About attitudes and perceptions: finding the proper way to consider latent variables in discrete choice models

Abstract

We provide an in-depth theoretical discussion about the differences between individual-specific latent constructs (representing attitudes, for example, but also other characteristics such as values or personality traits) and alternative-specific latent constructs (that may represent perceptions) affecting the choice-making process of individuals; we also carry out an empirical exercise to analyze their effects. This discussion is of importance, as the majority of papers considering attitudinal latent variables just take these as attributes affecting directly the utility of a certain alternative, while systematic taste variations are rarely considered and perceptions are mostly ignored. The results of our case study show that perceptions may indeed affect the decision making process and that they are able to capture a significant part of the variability that is normally explained by alternative specific constants. Furthermore, our results indicate that attitudes may be a reason for systematic taste variations, and that a proper categorization of latent variables, in accordance with underlying theory, may outperform the customary assumption of linearity.

Introduction

The last decades have seen discrete choice models (DCM) become a key element in travel demand modelling and forecasting (Ortúzar and Willumsen 2011). Their current state-of-practice considers objective characteristics of the alternatives and the individuals as explanatory variables, and yield as output individual probabilities of choice between different alternatives. It is also well known that individual specific latent attributes (i.e. attitudes) and alternative specific latent attributes (i.e. perceptions) play a role in the decision making process. The usual approach to take these into account considers the estimation of multiple indicator multiple cause (MIMIC) models, as suggested by Bollen (1989). The joint use of MIMIC models and DCM leads to state-of-the-art hybrid discrete choice (HDC) models (Ashok et al. 2002; Ben-Akiva et al. 2002; Bolduc and Alvarez-Daziano 2010).

The transport literature has provided abundant empirical and theoretical evidence about the advantages of the HDC approach and the use of these models has gained popularity (van Acker et al. 2011; Bahamonde-Birke et al. 2010; Raveau et al. 2012; Daziano and Bolduc, 2013; Paulssen et al. 2014; among others). Notwithstanding, attitudes and perceptions are usually not differentiated, ignoring that both may be expressions of different value judgments. While attitudes express a characteristic of the individuals toward life, society, etc. and are intrinsically related to them, perceptions are exclusively related to the way certain alternatives are perceived. Thus, an attitude resembles an individual’s socio-economic characteristic, while a perception is intrinsically associated with an alternative.¹ This difference has important implications and the way in which both should be treated in a DCM is completely different. In turn, this issue affects not only the way in which latent variables (LV) are estimated but almost all hypotheses concerning them. Hence, different assumptions ma have an effect on both the way the LV are constructed through the MIMIC model as well as on the manner in which these constructs are reflected in the utility function of the DCM.

This paper aims to provide an in-depth discussion about the different ways to treat LV in DCMs. We discuss the implications of the latent constructs being individual or alternative specific and different approaches to deal with them. Along this line, we conduct an empirical experiment to test the aforementioned approaches (e.g. analysing attitudinal LV in continuous and categorized fashions, or considering interactions between attitudinal LV and attributes of the alternatives). Furthermore we discuss strategies to deal with perceptual indicators that depend on different attributes of the alternatives; the latter allows constructing perceptual LV that are sensitive to changes in the alternatives.

The rest of the paper is organized as follows. “Theoretical background” section offers a theoretical overview of HDC models, while in “Attitudes, perceptions and latent constructs in choice modelling” section presents the above-described discussion. “Case study” section describes an experiment carried out to test the hypotheses of the previous section, and its results are discussed in “Model estimation” section. Finally, “Conclusions” section summarizes our conclusions.

