# Analyzing heterogeneity in young's preferences for leisure activities

### Analyzing heterogeneity in young's preferences for leisure activities at nighttime: indicators of alcohol's attitude and behaviors in a stated choice experiment

### Introduction

This paper examines the distribution of preferences in a sample of university and high school students who chose between hypothetical nighttime leisure activities with different characteristics. In this sense it is an explorative paper that aims to clarify two aspects: which is the more appropriate model to understand heterogeneity in young's preferences and which is the most appropriate set, if it exist, of the individual's variables to use for implement this analysis.

A specifically relevant issue in this context regards aspects of behavior that are not directly linked to socioeconomic characteristics, but to attitudes, group behavior, networks, life styles and people's social contacts. All this holds especially for the probably most important segment of nighttime leisure activity, i.e. the youth.

Data from stated choice experiments are usually analyzed using probit or logit models or random effects extensions of them. These approaches produce estimates of the mean taste weights attributed to the attributes in the experiment by the sampled individuals. If researcher think that different socioeconomic groups have entirely different preferences, then it is possible to develop a distinct model for each group. However, some of the preference heterogeneity is unrelated to observable personal characteristics.

In addition to standard multinomial logit models, mixed and latent class logit models are used to analyze the data from our stated choice experiment. Mixed and latent class logit models are extensions of the standard logit model which make possible, given certain assumptions, to estimate the distribution of preferences for the attributes in the experiment. Another advantage is that they account for the fact that each individual makes several choices which cannot be assumed to be independent. These properties have been recognized in the discrete choice models literature for some time (…) and there have been a huge number of mixed logit model applications (…). The latent class logit model is frequently applied in marketing research. However, the methodological contribution of the current paper is just to conduct a comparison of these two approaches to modeling preference heterogeneity using stated choice experiments data.

The analysis reveals significant preference heterogeneity for all the attributes in the experiment and both the mixed and latent class logit models lead to significant improvements in fit compared to the standard logit model. Moreover, the distribution of preferences implied by the preferred mixed and latent class models is similar for many attributes.

These results underline the additional insights that can be made from accounting for preference heterogeneity when analyzing data from discrete choice experiments.

Section 2 outlines the mixed and latent class logit models, Section 3 describes the discrete choice experiment and

Section 4 reports the results of the analysis. Section 5 offers a discussion.

### Methodology

Mixed Multinomial Logit (MLM) and Latent Class Logit (LCM) models extend the standard Multinomial Logit (MNL) model by allowing the parameters - which represent taste weights - to vary between respondents. This capacity to model preference heterogeneity has the potential to greatly enhance the behavioral realism of the model compared to the standard logit. In the present context, for instance, some students might have a strong preference for pub regardless of the other attributes or activities of the night, whereas others may prefer cinemas. While in the MNL model this variation in preferences may be captured by interacting design attributes with the socio-demographic characteristics of the respondents, it is likely that some of the preference heterogeneity is unrelated to observable personal characteristics. An additional limitation of the MNL is that it makes the assumption that the observations are independent, which is unlikely in data from discrete choice experiments where the respondents complete several hypothetical choices.

The mixed and latent class models have the potential to overcome these limitations of the standard logit model and they offer different ways of capturing heterogeneity. A paper by Greene and Hensher (2003) compared the MLM with the LCM by using a dataset of road type's choice in New Zealand in 2000 where drivers where surveyed with the intent of establishing their preferences for road environments. They concluded that MLM and LCM give attractive specifications than the MNL, but it is not possible to decide that one approach is unambiguously preferred to the other. In the following these models are described in more detail.

Following the Random Utility Models (RUM) the individual chooses the alternative providing the high level of utility and assuming that the alternatives in the choice set are mutually exclusive alternatives we can rely to discrete choice literature (see …).

Consider a sample of N decision makers with the choice of J alternatives on T choice occasions, it is possible to define the utility that individual n derives from choosing alternative j on choice occasion t is given by:

Unjt=Vxnjt,sn+εnjt

On one hand εnjt is the random part of the utility function, also called disturbance (or random component). It captures the factors reflecting the individual specific idiosyncrasies of tastes which are not observed from the researcher.

On the other hand Vnjt is called the systematic (or representative) component of the utility, a sort of mean of Unjt, and it describes the role of measured (observed from the researcher) attributes on choices. In this sense, xnjt is a vector of the attribute values for alternative j on choice occasion t as viewed by the decision maker n and it common to all the individual. Instead, sn is a vector of characteristics of individual n and it is individual specific. The distinction between random and utility part of the utility function does not mean that the individuals maximize utility in a random way. Manski (1973) identify the following distinct sources of randomness: unobserved attributes, unobserved taste variations, measurement errors and instrumental variables. For this reasons, in general, it is possible to express the utility of an alternative as a sum of observable and unobservable components. Imposing different structure on the random component imply different assumptions on the sampled population distribution across the alternative in the choice set. …

The random component is assumed to be distributed IID extreme value.

The distribution of β can be either continuous or discrete. A model with continuously distributed coefficients is usually called a mixed logit (ML) model. Since the contributions by Bhat (1998), Revelt and Train (1998) and Brownstone and Train (1999) the mixed logit model has been applied in several contexts in economics including environmental and transport economics (e.g. Train, 1998; Hensher, 2001; Greene and Hensher, 2003; …). A model in which the coefficients follow a discrete distribution, on the other hand, is called a latent class logit model. The latent class logit model has been frequently applied in marketing (see McLachlan and Peel, 2000, for a review) and, more recently, in environmental and transport economics (e.g. Greene and Hensher, 2003; Scarpa and Thiene, 2005; …).

