (as the reference}

category) due to the fairly larger number of respondents in this category.

The initial full model was not the best-fit model because not all the assumed important variables turned out to be truly important variables in the modelling results. Moreover, the Principle of Parsimony27

Interestingly, while the importance of including all possibly important variables in the full model is generally well attended, the Principle of Parsimony and the necessity of model simplification and improvement seemed largely neglected in the Contingent Valuation literature. It is common to see logit/probit models with a number of variables in the literature and only some of them are significant, but it is not known whether the models can be further simplified and improved by removing some or all of the insignificant variables (Vasquez et al. 2009; Ramajo-Hernandez and del Saz-Salazar 2012; Wang et al. 2013b). This study introduced two powerful automatic model selection techniques, i.e. the Stepwise Regression and the Best Subset Regression in Contingent Valuation, and integrated them with manual adjustment for model construction and improvement.

means that statistic models should be simplified to have as few parameters as possible until removal of any variable would considerably reduce the model fit (Crawley 2007). Therefore, variables in the initial full model should be screened in order to obtain the improved model in terms of goodness of fit and simplicity.