The Value of Cultural Heritage Sites in Armenia: Evidence From a Travel Cost Method Study

18

trip faced by the respondent, and q _j is a vector of three dummies capturing the
presence/absence of a specific type of hypothetical program. β1, β₂ and β₃ are unknown
coefficients. The subscripts i and j denote the respondent (i=1, 2, ..., n) and the scenario
within the respondent, respectively (j=1, 2, 3, where j=1 refers the current conditions, and
j=2, 3 refer to the scenarios with the hypothetical programs (see table 5).

Estimation of the βs is further complicated by the nature of our sample. Because
we intercept people on site, Y is truncated from below at 1, and the people that we are
more likely to run into are the most avid visitors, i.e., those persons with the highest λ_ij s.

Accordingly, if we wish to estimate the parameters βs using the method of maximum
likelihood, the correct contribution to the likelihood is:

h(_y) = У ' P^r(У ) = У ' P^r(У)
∑ w ∙ Pr(w )     ^λ

w=1

where Pr(∙) is the Poisson distribution function (equation (7)), and the subscripts have
been omitted to avoid notational clutter. This amendment allows us to infer the demand
for trips in the population from our on-site sample.

Assuming that the observations on trip frequencies are independent within and
across respondents, the likelihood function of the sample is thus∏∏h ( yj ), and the log
ij

likelihood function is

⁽⁹⁾          ∑∑ log ^h ( y a ).

ij

It is easily shown (see Shaw, 1988) that (8) is simplified to the probability function of a

Poisson variate defined as Y' = Y -1.

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