Theoretical background

Under the assumption of rational decision makers, it can be postulated that individuals q facing a set of available alternatives A(q), will choose the alternative i that maximizes their perceived utility. In a random utility theory framework (Thurstone 1927; McFadden 1974), it is possible to represent this utility as the sum of a representative component (V _iq ) and an error term (ε _iq ). When considering a HDC modelling framework (Ben-Akiva et al. 2002), the modeller attempts to depict abstract attributes as measurable variables in order to include them as part of the systematic utility. Hereby, immaterial constructs, known as LV ($\eta_{liq}$), are also included into the modelling. These variables are supposed to represent attitudes and/or perceptions (or other unobservable characteristics) of the individuals and, as cannot be directly observed, they must be constructed as a function of other positively observed variables. The usual approach to construct these LV relies on a MIMIC structure (Zellner 1970; Bollen 1989). Here, the LV are explained by a set of characteristics of the individuals and the alternatives (s _iqr ), through so called structural equations, while explaining, at the same time, a set of attitudinal and/or perceptual indicators (I _ziq ), previously gathered from the individuals, through so called measurement equations. If we assume a linear distribution for the indicators, this framework can be represented through the following equations:

$$ \eta_{liq} = \sum\limits_{r} {\alpha_{lri} \cdot S_{riq} + v_{liq} } $$

(1)

$$ I_{ziq} = \sum\limits_{l} {\gamma_{lzi} \cdot \eta_{liq} + \zeta_{ziq} } $$

(2)

where the indices i, q, r, l and z refer to alternatives, individuals, exogenous variables, LV and indicators, respectively. The error terms υ _liq and ζ _ziq can follow any distribution but they are typically assumed to distribute Normal with mean zero and a certain covariance matrix. Finally, α _lri and γ _lzi are parameters to be jointly estimated.

If we assume a linear specification in V _iq , the utility function can be expressed as (3).

$$ U_{iq} = \sum\limits_{k} {\beta_{ki} \cdot X_{kiq} + \sum\limits_{l} {\theta_{li} \cdot \eta_{liq} + \varepsilon_{iq} } } $$

(3)

Under the assumption that the error terms ε _iq in (3) are independent and identically distributed (IID) Extreme Value Type 1 (EV1), the differences between the utilities associated with the alternatives follow a Logistic distribution, leading to the well-known multinomial logit (MNL) model (Domencich and McFadden 1975).

The estimation of both parts of the model should be performed simultaneously, as a sequential estimation considering first the MIMIC part as an isolated system and evaluating afterwards the expected values for the LV cannot guarantee consistent and unbiased estimators (Train et al. 1987; Ben-Akiva et al. 2002). However, empirical evidence sustains the thesis that the sequential estimation produces no major discrepancies regarding the ratios between the estimated parameters and, therefore, the marginal rates of substitution (Raveau et al. 2010; Bahamonde-Birke et al. 2010). Nevertheless Bahamonde-Birke and Ortúzar (2014a, b) prove that the estimators may indeed be affected by a significant deflation bias (affecting all estimated parameters).

An intermediate path between the simultaneous and classical sequential estimation consists of estimating the model sequentially, but taking into account the variability of the LV. Despite the fact that this approach also requires integrating over the domain of the LV, it offers significant advantages in terms of computational costs. This approach leads to consistent but inefficient estimators (Ben-Akiva et al. 2002) and avoids the bias described by Bahamonde-Birke and Ortúzar (2014b).

When estimating the model simultaneously, or sequentially integrating over the domain of the LV, the process is usually performed by simulated maximum likelihood, employing random draws to depict the probability distributions associated with the LV (Ben-Akiva et al. 2002; Bierlaire, 2003).