Apart from the difference in the specification of the distribution of the coefficients the mixed and latent class models differ in another respect: while both models can handle correlations between the coefficients the mixed logit is often estimated with uncorrelated coefficients while the latent class model implicitly allows the coefficients to be correlated. Whether allowing for correlations between the coefficients matters is an empirical question that in the mixed logit case can be tested by comparing two models with and without correlated coefficients using a likelihood ratio test.

Following Revelt and Train (1998) we assume a sample of N respondents with the choice of J alternatives on T choice occasions. The utility that individual n derives from choosing alternative j on choice occasion t is given by

Unjt = β nxnjt + εnjt

where βn is a vector of individual-specific coefficients, xnjt is a vector of observed attributes relating to individual n and alternative j on choice occasion t and εnjt is a random term which is assumed to be distributed IID extreme value. The density for β is denoted as f (β|θ) where θ are the parameters of the distribution. Conditional on knowing βn the probability of respondent n choosing alternative i on choice occasion t is given by

Lnit (βn) = exp(β nxnit )

which is the logit formula (McFadden, 1974). The probability of the observed sequence of choices conditional on

knowing βn is given by

Sn(βn) =

where i(n, t) denotes the alternative chosen by individual n on choice occasion t. The unconditional probability of the

observed sequence of choices is the conditional probability integrated over the distribution of β:

Pn(θ) =

_

Sn(β)f (β|θ) dβ (3)

The unconditional probability is thus a weighted average of a product of logit formulas evaluated at different values

of β, with the weights given by the density f.

Another difference between the models is the estimation method. While the log-likelihood for both models is given

by LL(θ) = _N

n=1 ln Pn(θ) this expression cannot be solved analytically in the mixed logit case, and it is therefore approximated using simulation methods (see Train, 2003). The simulated log-likelihood is given by

SLLML(θ) =

(4)

where R is the number of replications and βr is the r th draw from f (β|θ). Estimation of the latent class logit on the other hand does not require simulation methods. The log-likelihood for the latent class logit model with Q latent classes is given by

LLLC(θ) =

⎦ (5)

where Hnq is the probability that individual n belongs to class q and βq is a vector of class-specific coefficients.

Following Greene and Hensher (2003) Hnq is specified to have the multinomial logit form:

Hnq =

(6)

where zn is a vector of observed characteristics of individual n and γq are vectors of parameters to be estimated. The

Q th parameter vector is normalised to zero for identification purposes.

Both the mixed and latent class logit models can be used to estimate respondent-specific taste parameters (Revelt

and Train, 2000; Greene and Hensher, 2003). The expected value of β conditional on a given response pattern yn and

a set of alternatives characterised by xn is given by

E[β|yn, xn] =

_

Intuitively this can be thought of as the conditional mean of the coefficient distribution for the sub-group of individuals who face the same alternatives and make the same choices. Revelt and Train (2000) show that E[β|yn, xn] can be estimated based on a mixed logit specification by simulating Eq. (7):

(8)

where βr is the r th draw from f (β|ˆθ ). In the latent class logit case Greene and Hensher (2003) show that an estimate

of E[β|yn, xn] is given by3

ˆβ

In the present paper we follow Hensher and Greene's approach of plotting the estimated distributions of individualspecific parameters as a means of comparing the results of the different models.

### Attitudinal and Behavioral Indicators Variables

### The choice experiment

Delivering services to young people during nighttime such as collective means of transport or … requires an understanding of their behavior and preferences.

There are two data types used to explore discrete choices and they are Revealed Preference (RP) and Stated Preference (SP) data. The RP approach collects real choice data…. On the contrary, stated choice method analyses how individuals respond when faced with hypothetical choice situations, defined by a set of alternatives, attributes and levels.

Since little relevant revealed preference data is available a stated preference discrete choice experiment was developed at University of Lugano and High School … with the aim of quantifying the relative strength of students' preferences for nighttime activities. After two focus groups (…) and pilot testing the activities in Table 1 were chosen for inclusion in the experiment. There are two points that need some additional explanation. The first is the… is controversial…

The second is the inclusion of the cost attribute … is controversial since the British health system is free at the point of care and could potentially increase non-response. On the other hand including cost has the substantial advantage of facilitating estimation of willingness to pay, and the pilot indicated that students found it acceptable.

On the basis of the … combinations of attribute levels in the full factorial design, 24 choice sets with 2 alternatives and a no choice option were constructed using a orthogonal.. . The 32 choice sets were then randomly ‘blocked' into two sets of 12 choices. A sample of students was selected from ….

Each student received a questionnaire including 12 choice sets and a limited set of questions regarding sociodemographic characteristics and … TPB questionnaire.. . In each of the choice sets the student was presented with two alternative night programs with different characteristics (see Fig. 1 for an example).

It is expected that students generally prefer to … , lower cost, a … ,. See the appendix for a detailed description of the questionnaire development.

The response rate was … . The estimation sample consists of …. usable responses by … respondents.

### Results

Alternative specifications of the choice model