A hybrid compensatory-noncompensatory model of residential preference structures Borgers, A.W.J.; Timmermans, H.J.P.; Veldhuisen, K.J.

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1 A hybrid compensatory-noncompensatory model of residential preference structures Borgers, A.W.J.; Timmermans, H.J.P.; Veldhuisen, K.J. Published in: Netherlands Journal of Housing and Environmental Research DOI: /BF Published: 01/01/1986 Document Version Publisher s PDF, also known as Version of Record (includes final page, issue and volume numbers) Please check the document version of this publication: A submitted manuscript is the author's version of the article upon submission and before peer-review. There can be important differences between the submitted version and the official published version of record. People interested in the research are advised to contact the author for the final version of the publication, or visit the DOI to the publisher's website. The final author version and the galley proof are versions of the publication after peer review. The final published version features the final layout of the paper including the volume, issue and page numbers. Link to publication Citation for published version (APA): Borgers, A. W. J., Timmermans, H. J. P., & Veldhuisen, K. J. (1986). A hybrid compensatory-noncompensatory model of residential preference structures. Netherlands Journal of Housing and Environmental Research, 1(3), DOI: /BF General rights Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights. Users may download and print one copy of any publication from the public portal for the purpose of private study or research. You may not further distribute the material or use it for any profit-making activity or commercial gain You may freely distribute the URL identifying the publication in the public portal? Take down policy If you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim. Download date: 22. Dec. 2018

2 A HYBRID COMPENSATORY-NONCOMPENSATORY MODEL OF RESI- DENTIAL PREFERENCE STRUCTURES Aloys Borgers, Harry Timmermans and Jan Veldhuisen Introduction The modelling of residential and housing choice behaviour and preference structures has continuously been an area of major attention in housing and building research over the last decades. Especially discrete choice models have frequently been adopted to portray these processes. Examples include Onaka (1983), Onaka and Clark (1983), Van Lierop (1981, 1985), Van Lierop and Nijkamp (1984), Van Lierop and Rima (1984), Longley (1984), Veldhuisen (1984, 1985). Both the standard multinomial logit model and the nested logit model have received major attention, the latter type enabling the researcher to incorporate the similarity between the choice alternatives in the model (see Mc.Fadden, 1978 for details). Both these types of models implicitly assume some kind of compensatory decision-making process. That is, low scores on some attribute may, in theory at least, be compensated by high scores on one or more of the remaining attributes. Although satisfactory predictive results have been obtained with these models in the past, the assumption of compensatory decision-making seems at least to some degree counterintuitive. People may screen the available choice alternatives according to some attributes, and choice alternatives failing such a test are no longer considered as viable alternatives. In theory, noncompensatory decision rules, such as the conjunctive rule and the lexicographic rule, may describe such decision processes. The conjunctive rule states that in order to be chosen an alternative must exceed specific acceptable attribute values which are defined on each attribute. Alternatives that have values outside the acceptable range are rejected as unacceptable, which implies that the worst attribute of an alternative is vital in the decision-making process. Note that compensation is not admitted. The lexicographic rule states that the alternatives are first compared on the most important attribute. If two or more alternatives are equivalent at this stage, they are compared on the next most important attribute. This process is assumed to continue until all alternatives are (weakly) ranked or until all alternatives have been considered. Previous work of the authors has indicated however that thes e strictly noncompensatory decision rules were unable to reproduce individual choice behaviour and preference structures. So Neth. J. of Housing and environmental Re.s., Vol.1 (1986) No.3 227

3 individuals may apparently use certain attributes as screening devices for delimiting their choice set, while other attributes are used in a compensatory fashion to arrive at some overall utility for those alternatives that remain in their choice sets. If such behaviour is prevalent, a hybrid compensatory-noncompensatory model is needed to uncover residential and housing choice processes and preference structures. The aim of this article is to develop and test such a hybrid model. The article isorganised as follows. First, in the next section, the hybrid compensatory-noncompensatory model of residential and housing preference formation will be outlined. This is followed in section 3 by a description of the data and the results of a test of the model on these data referring to residential preferences in the province of Zuid-Holland, The Netherlands. The paper is concluded by discussing the implications of the empirical findings and some possible improvements of the model. The model Assume that residential preference formation is regulated by a mixture of compensatory and noncompensatory mechanisms. Suppose an individual attaches to each attribute some threshold Tj. If a choice alternative's attribute level is greater than or equal to the corresponding threshold, the alternative passes the noncompensatory test and enters the compensatory part of the decision making process. If it does not pass this test, the choice alternative is no longer considered. Assume that the thresholds are stochastic variables to account for measurement errors, instability or heterogeneity at the aggregate level. It follows that the probability of the i-th choice alternative passing the test is equal to: Pij = Pr ( Xij > Tj + ~j) (i) where, Pij is the probability that the i-th choice alternative passes the test on the j-th attribute; Xi] denotes the j-th attribute level of alternative i; j is the threshold associated with the j-th attribute; ~j Is an error term It is assumed that the z :'s are normally distributed. The probability that choice alternative i satis}ies all selection criteria, chat is the probability that choice alternative i belongs to the set ~ of feasible choice alternatives under the assumption of independent screening of the attributes then equals: p( i~c~ ) = ][jpij (2) 228