Attitudes, perceptions and latent constructs in choice modelling

Prior to discussing the different ways in which LV may be considered in a HDC-model, it is necessary to understand the difference between individual-specific (e.g. attitudes, but also other characteristics such as values or personality traits, etc.) and alternative-specific latent attributes (e.g. perceptions). The former may be considered as a mind-set or a tendency to act in a particular way based on the individual’s experience and temperament (Allport 1935; Pickens 2005). Therefore, in our approach indicators representing individual-specific latent constructs depend only on the individuals and are considered constant for all alternatives. Thus, one set of attitudinal indicators would be enough to describe the individual in question. Contrariwise, perceptions (although closely related to attitudes) may be interpreted as the process by which individuals experience their environment (Lindsay and Norman 1972) and depend, therefore, on both the person and the stimuli (Pickens 2005). As a corollary, perceptual indicators should be a function of both the individual and the alternatives. Even more, any variation in the alternatives may lead to a different valuation of them, as every detail may affect the way in which the population perceives the various alternatives. Therefore, in order to analyse the role of perceptions and perceptual indicators, it is necessary to gather a new set of indicators for every alternative (defined as every possible combination of attributes) that the individual faces.

This issue can lead to a significant increase in the information collected in the experiment, as normally the alternatives would consist of different attributes that are subject to variations. Therefore, it is mandatory to make certain simplifying assumptions. First, it may be assumed that certain attributes will not affect the way in which a given alternative is perceived and, consequently, this dimension may be excluded from the design (e.g. price may not affect accessibility indicators). Second, it can be assumed that the model is valid across individuals (avoiding the need that all of them state their perceptions for every combination of possible attributes, as long as some are faced with the remaining combinations).

Once the indicators are gathered it is possible to construct the latent variables. Obviously, attitudinal variables will be related to attitudinal indicators and vice versa. Thus, while attitudinal variables must be solely explained by characteristics of the individuals (as no variation across alternatives will be observed), perceptions should be explained also by the attributes of the different alternatives in the experimental design.

On the few examples when perceptual indicators are considered, researchers just allow one attribute of the alternatives to vary and then adjust independent alternative-specific models (one model per indicator set) that depend exclusively on the characteristics of the individuals (e.g. Yáñez et al. 2010). These models are, therefore, insensitive to changes in the alternatives; moreover, as the model does not depend on the stimuli, it is disputable if it can adequately treat actual perceptions.

Alternatively, different sets of indicators, associated with different combinations of attributes describing an alternative, may be treated jointly. This allows observing variation associated with these alternative-related attributes, and the model would be no longer indifferent to the stimuli. Although such an integrated HDCM would offer a poorer goodness-of-fit, as no ad-hoc model is being estimated for each independent attribute (or combination of attributes, if more than one dimension is allowed to vary), it should reflect how certain attributes affect perceptions in a more adequate manner. If one follows this approach, it is possible to gather more than one set of indicators per person (associated with different combinations of the alternative’s attributes). In this case, correlation among the responses provided by the same individuals should be taken into account.

Kamargianni and Polydoropoulou (2014) provide a good example in this regard by using the characteristics of the individuals’ living environment as explanatory variables to explain the perception of walkability. Even though they did not attempt to analyse directly how changes in the attributes affected the perceptions of specific individuals (gathering more than one set of perceptual indicators per individuals, for instance), nor if these attributes could be linked undoubtedly to the specific alternative, their approach appears appropriate to deal with alternative-specific latent constructs.

Finally, the treatment of both kinds of variables (attitudes and perceptions) in the DCM should not be equal, as some attitudes, just as socio-economic variables (which affect the way in which the attributes of the alternatives are perceived), should be incorporated through systematic taste variations and not linearly into the utility function.

Against this background, we distinguish three kinds of LV, which will be treated in our case study (see “Case study” section):

