Can your personality explain where and withwhom you choose to recreate? A latent-classchoice model of site characteristics, companion,and companion’s ability–with estimated latent

personality-traits as covariates∗

Edward R. Morey†and Mara ThieneDept of Economics, U. of Colorado, Boulder CO 80309 USA

Dept of Land and Agriculture-Forestry Systems,U. of Padova, Padova, Italy

January 12, 2014

Abstract

4605 mountain bikers answered five pairwise-choice questions: "Wouldyou rather go on mountain-bike ride A or B?" Each ride is describedin terms its trail attributes, whether one has a companion and, if so,the companion’s relative ability. Respondents also answered questions onsensation-seeking, competitiveness and extroversion. For each personalitytrait, a "mixed-mode" latent-class cluster model was estimated, account-ing for the ordinality of Likert-scale questions, and allowing the answersto be correlated (something expected but typically assumed away). Alatent-class choice model of trail attributes and companion’s ability wasthen estimated using the choice-pair data with the estimated latent per-sonality traits as covariates. Three choice classes are identified and theodds of being in each varies significantly and substantially by personality.

While we utilized the mixed-mode latent-class model to to estimatepersonality clusters, one can use it for any type of indicator data.

∗Keywords: personality, choice, choice experiment, latent-class, mixed-mode, correlatedindicators, competetiveness, sensation-seeking, introversion/extroversion, companion, relativeability, ordinal, and behavioral economics.†corresponding author: Edward.Morey@Colorado.edu

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1 Introduction:

The goal was to estimate preference heterogeneity for a site-specific recreationalactivity both in terms of the physical attributes of the site, and for whether onehas a companion, and their relative ability. And, to determine if personalitytraits explain this heterogeneity. Our hypothesis was that people vary in termsof how, and how much, they want to be challenged. Site characteristics canmake a site more or less challenging (consider technical climbs and ski runs).If one does the activity alone one can choose the pace (relaxed to challenging),but if one has a companion one loses some control over how the activity willplay out, particularly if the companion is of a different ability level. In addition,one’s relative technical skill, strength, and endurance are revealed. Specifically,our hypothesis was that the personality traits, sensation-seeking/sensation min-imizing, extroversion/introversion, and whether one has a inclination/need tocompare with others competitively influences choice.A recreational activity/sport was chosen because they require technical skills

and physical ability, have inherent risks (both physical and psychological), andbecause one has varying degrees of control over the how the activity plays out.Our application is to mountain bike rides but there are many site-specific

recreational activities where the attributes vary dramatically across sites (down-hill ski areas, golf courses, hikes, fishing sites, technical climbs, road cycling,etc.) and where one can do the activity with or without a companion, andwhere the companion’s relative ability will influence how the site is experienced(competing, socializing, challenging, etc.).Each respondent was asked psychological questions about sensation-seeking,

extroversion and competitiveness. These questions were used to estimate alatent-class (LC) cluster model for each of these personality traits, dividing, forexample, sensation-seeking into three classes/clusters ( sensation-seekers, thecautious, and everyone in between). A LC ride-choice model was then estimatedwith the psychological traits as covariates.The typical LC cluster specification is rejected; it imposes conditions in-

consistent with our data. Specifically, it requires that (1) All of the indicatorquestions are of one mode/scale: either categorical nominal, or categorical ordi-nal, or continuous with cardinal meaning. (2) Categorical answers are assumednominal, but ours are ordinal (specifically Likert—scale questions). And (3), theanswers to the indicator questions are restricted to be statistically independentonce one has conditioned on cluster.The LC cluster model we present and estimate does not impose these restric-

tive assumptions: it allows for the simultaneous inclusion of indicator questionsof all three modes, accounting for their different properties– a "mixed-mode"model. In addition, the estimated model allows the answers to be correlatedeven after one has conditioned on cluster, something one would often expect.The model allows one to estimate correlations amongst the indicators and totest their significance. This paper is one of the first economic applications torelax and test the standard independence assumption.