4 The probability that the choice is made from a particular choice set A thus equals: PA =Ei{P(i s - p (i's i'zi (3) The above equation results after finishing the noncompensatory part of the choice process. The second component of the assumed decision-making process consists of a compensatory choice process in which the attributes of the alternatives remaining in the choice sets are evaluated in a compensatory fashion. It is assumed that the hybrid choice model may be written as: Pi =ha{(exp(gj{gjxij) /gi,ca(exp(zjsjxi, j)} PA (4) The above equation assumes the standard logit expression for the utilities of the choice alternatives, but other functional relationships could be assumed as well. Although the model itself is new, some of its components can be found in other work on decision-making and choice processes. Thresholds have been used in the field of spatial analysis on several occasions (Young, 1986). Especially the concept has been used in studies of accessibility. However, thresholds have also been incorporated in models of choice behaviour. Krishnan (1977) developed a logit model which postulated that an individual will only prefer an alternative over another, if its utility exceeds that of the other alternative by at least a positive value. His model has been extended by Lioukas (1984) to the case of more than two choice alternatives. In the same way, Young and his associates have incorporated thresholds in elimination-by-aspect models, which they applied to location problems and residential choice behaviour (Young, 1983, 1984; Young and Ogden, 1983; Young and Richardson, 1980, 1983}, while Recker and Golob (1979) and Gensch and Svestka (1979) included thresholds in lexicographic decision rules. Finally, Meyer and Johnson's stochastic elimination model is also based on the idea that choice alternatives should meet certain threshold values to remain in an individual's choice set (Johnson and Meyer, 1984). The idea of determining all possible choice sets is similar to the approach adopted by Smith and Slater (1981) for including choice set constraints in models of labour flows. Data The hybrid choice model was tested on data pertaining to respondents residing in the province of Zuid-Holland, The Netherlands. A variety of data was collected but for the present study only few of these were relevant. As pointed out in the introductory section the model could be applied with minor modifications to actual choice processes, but in the present case the model was used to uncover residential preference formation since data on actual choice behaviour were not collected in the Zuid-Holland sample. Only 229

5 if one assumes that people will choose their most preferred residential environment, the results of the present study can be interpreted in terms of residential choice behaviour. Household's preferences were elicited in the following way. To each respondent a set of 13 descriptions of residential environments, selected according to the principals of experimental design was shown. In addition photographs were used to visualise the descriptions of the hypothetical environments, which differed in terms of the following four attributes: tenure, type of dwelling, number of rooms, and traffic situation (see Veldhuisen and Hacfoort, 1985). These attributes were selected because previous analysis on the same sample had shown these to be among the most important attributes influencing residential decision-making. Respondents were requested to sort the thirteen descriptions into two sets, one consisting of residential environments which they liked less than their present environment and the other consisting of those environments for which their evaluation was higher than for their present residence. Each respondent was asked to rank the latter set of hypothetical residential environments in terms of overall preference. This procedure yields a ranking of the residential environments in terms of overall preference. The alternative with the highest overall preference was used to form the dependent variable. TABLE I. Parameter values of the hybrid model. attribute parameter threshold error tenure traffic situation number of rooms type of dwelling As described in the previous section, the actual attributes of the choice alternatives can be taken as the independent variables of the model. The advantage of such an approach would be that the findings of the model can be interpreted directly in terms of housing characteristics. On the other hand, households may evaluate a particular environment differently and hence subjective evaluations could be used as well. In the present study the latter approach was therefore adopted. Respondents were invited to express their evaluation of the set of housing attributes and the set of attributes describing the residential environment on a nine point category scale ranging from excellent to extremely bad. These measurements constitute the independent variables of the model. Findings The calibration of the model involved a time-consuming process. Since the properties of the parameter space are not well known and are likely to be rather irregular, a series of searches was used to explore the parameter space. In particular a combination of sequential linear searches and gradient searches was used to calibrate the model. First, the thresholds and error terms were calibrated. These terms given, the probabilities associated with 230