• (a) Non-alternative related individual-specific latent attributes (e.g. attitudes) Most researchers working with HDC models consider this kind of variables (Bolduc and Alvarez-Daziano 2010; Abou-Zeid et al. 2011; Jensen et al. 2014, among many others). They represent general attitudes of the individuals toward their social and physical environment, such as a more ecological mind-set or a higher valuation of social status. Even when using variables that may be understood as perceptions, such as comfort and security, the modeller is, in fact, dealing with a non-alternative related attitude, as in this case the variable stands for the importance assigned by the individual to a given aspect and not to the perception of the alternative itself (Daziano, 2012). Thus, inferences such as “Alternative A is perceived as more comfortable” would not be accurate, but rather, “Individuals caring for comfort favour alternative A”, which is not equivalent. Chorus and Kroesen (2014) argue (in our opinion rightly) that this kind of models does not allow deriving policy implications, as these attitudinal variables are intrinsic characteristics of the individuals (like sex or age) and therefore not sensitive to changes in the alternatives (longitudinal data could be an exception, as it allows capturing how attitudes may change depending on external circumstances, and thus deriving policy implications). In the same line, Chorus and Kroesen (2014) criticise the causal relation between attitudes and choices, as attitudes and stated attitudinal indicators may be indeed affected by the individual’s choices (e.g. the stated attitude toward the comfort provided by a given alternative, may depend on whether the alternative is selected). However, this criticism may be substantially reduced if no direct link can be established between indicators and choices. In that case, both would be indeed an expression of deeper underlying attitudes, such in the case of environmental attitudes, political views, values, and so on.

  As these variables resemble socio-economic characteristics, to identify the DCM they must be considered together with alternative specific attributes in the utility function. However, in most reported cases they are just considered in conjunction with alternative specific constants (Vredin-Johansson et al. 2006; Bolduc et al. 2008); this restriction may neglect important aspects of the decision, as it can be expected that individuals with different attitudes toward life exhibit a different valuation of the attributes of the alternatives, and therefore systematic taste variations should be allowed for (Ortúzar and Willumsen 2011, p. 279).

  Furthermore, similar to socio-economic variables, it is not clear that attitudes should have a linear impact on utility. Therefore, a categorization of the LV should be considered. For instance, it is plausible that a low or intermediate appraisal of security (or safety) may have no effect whatsoever over the decision, but a high concern could lead to a significantly different valuation. If this were the case, treating the variable linearly would not properly reflect individual behaviour.

  Categorizing the LV offers also significant advantages in terms of flexibility, as it allows estimating different utility functions for every category, resembling a latent class model, but expanding it in order to account for the behavioural information. This categorization may be performed using a latent variable-latent class structure (Hess et al. 2013) or attempting a direct categorization (i.e. a dummy variable that takes a positive value if the LV surpasses a certain threshold).

• (b) Alternative related individual-specific latent attributes (e.g. attitudes) These variables are similar to those above, with the exception that attitudes are unequivocally related to a given alternative. Thus, they must be considered in conjunction with the alternative specific constants. For instance, Daziano and Barla (2012) allowed for the effect of a favourable predisposition toward automobiles or transit systems in this way. As in the previous case, systematic taste variations (within the same alternative) and a possible categorization should also be analysed.

• (c) Alternative-specific latent attributes (e.g. perceptions) These variables are alternative related (i.e. they exhibit a different valuation depending on the alternative considered) and as such they resemble observed attributes such as price or travel time; hence, both kinds of variables (observed and alternative-specific latent attributes) should be treated in the same fashion. In this case, both alternative specific and generic estimators may be considered.

  These variables allow evaluating how changes in alternatives may affect the perceptions, and thus the choices. As in this case the perceptions and indicators are driven by exogenous attributes of the alternatives, causality issues as described by Chorus and Kroesen (2014) may be overcome.

Regarding the model’s identifiability, necessary and sufficient conditions have not yet been developed. Therefore, most studies relying on HDC models achieve identification by not letting some explanatory variables impact the utility of a given alternative, both directly and through a latent variable (Bhat, 2014).² This is indeed a sufficient but highly restrictive condition and, especially when dealing with perceptual LV, the modeller may be forced to employ the same attributes in the structural equations as well as in the utility functions to represent behaviour properly (e.g. air conditioning may have an effect over perceived comfort, but still have a direct impact on the decision due to other considerations). Under these circumstances identification must be analysed on a case-by-case basis (see Vij and Walker 2014, for a good discussion about the identifiability of HDC models).

