A Latent Class Model for Discrete Choice Analysis: Contrasts with Mixed Logit

The multinomial logit model (MNL) has for many years provided the fundamental platform for the analysis of discrete choice. The basic model’s several shortcomings, most notably its inherent assumption of independence from irrelevant alternatives (IIA) have motivated researchers to develop a variety of alternative formulations. The mixed logit model stands as one of the most significant of these extensions. This paper proposes a semi-parametric extension of the MNL, based on the latent class formulation, which resembles the mixed logit model but which relaxes its requirement that the analyst makes specific assumptions about the distributions of parameters across individuals. An application of the model to the choice of long distance travel by three road types (2-lane, 4-lane without a median and 4-lane with a median) by car in New Zealand is used to compare the MNL latent class model with mixed logit

Ordered choices and heterogeneity in attribute processing

A growing number of empirical studies involve the assessment of influences on a choice amongst ordered discrete alternatives. Ordered logit and probit models are well known, including extensions to accommodate random parameters and heteroscedasticity in unobserved variance. This paper extends the ordered choice random parameter model to permit random parameterization of thresholds and decomposition to establish observed sources of systematic variation in the threshold parameter distribution. We illustrate the empirical gains of this model over the traditional ordered choice model in the context of identifying candidate influences on the role that specific attributes play, in the sense of being ignored or not, in an individual’s choice amongst unlabelled attribute packages of alternative tolled and non-tolled routes for the commuting trip. The empirical ordering represents the number of attributes attended to from the full fixed set. The evidence suggests that there is significant heterogeneity associated with the thresholds, that can be connected to systematic sources associated with the respondent (i.e., gender) and the choice experiment, and hence the generalized extension of the ordered choice model is an improvement, behaviourally, over the simpler model

Ordered choices and heterogeneity in attribute processing

A growing number of empirical studies involve the assessment of influences on a choice amongst ordered discrete alternatives. Ordered logit and probit models are well known, including extensions to accommodate random parameters and heteroscedasticity in unobserved variance. This paper extends the ordered choice random parameter model to permit random parameterization of thresholds and decomposition to establish observed sources of systematic variation in the threshold parameter distribution. We illustrate the empirical gains of this model in the context of an individual’s choice amongst unlabelled attribute packages of alternative tolled and non-tolled routes for the commuting trip, and the role that each attribute plays, in the sense of being ignored or not. The ordering represents the number of attributes attended to from the full fixed set. The evidence suggests that there is significant heterogeneity associated with the thresholds that can be connected to systematic sources associated with the respondent (i.e., gender) and the choice experiment (i.e., aggregation treatment of components of travel time)

Non-attendance and dual processing of common-metric attributes in choice analysis: A latent class specification

There is a growing literature that promotes the presence of process heterogeneity in the way that individuals evaluate packages of attributes in real or hypothetical markets and make choices. A centerpiece of current research is the identification of rules that individuals invoke when processing information in stated choice experiments. These rules may be heuristics used in everyday choice making as well as manifestations of ways of coping with the amount of information shown in choice experiment scenarios. In this paper, using the latent class framework, we define classes based on rules that recognise the non-attendance of one or more attributes, as well as on the addition and the parameter transfer of common-metric attributes. These processing strategies are postulated to be used in real markets as a form of cognitive rationalization. We use a stated choice data set, where car driving individuals choose between tolled and non-tolled routes, to translate this new evidence into a willingness to pay (WTP) for travel time savings, and contrast it with the results from a model specification in which all attributes are assumed to be attended to and are not added up with parameter preservation. We find that the WTP is significantly higher, on average, than the estimate obtained from the commonly used full relevance and attribute preservation specification

The Mixed Logit Model: The State of Practice

The mixed logit model is considered to be the most promising state of the art discrete choice model currently available. Increasingly researchers and practitioners are estimating mixed logit models of various degrees of sophistication with mixtures of revealed preference and stated choice data. It is timely to review progress in model estimation since the learning curve is steep and the unwary are likely to fall into a chasm if not careful. These chasms are very deep indeed given the complexity of the mixed logit model. Although the theory is relatively clear, estimation and data issues are far from clear. Indeed there is a great deal of potential mis-inference consequent on trying to extract increased behavioural realism from data that are often not able to comply with the demands of mixed logit models. Possibly for the first time we now have an estimation method that requires extremely high quality data if the analyst wishes to take advantage of the extended behavioural capabilities of such models. This paper focuses on the new opportunities offered by mixed logit models and some issues to be aware of to avoid misuse of such advanced discrete choice methods by the practitioner

Specification and Estimation of Nested Logit Models

The nested logit model is currently the preferred extension to the simple multinomial logit discrete choice model. The appeal of the nested logit model is its ability to accommodate differential degrees of interdependence (i.e. similarity) between subsets of alternatives in a choice set. The received literature displays a frequent lack of attention to the very precise form that a nested logit model must take to ensure that the resulting model is invariant to normalisation of scale and is consistent with utility maximisation. Some recent papers by Koppelman and Wen (1998a, 1998b) and Hunt (1998) have addressed some aspects of this issue, but some important points remain somewhat ambiguous. When utility function parameters have different implicit scales, imposing equality restrictions on common attributes associated with different alternatives (i.e. making them generic) can distort these differences in scale. Model scale parameters are then ‘forced’ to take up the real differences that should be handled via the utility function parameters. With many variations in model specification appearing in the literature, comparisons become difficult, if not impossible, without clear statements of the precise form of the nested logit model. There are a number of approaches to achieving this, with some or all of them available as options in commercially available software packages. This note seeks to clarify the issue, and to establish the points of similarity and dissimilarity of the different formulations that appear in the literature

Heteroscedastic Control for Random Coefficients and Error Components in Mixed Logit

Developments in simulation methods, and the computational power that is now available, have enabled open-form discrete choice models such as mixed logit to be estimated with relative ease. The random parameter (RP) form has been used to identify preference heterogeneity, which can be mapped to specific individuals through re-parameterisation of the mean and/or variance of each RP’s distribution. However this formulation depends on the selection of random parameters to reveal such heterogeneity, with any residual heterogeneity forced into the constant variance condition of the extreme value type 1 distribution of the classical multinomial logit model. In this paper we enhance the mixed logit model to capture additional alternative-specific unobserved variation not subject to the constant variance condition, which is independent of sources revealed through random parameters. An empirical example is presented to illustrate the additional information obtained from this model