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Section 2 reviews how personality influences choices; Section 3 describes thesurvey and the data; Section 4 presents our three LC cluster models, first forcompetitiveness. Section 5 is the LC choice model; Section 6 concludes.

2 The literature

2.1 Personality and choice

Personality affects choice: Hopwood, Baker and Morey (2008) consider how thetraits internalizing and externalizing affect one’s choice of illegal drugs (e.g.heroin vs. cocaine). Jonason, Luevano and Adams (2012) consider how the"Dark Triad" traits (narcissism, psychopathy, and Machiavellianism) predict re-lationship choices. A number of studies (see, for example, Mascie-Taylor(1988);and Bereczkei, Vörös, Gál, and Bernáth (1997)) indicate that individuals tendto choose mates that have a similar personality. Corulla and Coghill (1991)link choice of school subject to personality traits. And, numerous articles relatepersonality traits to eating habits (e.g. MacNicol, Murray and Austin (2003)).Sit and Linder (2005) find that Paratelic-dominant individuals (playful, un-

concerned, fun seeking) prefer risky sports while telic-dominant individuals (se-rious, goal-directed, achieving) prefer safe sports and endurance activities. Moresport-competitive individuals tend to be more telic (Kerr (1987) and Kerr andvan Lienden (1987)).

2.1.1 Sensation-seeking, extroversion/introversion, and competitive-ness

Quoting Thomson, Carlson and Rupert (2012):

Sensation-seeking involves the desire to seek out new and thrilling sen-sations and has been associated with high-risk social activities includingpromiscuous sex, illicit drugs, and crime as well as with high-risk sports.

Thomson, Carlson and Rupert identify a link between a D3 dopamine re-ceptor gene variant and sensation seeking in skiers and snowboarders. Theydescribe sensation seeking as an "approach" trait. Quoting Roberti (2004):

Sensation seeking individuals tend to engage in behaviors that increasethe amount of stimulation they experience...Risk taking is a correlate ofsensation seeking but is not a primary motive in behavior...

More generally, Jack and Ronan (1998) and De Moor et al. (2006) find thatsensation-seeking is positively correlated with physical activity.

Merriam Webster define Extroversion as "the act, state, or habit of beingpredominantly concerned with and obtaining gratification from what is out-side the self." Introversion is "the state of or tendency toward being wholly orpredominantly concerned with and interested in one’s own mental life." Extro-

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version, like sensation seeking, is an approach trait. Kirkcaldy and Furnham(1991) find that more extraverted individuals compete more. Egloff and Gruhn(1996) find that endurance athletes are more extraverted than non exercisers,and that endurance athletes that exercise more are more extroverted. Daviset al. (1995) find that extroversion and neuroticism ("the tendency to be anx-ious, insecure and emotionally unstable in general, and to be susceptible to bestressed or depressed") are both positively correlated with the propensity toexercise, for the latter group to improve mood. Tolea (2012) find that extrover-sion is positively correlated with muscle strength, "independent of covariates."Looking ahead, our results contradict some of these findings.

Competitiveness is the inclination/need to compare with others and to demon-strate one is better than one’s peers.1 (See the discussion below on ego-orientation.)Our goal is estimate how this trait influences the choice of trail attributes andcompanion, not to estimate how it influences how often one enters a mountian-bike race. While there is literature on how other personality traits influenceone’s propensity to compete in sports, there seems to be little literature on howthe trait competitiveness influences other choices.

2.2 Why might a companion matter?

Social psychology asserts a native desire to seek the company of others– it isthe premise of the field. Social psychologists offer numerous reasons for wantingcompanions. Here we discuss a few that likely influence whether you ride aloneor with others. First, and foremost, people get utility from friendship andhuman contact. This category includes the feelings of security provided by acompanion, and also the joy of interacting with others, including games andcompetitive situations.Third, having company during an activity allows one to gauge one’s own

abilities: we use other people to gather information about ourselves—social com-parison (Festinger (1954)),

There exists in the human organism, a drive to evaluate his opinionsand abilities...People evaluate their opinions and abilities by comparisonrespectively with the opinions and abilities of others...The tendency tocompare oneself with some other specific person decreases as the differencebetween his opinion or ability and one’s own increases.