Case study

Departing from usual practice (which typically considers only attitudes), we designed an experiment considering both attitudinal and perceptual indicators in a transport choice framework. This allowed us testing for the appropriate manner to consider both kinds of LV in a DCM, regarding the underlying theoretical concerns.

We conducted a stated choice (SC) experiment where respondents were asked to choose between different interurban public transport alternatives in Germany (regional³ and intercity trains, and interurban coaches). The experiment was carried out in three waves (January 2014, March 2014 and April/May 2014), contacting both students and employees from two universities in Berlin (the Technische Universität Berlin and the Humboldt-Universität zu Berlin), as well as employees of member institutions of the Leibniz-Gemeinschaft.⁴ After data cleaning the survey yielded a total of 1832 responses.

The questionnaire had four parts. In the first, respondents were asked to describe the main characteristics (fare, travel time, number of transfers, etc.) of their last trip with the regional and intercity trains of Deutsche Bahn. Respondents were also asked to state their general experience of travelling with Deutsche Bahn. It was considered that attributes such as fare or travel time, would have no effect over the indicators (which was confirmed in a pilot study), but that the number of transfers or the transport mode could. Participants were required to state their level of agreement with the statements below, using a ten-point Likert scale which ranged from strongly disagree (1) to strongly agree (10), provided that the trip might be carried out with both transport modes (regional and intercity trains) and considering a given number of transfers (which was equivalent to that reported in the previous module, to ensure that respondents had previously faced the combination of attributes).

I was able to relax during the trip (y 11)	Relax
I felt secure from thefts and losses (y12)	Security
Traveling with heavy luggage was (would have been) uncomplicated (y 13 )	Luggage
The departure time was reliable (y 14)	Departure
The arrival time was reliable (y 15)	Arrival
It was possible to use the travel time productively (y 16)	Productivity
The station was easily accessible (y 17)	Station
Purchasing the ticket was uncomplicated (y 18)	Tickets

Respondents were also asked to state their level of agreement with these statements under the assumption that a bus carrier with no transfers would offer the service.

The second part of the survey gathered travel behaviour data as well as indicators related to traveller’s attitudes toward current political issues discussed in Germany, stating their level of agreement with the following sentences using again a 10 point Likert scale:

I agree with the nuclear power phase-out (y 21)	NuclearPhaseOut
Environment protection is more important than economic growth (y22)	Environment
I am willing to pay a 25 % surcharge on my electric bill to reduce CO2 emissions from coal power plants (y23)	ElectricSurcharge
Highway tolls should be introduced to compensate CO2 emissions (y24)	HighwayTolls
Automobiles with higher engine power should pay more taxes (y25)	CarTax
Investing on the development of high-speed trains should be encouraged (y26)	HSTrains
New highways or additional lanes to the existing ones should be built (y27)	Highways
New high-speed rail lines should be built (y 28)	RailLines
I agree with the introduction of speed limits on highways (y29)	SpeedLimits

The third part of the questionnaire was the SC experiment itself. Respondents were required to choose between a first (pivotal) alternative, representing the trip previously described, and a new travel alternative (either the same mode or a different one). Altogether, respondents were confronted with twelve choice situations; the first six used a pivotal alternative based on a trip with Deutsche Bahn regional trains and the last six considered a trip with Deutsche Bahn intercity trains. Alternatives were described in terms of their travel time, fare, number of transfers, mode of transport—regional trains (RE), intercity trains (FVZ) and coaches (LB)—and a safety level, represented through the number of severely injured passengers and the number of fatalities in the overall network over a year for each mode (this value was highest for the coach alternative⁵). The appendix presents a translated sample screen of the SP-experiment.

The attribute levels of the alternatives were optimized maximizing the D-efficiency for a pivotal design as proposed by Rose et al. (2008). As it was not possible to personalize the attribute levels during the survey, they were fixed a priori based on the average levels of the attributes. These average levels, as well as the priors used for computing the D-error, were established in accordance with models previously estimated, based on the answers gathered during the pre-test of the survey (48 individuals).

