Combining Discrete And Continuous Representations Of Preference Heterogeneity: A Latent Class Approach

In this article, we will be reviewing a research paper, titled: Combining Discrete and Continuous Representations of Preference Heterogeneity: A Latent Class Approach. Possible methods to incorporate variability in leisure requirements are examined in this research paper.

The focus of the paper is on finding alternative methods to incorporate heterogeneity in recreational demand. The researchers have applied a hybrid model combining discrete and continuous heterogeneity representations of tastes to capture the defining features of both latent class (LC) and random parameter logit specifications (LC-RPL).

A database of recreational trips to forest sites in Mallorca (Spain) was used to compare the empirical performance of this new approach with common estimation approaches in recreational demand modeling such as the conditional logit, the Random Parameter Logit (RPL), and the Latent Class (LC) model.

The Issue With Unobserved Preference Heterogeneity

Distinctive preferences and choices of people for a given commodity differ enormously among individuals, which is referred to as preference heterogeneity (Feick & Higie, 1992). Researchers have become more curious about the examination of preference heterogeneity and so it has become a major topic in the choice modeling research.

When heterogeneous preferences are not adequately accommodated, this results in the loss of important data that is needed, and this ultimately leads to inaccurate estimations and misleading welfare assessments, according to studies. Furthermore, when heterogeneous preferences are not adequately compensated for, inaccurate predictions and skewed welfare measures may be generated.

In this context, the computing revolution of the last two decades consequent generalization of simulation methods (e.g. simulated maximum likelihood estimation), has allowed researchers to estimate models with more flexible specifications overcoming the potentially restrictive assumptions implicit with conventional specifications such as conditional or nested logit models

Two techniques have been developed and are often compared in recreational demand studies:

  • Latent Class Model (LC)
  • The Random Parameter Logit (RPL)

Both of these techniques are popular methods for handling choice heterogeneity that is constantly referred to in studies involving recreational needs. 

The concept of homogeneity existing inside a group is too limiting to effectively depict consumer choices because it is improbable that all of the people with similar socioeconomic features will also have similar choices.

However, empirical data suggests that applying the LC definition to a population’s preferences may oversimplify them, particularly when only a few classes are specified and the underlying distribution of choices is continuous within classes (Allenby & Rossi, 1998).

The Proposition Of The Hybrid Model

To deal with the challenges of the traditional Random Parameter Logit and Latent Class approaches, this research proposes a hybrid modeling technique (LC-RPL) that combines continuous and discrete descriptions of choices.

The Latent Class—Random Parameter Logit model (LC-RPL) has been used in a recreational consumption context to explain taste heterogeneity through two different methods:

  • Recognizing dissimilar groups based on socioeconomic features
  • Taking taste preferences between many people in the very same group into consideration (also referred to as within-group heterogeneity).

The experimental effectiveness of this new technique was compared to standard approximation methods in leisure need analysis like the conditional logit (CL), the Latent Class model, and the Random Parameter Logit model (RPL) using a dataset of leisure visits to forest places in Mallorca (Spain).

To reveal details on simulation results, a study of goodness-of-fit metrics and in-sample predictions across parameters was employed. Furthermore, the welfare consequences of two policy situations were evaluated by comparing. These were: 

  • A Quality Improvement
  • Location restrictions

These welfare consequences of two policy alternatives were contrasted to see if Willingness-To-Pay (WTP) for these two policy scenarios and its dispersion across people vary hugely between different representations of taste heterogeneity in choice modeling.

Theoretical Background Behind LC-RPL

The LC-RPL model, like the normal Latent Class specification, presupposes the occurrence of K groups or segments in a collection of N respondents, where K is exogenously defined by the researcher. The objective functions of a person can differ between these divisions.

However, as these classes are latent, not observable by the analyst, a probabilistic equation on explaining the assignment of each individual n into the K segments has to be defined.

For the Conditional Logit Model (Hanemann, 1982), the Random Parameter Logit model (RPL) (Train, 1998, 230-239), the Latent Class model (LC) (Boxall & Adamowicz, 2002, 421-446), and the LC-RPL, WTP measurements based on a study conducted by Small and Rosen (1981) have been established. Just the formula for the LC-RPL is presented in the study, which compares the WTP measurements of the four different classifiers.

In this model, heterogeneity enters in two ways:

(a) The anticipated WTP is dependent on individual preferences βn

(b) The anticipated WTP must be weighted by segment membership for every person.

The Findings Of The Authors Based On The Data Collected

The researchers of this study employed disclosed data from one-day leisure outings to woodlands on the Spanish island of Mallorca. The parts that followed the data section of the article went over the facts on both the environmental considerations of forest locations and the leisure activity of Mallorcans.

Strongly differentiated location criteria were utilized to define up to 59 forest areas to evaluate all leisure options on the territory.

Figure 1 shows some detailed information about the fifty-nine sites’ ecological and leisure characteristics.

Figure 1: The parameters of the site

Regarding information collection of recreational behavior, the researchers used a regional-wide questionnaire administered at the residences of 1043 Mallorcan inhabitants by expert surveyors.

