Model Structure and Rationale

In order to test the hypotheses, several analytical models have been developed. The primary model, which accounts for panel effects, is a pooled model for the binary, one and two stage Likert elicitation methods. In this case, the binary data is analysed using a binary logit model while the one and two stage Likert data are analysed using a multinomial logit (MNL) model. The MNL model treats each preference level on the Likert scale as a separate alternative. Thus, in the case of the one stage Likert data, five preference levels are obtained and are treated as separate alternatives (Definitely A, Probably A, Uncertain, Probably B and Definitely B) while in the case of the two stage Likert data, four preference levels are obtained and are treated as distinct alternatives (absolutely (Abs.) certain A, not so (N.s.) certain A, Abs. certain B and N.s.certain B).

In the pooled BL-MNL model, the attribute coefficients are held common across the different elicitation methods while different scale parameters across the elicitation methods are estimated. Based on the estimated scale parameters, one can thus evaluate the effect of different preference elicitation techniques. By fixing each of the scale parameters to unity and comparing the model results obtained, the reference scale parameter was thus chosen for the final model. Thus, in case of the location ratings, dummy and linguistic dummy specifications, the scale parameter for ‘one stage Likert’ (reference scale parameter) is held at unity while in the case of the linguistic ratings model, the scale parameter of ‘binary’ elicitation is fixed at unity.

For each of the models developed, the level of the attributes in the utility function is incorporated into the model using the attribute ratings method and the dummy specification method. As explained in Section 5.4 of the previous chapter, respondents were asked to give a perception rating from 0 – 100 (very bad – very good) for view, noise and sunlight attributes. The average ratings obtained for each of the attribute levels across the different representation methods is given in Table 6.3.

The numeric rating obtained from the perception rating exercise is used in the attribute ratings model as the data input method. For both the attribute ratings as well as the dummy data input method, the ‘housing service charge’ is in the units of Euro. In case of the dummy specification method, the dummy categorical level of each of the attributes (except charge) is incorporated into the model. The number of dummy levels for each of the attributes varied based on the method of attribute representation. For the location method, the number of dummy levels for view, noise and sunlight were fixed to four, based on the number of apartment locations.

Thus, the following four dummy levels are observed for the location method:

Table 6.1 Attribute dummy levels with location method

Level 1 Level 2 Level 3 Level 4

View,

Noise, Sunlight

6F 6T 3F 3T

In the case of the linguistic representation method, the number of levels for each of the attributes varied and in this case, the following levels were incorporated into the model:

Table 6.2 Attribute dummy levels with linguistic method

Level 1 Level 2 Level 3

View good neither

Noise noisy neither quiet

Sunlight v.good good neither

The following average ratings were obtained for each of the attribute levels across the different representation methods:

Table 6.3 Average ratings for attribute levels across different representation

For each of the model structure created, results from both the ratings and dummy input methods are reported.

For the binary choice, the general utility expression for a linear in parameters model with attribute ratings can be given as:

A A

VA, NA, SA and CA are view, noise, sunlight and housing service charge for option A;

VB, NB, SB and CB are view, noise, sunlight and housing service charge for option B and,

ASC is the alternative specific constant

The utility function using the attribute dummy level is constructed by omitting one level as the ‘reference case’ for each attribute. In case of the location method thus, the utility function using the dummy level specification can be given as follows where the fourth level of the ‘view’, ‘noise’ and ‘sunlight’ attributes is fixed as the reference level:

As the number of attribute dummy levels in the case of the linguistic representation is lesser than that in the location method, it should be noted that the number of levels in the corresponding utility functions will also be less compared to the location method. Thus, in this case, there is one dummy level for view while two dummy levels for noise and sunlight.

The one stage, five point Likert choice elicitation was carried out by offering the respondents the following range of preference levels to indicate their choice of alternative – Definitely A, Probably A, Uncertain, Probably B and Definitely B.

The general utility expression for the MNL model using attribute ratings can be given as:

Where,

As only difference in the utilities of the alternatives matter for choice (Train, 2003), the utility for the ‘uncertain’ alternative could be stated as a difference between the utilities of alternative A and alternative B. However, as in the case of the linguistic representation method, the orthogonal design was compensated in order to avoid the dominant choice problem, the difference specification cannot be employed due to non-orthogonality conditions. Moreover, the constant associated with the

‘uncertain’ alternative is set to capture any effects associated with the choice of the alternative, without incorporating the utility difference design in modelling, thus this specification was adapted for both the location and the linguistic methods.

The utility expression for the dummy variables approach can be given as the following (it is to be noted here that the following equations are for the utility expression for the location method and the utility expressions for the linguistic representation method will vary based on the linguistic dummy levels provided in Table 6.2, where (n-1) levels will be incorporated in the equation for each of the attributes):

The two stage Likert choice elicitation was carried out by asking respondents to choose between options A and B and then indicate their level of choice certainty (by indicating whether they have ‘absolute certainty’ or ‘have some doubts’ in their choice). Each level of the preference certainty was again treated as a separate

alternative. A full set (n-1) of ASCs were used in the model building with the following utility functions for the ratings model:

AcA AcA

The ASCs capture any other effects affecting the alternative and in this case are used to examine additional effects related to each preference level. It is hypothesised that in case where less randomness is associated with choice, more plausible ASC values will be obtained across the different preference levels. Thus the ASC values are used to examine additional effects associated with the choice of the alternative as well as the level of randomness involved in choice across the different preference elicitation and attribute representation methods.

For the sake of simplicity in the above utility models, ‘Abs. certain’ A is denoted by AcA and ‘N.s.certain’ A is denoted by nsA. The same procedure is followed for Option B.

The utility functions for the dummy model followed closely to that developed for the MNL model with one stage Likert choice data, with the exception on the number of utility functions developed.