Comparison is part of our quest to make ourselves feel better.2 Riding withbetter riders and keeping up allows one to identify with those better riders,riding with lesser riders and beating them confirms you are not one them– you

1Contrast comparision with another person to comparision with one’s former self: whetherone has improved.

2Motives for the drive include self-enhancement, perceptions of relative standing, main-taining a positive self image, and closure (Suls, Martin and Wheeler (2002)). See also Buunkand Gibbons (2007).

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have drawn a contrast/distinction between them and you. Both processes canbe self-enhancing. The drive to compare is not limited to humans (Gilbert,Price and Allan (1995)), so likely has a genetic component.In mountain biking the comparisons can be on technical skill, anaerobic

strength, or aerobic endurance: one needs a technical ride to assess skill level,and only one short, steep climb to assess strength, but a long hard ride to assessendurance.Referencing, again, Sit and Linder (2005),

Achievement Goal Theory posits that the basic motive of individualsis to demonstrate their competence or achievement...individuals have twodifferent goal orientations which influence how individuals construe theircompetence...Task orientation is concerned with mastery, self-learning,and personal improvement. The task-involved individual employs a per-ception of ability which is self-referenced. Ego orientation constitutes thecomparison of own performance to that of others. An ego involved individ-ual adopts an other-referenced perception of ability. He/she experiencessubjective success when he/she has a better performance than others...

We generally prefer to compare ourselves to those who are slightly better,but there are costs to doing so (Buunk and Gibbons (2007), Brickman andBullman (1977)). Ignoring the costs, the implication for mountain biking is youwould choose a slightly better rider over a slightly worse rider. Individuals whocompare themselves to those better feel it is the way to improve, and, in fact,improve faster (Blanton, Buunk, Gibbons, and Kuyper (1999)).However, participating in an activity with those better can be threatening.

The threat is eliminated by riding alone or by choosing a riding companion "outof one’s league"—termed "self-handicapping" ((Shepperd and Taylor (1999)).Some individuals, to protect their egos, purposively handicap their ability (Jonesand Berglas (1978)) by, for example, riding hard the day before.There is evidence that some individuals compare downward– downward so-

cial comparison theory (Wills (1981)). As noted above, one way to improveself-esteem, if it is low, is to ride with lesser riders and demonstrate you are notone of them.Alternatively, one might not ride alone because one has no need to compare.

3 The survey and the respondents

Our population of interest were those individuals who take most of the mountain-bike rides– an imprecisely defined group– what we would call serious mountainbikers. The vast majority of mountain-bike rides are taken by serious riders.Nine-hundred and thirty-seven identical solicitation emails were sent out,

most to organizational lists of mountain bikers. The solicitation email askedthem to complete our online survey and to forward our e-mail to other potential

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mountain bikers. Our expectation was that the vast majority of our respondentswould be serious mountain bikers.No claim is made that the result of this process is a true random sample

of serious mountain bikers. That said, the preferences of the respondents likelyreasonably approximates the preferences of those who take most of the rides.Two types of data was collected: answers to standard psychological questions

(some tweaked towards mountain biking)—see Table 1, and responses to choicepairs.34 Figure 1 (in color) is a snapshot of a choice-pair question from the sur-

vey.Figure 1: An example choice pair

3The questions on extroversion/introversion are from the Jung-Myers-Briggs in-ventories, the competitiveness questions are from the "Revised CompetitivenessIndex (CI-R)" (at http://www.rollins.edu/psychology/houston/research.html) and thesensation-seeking questions are from Hugh Stephens’ Sensation-seeking Scale (athttp://www.ithaca.edu/faculty/stephens/sss.html).