6 different choice sets could be calculated in a straightforward way. Next, the parameters for the utility expression were calibrated, given these choice probabilities. This process was repeated until no further improvement of model fit was obtained. To investigate the stability of the resulting solution, the calibration process was repeated a number of times with different starting values. Squared deviance was used as the optimization criterium. The findings of the calibration are given in table I. Table I suggests that the hybrid compensatory-noncompensatory model is capable of reproducing the preference formation process in a satisfactory manner. The squared deviance is equal to , implying that the average percentage error is only Table l also indicates that the traffic situation attribute is the most critical screening attribute in the sense that it has a low associated error term, which implies that a relatively low score on this attribute will exclude the choice alternative from the choice set. The highest threshold value is associated with the attribute 'type of dwelling', but the error term suggests a considerible degree of heterogeneity with respect to this attribute. TABLE 2. attribute Parameter values of the multinomial logit model. parameter tenure traffic situation number of rooms type of dwelling As stated in the introductory section of the present article, the rationale behind the hybrid model is to adjust for some properties of the standard multinomial logit (MNL) model in order to improve its predictive ability. Therefore it seems logical to compare the results obtained for the hybrid model with those found when the standard multinomial logit model is applied to the data. The MNL model has been applied in a straightforward manner. The first preference probabilities that were derived constituted the dependent variable. Again squared deviance was used as a goodness-of-fit criterium. The derived parameter values of the model are given in table 2. Table 2 shows that according to the multinomial logit model the type of dwelling is the most important attribute, followed by number of rooms, tenure and traffic situation respectively. Note that this ordering differs somewhat from the rank ordering obtained for the hybrid model in that the attributes type of dwelling and number of rooms have changed places. The multinomial logit model is able to reproduce the data in a very satisfactory manner: the squared deviance is only , which is just slightly worse than the value obtained for the hybrid model. These results indicate that, although the hybrid model performs somewhat better, (and one should keep in mind the larger number of parameters associated with the hybrid model), the MNL model performs almost equally well. Hence, it could be argued that theoretically the hybrid model should be preferred, but that from a practical point of 231

7 view one should preferably use the MNL model, since it requires considerably less computing time and is far more easy to use. In fact these results can be taken as another piece of evidence showing the robustness of the MNL model. Conclusion and discussion The main thrust of the present article has been to advance a new hybrid compensatory-noncompensatory model of housing and residential preference structures. The model is based on the idea that households first screen candidate housing environments on a series of attributes in a noncompensatory fashion. If choice alternatives do not meet such a set of minimum conditions they will not be considered as candidates for choice. The remaining alternatives are then evaluated in a compensatory fashion in which their advantages and disadvantages are compared. The results obtained in the empirical part of the paper suggest the theoretical value of the hybrid model. The model's predictive validity appears to be satisfactory. However, future research may tell whether the hybrid model performs better than the more commonly used multinomial and nested logit models on other data sets as well. It should also be stressed that the model as outlined in the present paper is only the most simple form one could think off. The model may be extended by including other effects, which may influence residential choice behaviour such as agglomeration and competition effects, effects of substitutability, ideal points etc. Such extensions may increase the predictive performance of the model and will probably increase its theoretical richness, but at the same time they will increase even further the computing difficulties in the calibration process. Acknowledgement This research project has been carried out partly with the financial assistance of The National Foundation for the Advancement of Pure Scientific Research (ZWO/SRO). References Gensch, D.H. and J.A. Svestka (1979) "An exact hierarchical algorithm for determining aggregate statistics from individual choice data", Management Science, vol.25: Johnson, E.J. and R.J. Meyer (1984) "Compensatory choice models of noncompensatory processes: the effect of varying context", Journal of Consumer Research, vol. 1 l: Krishnan, K.S. (1977) "Incorporating thresholds of indifference in probabilistic choice models", Management science, vol.23: Lierop, W. van (1981) Towards a new disaggregate model for the housing market, Amsterdam: Department of Economics, Free University. 232

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