Finally, the fourth part of questionnaire requested socioeconomic information about the respondents.

Model estimation

Model structure

To establish the structure of the MIMIC-model, the indicators were analysed using factor analysis to guarantee a correct specification of the LV (Atasoy et al. 2010). This way, it was possible to identify three components (with an eigenvalue greater than 1) explaining 70 % of the variance of the perceptual indicators (y ₁₁–y ₁₈). In the same way, it was possible to establish that two factors (with an eigenvalue greater than 1) captured 54 % of the variability associated with the attitudinal indicators (y ₂₁–y ₂₉). Table 1 presents the rotated component matrices for both types of indicators.

Table 1 Rotated component matrix of perceptual and attitudinal indicators

On the basis of these results, we constructed two generic and three alternative-specific LV (shown in bold in Table 1 ⁶). The first was identified as Comfort, as it was related to indicators such as ease of access, relaxation, or an environment that was comfortable enough to be used productively. The second component was called Stress-free, as it was associated with situations causing tension during the trip, such as worrying about the luggage or personal security. The third component was identified as Reliability.

In the case of the attitudinal indicators, the first component was associated with having a Green attitude, including a negative predisposition toward automobiles (y ₂₄ , y ₂₅ , y ₂₇ and y ₂₉). The second component related to individuals who had a great appreciation for the development of trains and rail lanes (for this reason, this LV was called TrainSupporter). These results are interesting for our analysis as it was possible to identify a generic (Green) and an alternative related (TrainSupporter) attitude.

MIMIC model components

Given the complex structure and size of the dataset (1832 individuals; 3,900 sets of perceptual indicators; eight latent variables—two generic and three alternative-specific variables⁷—and 13,138 observed decisions), it was not computationally possible to perform a simultaneous estimation of the HDC model.⁸ In addition, we wanted to analyse the effect of attitudinal LV both as continuous or as categorized variables, which complicated the structure of the model even more.

Therefore, a sequential estimation considering the own variability of the LV and integrating over their domain was attempted. Thus, the MIMIC model was estimated first and the LV considered in the DCM component were constructed according to these estimates. In fact, it was necessary to estimate two different MIMIC models, one for the attitudinal variables and another for the perceptual indicators.

The first only considered individual characteristics as explanatory variables. Figure 1 presents the final structure of the selected model (several specifications considering additional socio-economic variables and other combinations of those shown were also considered), and Table 2 its estimated parameters.

Fig. 1

Structure of the attitudinal MIMIC model. (The different line types are only used to ease the understanding of the figure)

Table 2 Estimated parameters for the attitudinal MIMIC model

The second MIMIC model was estimated for the perceptual indicators. In this case, not only the characteristics of the individuals but also the attributes of the transport modes were considered as explanatory variables. It is also important to consider interactions between these two kinds of variables, as different population groups may perceive differently the attributes of the alternatives (i.e. systematic taste variations).

It is important to note, that the model cannot be subdivided based on alternatives, as we are calibrating an integrated perceptual model, where the transport mode and the number of transfers do not describe the alternatives but are considered as further attributes. The structure of the estimated model is shown in Fig. 2. Here, Losses and Accidents indicate that the individual had suffered material losses during a trip in the past or had been involved in a train accident, respectively. The number of transfers is represented by a discrete variable ranging between zero and four, while BusUser indicates whether the individual had undertaken at least one trip using coach services during the last 3 years. Again identifiability was achieved by constraining the variance of the LV and the estimation was performed maximizing the likelihood. The estimation results are presented in Table 3.

Fig. 2

Structure of the perception MIMIC model

Table 3 Estimated parameters for the perceptual MIMIC model

Discrete choice models

This section reports the results of estimating the discrete choice component of the models. In addition to the previously described latent variables, socioeconomic characteristics of the individuals and attributes of the alternatives (transport mode, price, travel time, number of transfers and safety level) were considered. Further, an inertia variable taking the value of one for the status quo (in contrast with the new alternative) was introduced. As in every pivotal design, both alternatives were considered to be similar (with the exception of this inertia) and all parameters were considered generic. Utility was assumed to be linear in the parameters and the error terms to distribute EV1, with the same mean and scale factor λ equal to unity.