4One can see the survey as the respondents saw it athttp://www.colorado.edu/economics/morey/respondentview/bikefinal.htm

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The ride characteristics and their levels will be described below in moredetail.(Table 1 approximately here)

3.1 Characterizing mountain-bike rides

Mountain-bike trails vary in terms of six characteristics: trail length, proportionof trail that is singletrack versus doubletrack, total vertical feet of climbing,number of climbs, access fee, and speed of a companion rider relative to yourspeed; no companion is a possibility. Single-track is a trail, double-track is, oronce was, a two-track dirt road. Morey, Buchanan and Waldman (2002) foundthe first five to be significant and important determinants of site choice– theydid not consider companion. Table 2 reports the characteristic levels in thedesign. Some combinations of trail characteristics are infeasible or impossible,so excluded.

Table 2: Characteristic levels

Characteristic LevelsTrail length (miles) 7 14, 21 and 35Miles of singletrack 0, 3.5, 7, 14, 21, and 35Vertical ft. of climbing 0 , 500, 1000, 2000 and 5000Number of climbs 0, 1, 2 and 4Access fee $1, $3, $5, $8 and $20Time gap (minutes) solo, −10, −5, -2

0 (same ability), +2, +5 and +10

When one rides a trail alone one can choose, within one’s physical limits,how to ride it– any competitiveness comes from within, but there is no compan-ionship or socializing. If hurt or lost, one is on their own. All is different if onerides with a companion, and, how it differs depends on your relative abilities.One might struggle greatly to maintain contact with a riding companion, orconversely spend much of the ride waiting for him to catch up. Or, if evenlymatched, sometimes competing and sometimes socializing.To simplify and avoid the interactive aspects of choice, we present the re-

spondent with choices of trails where the presence (or absence) of a companionand their relative ability is another exogenous aspect of the ride.The lead rider typically stops at a number of points along the trail to wait

for his companion to catch up. We made the number of stopping points anincreasing function of the trail’s length, locating them at common stoppingpoints.Consider a gap of two minutes if both rider rode at their typical pace. This

does not imply that the gap would always be 2 minutes, but indicates the secondrider would have to struggle to stay with the lead rider. Depending on one’spersonality, this might generate more or less utility.An effi cient choice-pair design was generated (details on request) consisting

of fifteen versions of the survey, each with five choice pairs (“Would you preferto ride A or B?”).

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3.2 The respondents

The survey resulted in usable responses from 4605 mountain bikers. While87% of the respondents are U.S. residents; residents of 49 countries completedthe survey.5 Our sample took approximately twenty-eight thousand rides inthe "last 30 days," and a large proportion of these rides included at least onecompanion. Most respondents do some biking alone: 22% report they usuallyride alone, while another 39% report they often do.The mean age of respondents is 37; eighty-six percent are male; 80% make

$40K or higher, and 32% make $100K or greater. Sixty-five percent reportspending between $26 and $100 dollars on fun stuff per week. Most respondentslive with a significant other, and live in a household with more than one wage-earner. Respondents average .6 kids.That most respondents are serious mountain-bikers is illustrated by their

gear, their avidity, and their their skill levels. On average, they rode more thansix days in the previous thirty, and three and a half hours in the previous week,and 59% have participated in at least race.

4 Three LC cluster models, each of a differentdimension of personality (competitiveness, sensation-seeking and extroversion)

We use the adjective cluster to distinguish these three models from the LC choicemodel, not because they are akin to any non-statistical "clustering" techniques.The details of the LC cluster model are presented only for the competitivenessmodel.

