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

Table 3: Likelihood ratio tests for equality <strong>of</strong> model parameters.
Model
Likelihood Sum <strong>of</strong> sample 2 x (sum <strong>of</strong> sample A Critical values for chisquare
statistics at 5%
value A <strong>and</strong> B <strong>and</strong> B - pooled)
First 8 CS -2533.9
Last 8 CS -2414.6 -4948.6
Pooled -4303.5 -1290.13 18.31
Pooled with scaling -4299.7 -1297.81 16.92
This test also shows that the hypothesis <strong>of</strong> equal parameters in the two models can be rejected at the
5% level (with a test value at 1298), suggesting that the preference structure is clearly different in
the last 8 CS, even after an adjustment for differences in the error variance. 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). <strong>The</strong>
scale factor <strong>of</strong> 1.14 identified in table 2 implies that the variance <strong>of</strong> the error term or “noise” in the
model based on the last 8 CS is 23% smaller than in model based on the first 8 CS 3 . <strong>The</strong> appearance
<strong>of</strong> smaller error variance in the model based on the last 8 CS indicates that respondents’ preferences
have settled <strong>and</strong> that a learning effect has taken place during the first 8 CS. This corresponds to the
comparison <strong>of</strong> model fit between the two models (i) <strong>and</strong> (ii), where the model based on the last 8
CS clearly provides a better fit to the data. This is equivalent to the findings by Holmes & Boyle
(2005).
<strong>The</strong> above tests are joint tests that demonstrate a change in the overall preference structure. In a
more detailed analysis <strong>of</strong> how the preferences change, we compare the relative size <strong>of</strong> the attribute
coefficients across sub-samples. In order to avoid the confounding <strong>of</strong> scale <strong>of</strong> the Gumbel error <strong>and</strong>
structure <strong>of</strong> utility across the two sub-samples used in Models (i) <strong>and</strong> (ii) (Hausman & Ruud 1987,
3 (1/1.14 2 ) = 0.7695, hence there is a 23% difference in the variance between the two models.
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