In total, 841 people were a part of the sample of this program who had conducted one or more excursions to the woods in the year before the research questionnaire was conducted. As a result, forest leisure visits are distinguished by tourists with different socioeconomic characteristics and kinds of woods leisure activity.

This resulted in the creation of a suitable condition for evaluating the differences amongst choices of individuals and determining regardless of whether the variety of choices for on-site qualities leads to different WTP for different forest guidelines.

The latest form of the questionnaire was administered from April to July in 2006, with several respondents of somewhat more than 60%. This all was done after it had been tested in a preliminary survey. It was structured such that it collected information about things such as:

  • The number of journeys made,
  • The locations  that were paid a visit to, 
  • the kinds of activities done on the premises (such as trekking, having a picnic, going for walks, outdoor activities, noticing the plants and animals, outdoor pursuits such as bike riding, attempting to climb, etc.)
  • the participant’s family income-related questions (such as age, the year they were born in, which level of education they are at, etc.

A detailed description of these characteristics is given in Figure 2.

Figure 2: The statistics of the visitors

Figures 3a and 3b show the economic findings for the LC-RPL system described in section two of the paper (Table 3 of the original article).

Figure 3a: Economic Findings of LC-RPL system

Figure 3b: Economic Findings of LC-RPL system

The CL, RPL, and LC models were also computed and displayed in Figure 3 as baseline instances for contrast. Researchers utilized 1,000 quasi-random Halton draws to approximate log-likelihood values. They incorporate travel costs as well as a vast number of environmental features and leisure activities that characterize forest sites when developing the model.

The researchers incorporated travel costs as well as a vast number of environmental features and recreation centers behavior racterise forest areas when developing the model, the details of this are visible in Figure 1. 

Whereas more particular location variables were predicted in different requirements, only the main attributes that are the most important determinants of choice are included in the final model, avoiding considerable collinearity concerns.

Figure 4 summarizes the welfare outcomes of both policy conditions (Table 4 in the original article). Just as the researchers anticipated, mean and median WTP (as well as confidence intervals) differs dramatically between estimation procedures, and much of this difference depends on the treatment of heterogeneity. 

Figure 4: Welfare Outcomes

Taking the quality enhancement case initially, Figure 5 (Figure 1 in the original article) shows how the allocation of WTP varies by models for every level (stated in rows and levels in columns).


Figure 5: Histograms of the estimated individual WTP for a 25% increase in arboreal cover. This demonstrates how for every tier (given in columns) the allocation of WTP varies by model (reported in rows). This shows how for each tier the distribution of WTP differs by model. The distributional effects captured by the LC and LC-RPL are consistent with the findings from previous studies where individuals with higher income are willing to pay more for sie-specific attributes.

In both models, the ranges for welfare indicators connected to site closing strategy are shown in Figure 6 (Figure 2 in the original article). Visible variances across levels and models can be seen once again.

Figure 6: For both models, illustrates the distributions for welfare indicators connected to the site closure plan. Significant variances across tiers and models can be seen once more. This shows the distributions for welfare measures related to the site closure policy under both models, with significant differences seen between tiers and models.

The Wilcoxon non-parametric test was also used by the researchers to explicitly test for changes in dispersion across tiers) and intra-tier. Figure 7 (Table 5 in the original article) shows the outcomes of the screening for variances.

Figure 7: This illustrates that when shifting between tiers in the same model either with change in policy or shutdown, there are significant variations. The results show that significant differences exist when moving across tiers within the same model for either policy change, even for the case of closures. Apart from the mean welfare effect, the treatment of heterogeneity provides insight into population distribution.


Practical Implications Of Combining Discrete And Continuous Heterogeneity Representations

The LC-RPL approach developed in this paper has the potential to increase the effectiveness of policy decisions by analyzing the heterogeneous preferences of individuals in the context of destination choice.

Results calculated from the findings show that the potential of this hybrid model in those situations where representation by continuous preference is limited, the heterogeneity is significant within discrete group of individuals.

Then, the ability of the LC-RPL model to identify these groups, based on their socioeconomic characteristics, at the same time that allows for within-group taste heterogeneity towards different environmental sire attributes, can provide useful information to policy-makers in different contexts.


This paper reviews alternative methods for incorporating heterogeneity in models of recreational demand. The results show that the existence of heterogeneous preferences for environmental attributes related to socioeconomic characteristics (income, education, residence, etc.) and two behavioral groups with different socioeconomic profiles are identified in the empirical application. 

Preference heterogeneity demonstrates better performance for both, goodness-of-fit and in-sample forecasts. Whereas discrete (LC) and discrete-continuous (LC-RPL) representations of heterogeneity out-perform those specifications based on RPL alone. Lastly, the LC-RPL model outperforms all other models for goodness-of-fit and best in-sample predictions.

To conclude, the LC-RPL approach developed in this paper has the capability to enhance the effectiveness of policy decisions by analyzing the heterogeneous preferences of individuals in the content of recreational destination choice. Although, more research and empirical studies are needed in order to strengthen the choice models when heterogeneity in preferences is present.


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