4.1 A LC cluster model of competitiveness

On the basis of the answers to four Likert-scale questions about competitivenessplus the number of times the respondent raced in the last year (see Table 1), amixed-mode LC "cluster" model is estimated.The model appropriately assumes that the answers can be correlated even

after one conditions on latent cluster. Most LC cluster models assume thatonce one conditions on cluster the responses are uncorrelated, but this is notappropriate for five related questions about competitiveness.Assume the population of N mountain bikers consists of C different competi-

tiveness clusters. Each individual belongs to one, and only one, of the C clusters,but from the researcher’s perspective individual i′s cluster is latent/unobserved.Individuals in different clusters are different, or said in the opposite way, indi-viduals who belong to cluster c are more similar to each other than they are

5A static version of the survey with summary statistics can be found athttp://www.colorado.edu/economics/morey/static/index.html

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to individuals who do not belong to cluster c . Similarity can be in terms ofpreferences, constraints, beliefs, production, etc. In this application, similarityis in terms of competitiveness.The researcher observes (xi, zi) for each sampled individual, where both xi

and zi are vectors of random variables. Each element of xi is an indicator forindividual i. Each of the five competitiveness questions in Table 1 "indicate"an aspect of the individual’s competitiveness. (zi is defined below.)One estimates Pr(c), the probability of belonging to cluster c. Indicators

can be discrete or continuous, and nominal, ordinal or cardinal. All of the com-petitiveness indicators (questions) have a finite, and small number of responsecategories, S, so are discrete random variables, each with five response cate-gories, so S = 5. For a discrete indicator, the values it can take might mighthave an ordering, making that indicator ordinal, or it might have no naturalordering, so nominal. That is, discrete indicators can vary in terms of the typeof mathematical scale on which they are measured. Most LC cluster modelsassume the discrete indicators are nominal, not ordinal.Let Q, q = 1, 2, ..., Q denote the number of indicators, here Q = 5. For

discrete indicators, one estimates either the probability that an individual incluster c has category s for indicator q or, more generally, the probability ofeach possible response pattern.6

Answers to Likert-scale questions have an ordering, e.g., "strongly disagree,""somewhat disagree," "neither agree nor disagree," "somewhat agree," and"strongly agree", but meaning is not typically attributed to the cardinal prop-erties of the numbers/"scores" associated with each response category. Ourmodel accounts for this by assuming each of the indicators is a discrete, ordinalrandom variable.Indicators can also include measures of how much was produced or whether

an action was taken. Our question about how many times one has raced is ofthis form. Since the question allowed only five response categories (never, 1, 2or 3, 4 or 5, and 6 or more), this indicator is also assumed a discrete, ordinalrandom variable.7

The vector zi is a vector of U covariates. A covariate is not a variable onwhich one wants to group respondents– those are indicators– rather covariatesare variables that are observed that might influence the probability that in-dividual i belongs to cluster c. Like indicators, covariates can be discrete orcontinuous.The goal is to specify and estimate the joint density function of xi, con-

ditional on zi, f(xi |zi ), with a specification that parsimoniously explains andpredicts the number of clusters, how they differ in terms of the levels of theQ indicators, and that allocates each individual to a specific cluster with highprobability as a function of his or her covariates and indicators. Put simply,

6For continuous indicators that are independent, one estimates the parameters in eachcluster’s density function for that indicator; for jointly distributed continuous indicators, oneestimates the parameters in each cluster’s joint density functions.

7 In contrast, for an indicator such as the cost of one’s mountain bike, one might reasonablyassume cost is normally distributed.

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one wants to accurately characterize the variation in competitiveness, assumingcompetitiveness is discretely heterogeneous rather than continuously heteroge-nous.One often estimates C– but this is not warranted in this application: our

goal is to estimate a most and least competitiveness cluster to see if behaviorcan be explained in terms of the two extremes on this dimension of personality,so C is set to 3.Assume the following, quite general, LC cluster specification (Vermunt and

Magidson 2005)

f(xi |zi ) =3∑c=1

[∏H

h=1f(xhi |c ) Pr(c |zi )