Altogether, there were 13,138 observations available for estimation. The potential correlation between the responses of a given individual (panel effect) was considered but not included in the final models since it was not statistically significant.⁹ The LV Green and TrainSupporter were considered both linearly and categorized in two different levels. We attempted a direct categorization, with the dummies Green _(+67 %) and TrainSupporter _(+67 %) taking a positive value with the probability of the original LV being greater than a given threshold ψ _l . Thresholds were fixed to represent the fact that individuals belonged to the upper third of the population (regarding the distribution of these two LV). As mentioned above, estimation was performed sequentially using PythonBiogeme (Bierlaire 2003), integrating over the domain of the latent variables, so that the reported value for the log-likelihood refers only to the discrete choice component of each model. This takes the following form when the LV are considered as continuous variables:

$$ L = \int\limits_{\eta } {P(y\left| {X,\eta ;\beta ,\theta ,\varepsilon } \right.) \cdot f} (\eta \left| {s;\alpha ,v} \right.) \cdot d\eta $$

(4)

or the following one when a latent variable η _c is categorized:

$$ \begin{aligned} L = \int\limits_{\eta } {P(y\left| {X,\eta ,0;\beta ,\theta ,\varepsilon } \right.)} \cdot f(\eta \left| {s,\alpha ,v} \right.) \cdot d\eta \cdot P(d\eta_{c} < \psi \left| {s,\alpha ,v} \right.) \hfill \\ \quad + \int\limits_{\eta } {P(y\left| {X,\eta ,1;\beta ,\theta ,\varepsilon } \right.) \cdot f(\eta \left| {s,\alpha ,v} \right.)} \cdot d\eta \cdot P(d\eta_{c} \ge \psi \left| {s,\alpha ,v} \right.) \hfill \\ \end{aligned} $$

(5)

Table 4 presents the estimation results for five different specifications; all are good models easily surpassing the typical test of being better that their market shares reference model (Ortúzar and Willumsen 2011, pp. 281–283). The first (Linear LV) considers all LV (generic and alternative-specific) in a linear fashion. The second (Categorical Green) categorises the latent variable Green, while the third (Categorical LV) explores categorized specifications for both attitudinal LV. The fourth (No Stress-free) is similar to model Categorical Greene but ignores Stress-free (found not statistically significant in the second model¹⁰). Finally, the fifth (No Perceptual) ignores all perceptual LV.

Table 4 Estimated parameters for the discrete choice model

Two of the three perceptual indicators were found to be statistically significant. Thus, both the perception of reliability and comfort affect utility positively. On the contrary, the perception of a stress-free travel appears not to be statistically significant in the decision making process.

Note that when the perceptual attributes are omitted, the mode specific constants become highly significant (model No Perceptual). However, when perceptions are integrated they capture a large part of the variability previously ascribed to them and these become either not significant (Regional Train), or their impact on the decision decreases (Coach). This is accompanied by a significant improvement in goodness-of-fit.

These findings are in accordance with theory: the mode specific constants normally capture the omitted information regarding a specific alternative, but when perceptions are considered, this information is enriched and the importance of these constants decreases.

Re the attitudinal LV, we found that the generic attitude Green affects the way in which travel time is perceived (i.e. it was possible to identify a systematic taste variation related to this attitude). The variable is statistically significant both when considered linearly and when it is categorized, reflecting the importance of the systematic taste variation. However, when the variable is categorised (Green _+67 %) the model gets a substantially superior goodness-of-fit (models Categorical Greene and Stress-free), suggesting a considerably better representation of behaviour. This finding is in line with the perception that shorter travel times imply higher speeds and, therefore, more CO₂ emissions and a larger damage to the environment. Also, the fact that the effect of Greene is not linear, is in agreement with the notion that only highly environmentally concerned individuals are willing to accept larger travel times to reduce ecological harm.

