The Effect of Learning and Fatigue on Preferences and WTP in a ...

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In a st<strong>and</strong>ard logit specification, all parameter coefficients are fixed whereas a r<strong>and</strong>om parameter logit (RPL) model, as we apply in this paper allows for variations in personal tastes. <strong>The</strong> researcher cannot observe β i for each individual so it is not possible to condition on β i . However, by assuming that the β i coefficients vary across respondents with the density f(β i ), it is possible to obtain the unconditional probability P ij that individual i chooses alternative j, as the integral <strong>of</strong> the conditional probability on β i over all possible values <strong>of</strong> β i : ⎛ βi' S ⎞ ij e Pij = ⎜ ⎟ f ' ( βi ) dβ β i i Sin e ⎜ ⎟ ⎝ n ⎠ ∫ ∑ (3) We assume that all non-price attributes are normally distributed thereby allowing consumers to place positive as well as negative values on the non-price attributes as well as the alternative specific constant, which has been shown to work well in earlier studies. <strong>The</strong> price coefficient is being held constant because such an assumption <strong>of</strong> a constant price parameter allows straight forward calculations <strong>of</strong> the distribution <strong>of</strong> WTP. In testing for a potential learning or fatigue effects we apply the Likelihood Ratio test procedure suggested by Swait & Louviere (1993) <strong>and</strong> draw on the notion used by e.g. Holmes & Boyle (2005) <strong>and</strong> Savage & Waldman (2008) that larger error variance is caused by fatigue, while smaller error variance is caused by learning. In this test we compare a model based on the first 8 CS with a model based on the last 8 CS, but the test could easily be conducted on larger number <strong>of</strong> models within the 16 CS (see below for further details on the design). In the context <strong>of</strong> learning, it makes sense to assume that learning processes will lead to choices that exhibit a relatively lower degree <strong>of</strong> 8
unobserved variability, <strong>and</strong> thus a higher degree <strong>of</strong> estimation precision (Hole 2006). It makes similarly good sense to assume that fatigue would have the opposite effect. Recall that the scale parameter is the inverse <strong>of</strong> the st<strong>and</strong>ard deviation <strong>of</strong> the error term (Swait & Louviere 1993). This implies that the variance <strong>of</strong> the error term or “noise” can be estimated as 1/σ 2 . <strong>The</strong> coefficients (β) in the econometric models are usually expressed in their scaled form * ( β β σ ) = , where the scale parameter σ <strong>and</strong> the ‘original’ coefficients β * cannot be separately identified (Train 2003). <strong>The</strong> estimated parameter β indicate the effect <strong>of</strong> each observed variable relative to the variance <strong>of</strong> the unobserved factors (Train 2003). To test for differences in scale, the differences have to be isolated before comparing the parameters. <strong>The</strong> problem is though, that the scaling factor cannot be identified in any particular set <strong>of</strong> empirical data. But instead the ratio <strong>of</strong> the scale factor <strong>of</strong> one data set relative to another can be identified by normalizing one <strong>of</strong> them to the value <strong>of</strong> 1 <strong>and</strong> then defining a range <strong>of</strong> values <strong>of</strong> the other scale factor, within which we expect the log likelihood function to be maximized (Swait & Louviere 1993). In estimating the models we have used the s<strong>of</strong>tware package Biogeme (Bierlaire 2003), which allows for a direct estimation <strong>of</strong> the ratio <strong>of</strong> scale factors. <strong>The</strong> models are estimated with simulated maximum likelihood using Halton draws with 300 replications; see Train (2003) for details on simulated maximum likelihood <strong>and</strong> Halton draws. 4. Design 9
Page 1 and 2: The Effect
Page 3 and 4: Waldman 2008). However, results are
Page 5 and 6: not by changing preferences as have
Page 7: eginning and in th
Page 11 and 12: expectation of the
Page 13 and 14: Note: ASC is the alternative specif
Page 15 and 16: Scarpa et al. 2008, Swait & Louvier
Page 17 and 18: testing for impacts on WTP can be n
Page 19 and 20: preference structure. Turning to a
Page 21 and 22: Dellaert, B. G. C.; Brazell, J. D.

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