](1)

where Pr(c |zi ) is the probability that individual i belongs to cluster c con-ditional on her covariates. Eq.1 separates the Q indicators into H mutuallydistinct subsets, where the vector xhi denotes the observed levels of the indi-cators in set h. Conditional on c, indicators in set h are assumed statisticallyindependent of indicators in the other sets, but the indicators in h are allowedto be mutually dependent. f(xhi |c ) denotes the joint density for the xhi, con-ditional on cluster. Eq.1 is called a "mixed-mode LC cluster model" because itallows for a mixture of indicators with different scales (Everitt (1988), Lawrenceand Krzanowski (1996), Moustaki (1996). Hunt and Jorgensen (1999), Vermuntand Magidson (2002), and Moustaki and Papageorgiou (2004)).8

In this paper, we are not interested in explaining why an individual has thepersonality he has, so have no need for covariates in the cluster models. So Eq.1simplifies to

f(xi) =

C∑c=1

[∏H

h=1f(xhi |c ) Pr(c)

](2)

The Pr(c) are parameters to estimate subject to the restrictions that 0 ≤ Pr(c) ≤1 and

∑3c=1 Pr(c) = 1.

The standard, and basic, LC cluster model assumes that once one conditionson cluster all of the indicators are statistically independent; that is, Eq.2 is

replaced by its special case, f(xi) =∑C

c=1

[∏Qq=1 f(xqi |c ) Pr(c)

], where xqi is

a scalar, and in this restrictive case, each indicator has its own independentdensity.Restrictively assuming that, conditional on cluster, each indicator is indepen-

dent is a strong, and often questionable, assumption. Consider the Likert-scalestatement "I enjoy competing" and "Number of races done in the last year." Itis reasonable to expect that the answers to these two questions would remain

8Merz and Roesch (2011) recommend "latent profile analysis" as a way to model andestimate personality heterogeneity. They provide an example. LPA assumes the indicatorvariables are continuous (rather than nominal or ordinal categories), so LPA is a special caseof a mixed-mode latent-class cluster model. They inappropriately assume the responses totheir Likert-scale questions are continuous variables.

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correlated even after one has conditioned on cluster (and, looking ahead to theestimates, they remain, as expected, correlated. As explained in more detailbelow, E.q.2 allows one to test and relax the assumption of local independence.If one assumes that all the indicators are discrete random variables that can

only take a finite, and small, number of nominal values, f(xqi |c ) is simplythe probability of observing xqi conditional on belonging to cluster c; that is, ifxqi = s (individual i choose response s to question q)), f(xqi |c ) becomes πsq |c ,a number rather than a function, where πsq |c is the probability that individuali chooses level s of indicator q, conditional on being a member of cluster c.

4.1.1 Discrete indicators that take a small number of values

All indicators that take only one of a small number of values can be parame-terized as multinomial distributed in that the multinomial admits nominal indi-cators, and can admit, when appropriate, ordinal indicators, and dependenciesamong indicators.Turning to the f(xhi |c ), consider first the case of local independence, and

only nominal indicator categories. In which case each f(xqi |c ) is specified asa multinomial where the response probability– the probability of indicator qtaking category s for individual i, conditional on belonging to cluster c is

πsq |c =eRsq|c∑Sq

s′=1 eRs′q|c

(3)

where Sq is the number of response categories for indicator q. Rsq|c can beviewed as the relevance of response category s for indicator q for an individualin cluster c: categories that are more relevant are more likely to be selected.Parameterize Rsq|c by assuming

Rsq|c = µsq + αsq|c (4)

Explaining Eq.4, the relevance of category s for nominal indicator q is para-meterized with two terms: relevance independent of cluster, µsq, and a cluster-specific relevance shifter, αsq|c . (If, for example, indicator 1 has five cate-gories and there are three clusters, there are five µs1 parameters and fifteenαs1|c parameters.)If the response categories of indicator q have a "natural" ordering– are or-

dinal– as are ours– one can substantially reduce the number of parameters toestimate by restrictively assuming

αsq|c = (scoresq)αq|c (5)

where scoresq is a numerical value used to represent response category s forindicator q; scoresq is restricted to be increasing in s. We assume responsecategories are represented/"scored" with 1 for "definitely disagree" and 5 for"completely agree" with unit differences; the score for ’neither agree nor dis-agree" is 3. So, α1q|c = 1× αq|c , α2q|c = 2× αq|c ,..., α5q|c = 5× αq|c .