When considering interactions between continuous LV and travel time or travel expenses, assessing the value of travel time gets more involved as the LV do not drop out of the equation when deriving the utility over travel time or cost. Therefore, the value of time will depend on the attitudes of the individuals and to obtain a societal value of time it would be necessary to integrate over all individuals. When a LV is considered in a categorized fashion, the analysis is straightforward and similar to the one performed, when working with latent classes, and the same applies for demand elasticities.

Finally, as expected, our alternative related attitude (TrainSupporter) is statically significant in conjunction with intercity trains (FVZ). It was possible to detect a social group of train enthusiasts willing to favour the railways. However, this favouritism does not extend to regional trains. In this case, a model considering the variable in a categorized fashion (e.g. model Categorical Variables) does not outperform the linear specification. It was not possible either to identify a systematic taste variation within the alternative intercity trains.

Conclusions

The significant technical and methodological improvements in the estimation of HDC models during the last decade have not led to a significantly better understanding of the way in which perceptions affect the decision making process, as these aspects are mostly ignored by modellers. Even in the case of attitudes, which have been widely studied, the specification of LV has tended to be fairly simplistic and rarely departs from the linearity assumptions (fortunately latent class models have been an alternative in this regard), while the analysis of systematic taste variations in association with attitudes appears to be practically inexistent.

This reticence may be related to deeper concerns about artificial constructs, such as LV and the information that can be acquired from them. Nevertheless, it should not be forgotten that we, as modellers, aim to depict reality in the best way possible and, therefore, if we decide to work with latent variables, we should guide our efforts to represent the decision making process and the way in which the different variables take part in it as accurately as possible.

This paper ponders about the different ways in which attitudes and perceptions may affect the decision making process and derives practical recommendations about data collection and estimation issues. Basically, individual-specific latent attributes (e.g. attitudes) resemble socio-economic characteristics of the individuals, and thus they should be treated in a similar fashion. Hence, exploring alternatives as systematic taste variations (in conjunction with observable attributes of the alternatives) or through a categorization is highly recommended. Alternative-specific latent attributes (e.g. perceptions), on the other side, should be treated in a similar manner to the attributes of the alternatives. Along the same line, it is important for perceptual models, to consider the attributes of the alternatives as explanatory variables, to properly reflect the way in which perceptions arise in the population and to remain sensitive to changes in the alternatives.

With regard to the collection of perceptual indicators, it is important that questionnaire design allows capturing variability in the indicators associated with changes in the alternatives. Attempting to analyse how various combinations of alternative attributes may affect a perceptual indicator, may lead to a significant increase in the information required; so, it is important to rely on a careful survey design and to determine a priori which attributes are relevant to the perception.

We conducted an empirical analysis to test our hypotheses. This gave evidence sustaining the notion that perceptions may affect the way in which individuals ascribe utility to a certain alternative. In the same line, our empirical experiment suggests that perceptions may explain a significant portion of the variability normally captured by alternative specific constants, offering significant improvements in model goodness-of-fit. Also, our results support our hypotheses that attitudes may indeed be related to systematic taste variations and that attitudinal LV should be treated in the same manner as socio-economic variables.

Although we were able to identify systematic taste variations with our data, as well as a categorization for LV that outperformed the linearity assumption, this does not imply that every attitudinal latent variable should be considered in this way. Prior to estimation, or even better prior to constructing the experiment, the analyst should study which variables take part in the decision making process and decide the way in which they should be considered in accordance with underlying theory.

Although not treated in this paper, interactions among attitudes and perceptions represent an issue that should be considered in further research, as cognitive dissonance might affect the way in which different alternatives are perceived, leading to correlation and more complex error structures.

Appendix

Sample screen of the SP-Experiment