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This ordinality restriction is called the adjacent-category restriction or theadjacent-category ordinal logit model (Goodman (1979), Magidson (1996), Agrestiet al. (2000), Agresti (2002), and Vermunt and Magidson (2005)). Its use is notcommon in economics. The restriction is appropriate if one can hypothesize anunderlying continuous variable with the discrete response moving up (or down)the scale as the continuous variables passes successive thresholds, as is the casewith our five indicators. This adjacent-category restriction needs to be carefullyinterpreted.9

relaxing local independence with ordinal random variables For sets of

indicators that are dependent– even after one has conditioned on cluster– onecan generalize the multinomial, Eqs. 3, 4 and 5, to accommodate this (Ha-genaars (1988), Qu, Tan and Kutner (1996), Vermunt (1997), and Vermuntand Magidson (2005)). Vermunt and Magidson (2005) do this by specifying aset of indicators and estimating the relevance of every possible combination ofresponses to the indicators this set. For example, imagine that the first twoindicators (q = 1, 2) are discrete and one suspects they are statistically depen-dent, but independent of all the other indicators. If S1 = 5 and S2 = 5, thereare 25 different response combinations for these two discrete random variables.The joint density of (x1i, x2i |c ), the aggregate alternative, is a multinomial with

25 alternatives. For this example, let Rs′1s′′2s|c denote the joint relevance ofresponse category s′ to indicator 1 and response category s′′ to indicator 2,conditional on belonging to cluster c.

Rs′1s′′2s|c can be parameterized as

Rs′1s′′2|c = (µs′1 + αs′1|c ) + (µs′′2 + αs′′2|c ) + γ(s′1)(s′′2)

s′ = 1, 2, .., 5 s′′ = 1, 2, .., 5

where γ(s′1)(s′′2) is picking up the dependence of a response of category s′′ to

indicator 2 on response category s′ to indicator 1. (For example, the parameterγ(51)(32) indicates the dependence of a category 3 response to indicator 2 on acategory 5 response to indicator 1.) Given that S1 = 5 and S2 = 5 there areten γ(s′1)(s′′2). (Note that γs′1s′′2 = γs′′2s′1)

9 It, for example, does not imply that relevance of category s is always greater than (or lessthan) the relevance of s− 1. It also does not imply that the ordering of category relevance isthe same across all of the clusters. Rsq|c = µsq + (scoresq)αq|c implies that (1) If αq|c > 0 ,the larger the positive value of αq|c , the more likely it is that relevance is monotonicallyincreasing in s for Cluster c. (2) But If αq|c < 0 , the larger the absolute value of αq|c , themore likely it is that relevance is monotonically decreasing in s for Cluster c. So as αq|cincreases in absolute value, it becomes more likely that relevance will be monotonic (eitherincreasing or decreasing) in s for that cluster. And (3) the larger the value of µsq , the morerelevant is response level s, independent of cluster; so relevance need not be monotonic in s.Rsq|c = µsq + (scoresq)αq|c is restrictive in that it does not allow the cardinal relevances tovary independently acoss response categories and clusters.

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More generally, let sq∈h be a specific vector of responses to the indicators inset h.10 The joint relevance of this vector of responses to the indicators in seth is

Rsq∈h|c =∑

q∈h

∑s∈sq∈h

[µsq + αsq|c

](6)

+∑q,q′∈hq<q′

∑s,s′∈sq∈hs<s′

γ(sq)(s′q′)

The γ(sq)(s′q′) parameters capture the local dependence between response s toindicator q and response s′ to indicator q′. If the γ(sq)(s′q′) are all zero, all of theindicators in h are locally independent and Rsh|c =

∑q∈h

∑s∈sh

[µsq + αsq|c

]=∑

q∈hRqs|c .Our personal experience is that if multiple indicators indicate about similar

things, one will often reject the null hypothesis of local independence. Butassuming local dependencies between multiple indicators also makes estimationmore diffi cult, both in terms of computing time and identification of the globalmaximum.11

Since, in our competitiveness cluster model, all the indicators are discreteand ordinal, αsq|c and γ(sq)(s′q′) in Eq.6 are parameterized as

αsq|c = (scoresq)αq|c (7)

andγ(sq)(s′q′) = γqq′(scoresq)(scores′q′) (8)

Models with dependencies are easier to estimate if ordinality has been im-posed on the, potentially, dependent indicators because it reduces the numberof parameters to estimate.

The ln likelihood function is

lnL =

N=4605∑i=1

ln

[3∑c=1

[∏H

h=1f(xhi |c ) Pr(c)

]](9)

=

N=4605∑i=1

ln

[3∑c=1

[Pr(c)

∏H

h=1(πshi |c )

]]

where πshi |c is the probability, conditional on c, of observing the individual’sresponses to the indicators in set h. The maximum-likelihood parameters are

10For example, if there are three indicators in h, one sh is sh≡ (2, 4, 1, ) indicating acategory 2 response for indicator 1, a category 4 response of indicator 2, and a category 1response for indicator 3.11Vermunt and Magidson (2005) suggest that incorrectly imposing independence often leads

one to to choose too many classes.

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obtained by maximizing lnL with respect to the parameters: the three P (c),the twenty-five µsq (one for each of the five response levels for each of the fiveindicators), the fifteen αq|c (one for each each indicator for each of the threeclusters), and a γqq′ for each pair of indicators (questions) assumed dependent.Estimation is with the statistical software Latent Gold (Vermunt and Magidson(2005)).We chose which indicators to assume dependent (which γ(sq)(s′q′) to not

restrict to zero) based on how much the the ln of the likelihood function isimproved if a pair-wise dependency is allowed. Since all of our indicatorsare assumed ordinal, adding an additional pair-wise dependency adds a sin-gle parameter,γqq′ . For each of the γqq′ restricted to be zero, the estimationsoftware, Latent Gold, calculates an approximate, but lower-bound, measureof how much the fit would improve if one allowed, ceteris paribus, each of theγqq′ currently set to zero to be nonzero (Vermunt and J. Magidson 2005). Thehigher these "bivariate residuals" between q and q′, Bresidualqq′ , the morelikely indicators q and q′ are dependent– there is no clear statistical criterionfor drawing the line between significant and non-significant values. Estimationtypically starts by estimating the model with all γqq′ = 0; then if one or more ofthe Bresidualqq′ are large, one re-estimates the model allowing the qq′ pair withthe highest residual to have a non-zero γqq′ . One then checks the Bresidualqq′’sfor the new model, allowing, if appropriate, in the next estimation another γqq′to be non-zero.Re-estimation proceeds with additional dependencies until, based on the

estimated residuals, the most significant dependencies, in terms of p−values, areincluded. The process is somewhat ad hoc but highly preferable to assuming allof the indicators are independent after one has conditioned on cluster. Lookingahead, we estimate a number of significant γqq′ parameters.

4.1.2 The estimated competitiveness LC cluster model

Based on p − values, all of the estimated parameters are significant and forthose parameters that vary by cluster, the αq|c parameters, the estimates differsignificantly by cluster. The predicted membership probabilities for the threecompetitiveness clusters are .62, .20 and .18.

Estimated dependencies: Five of the γqq′ (dependence parameters) aresignificantly different from zero: γ15 > 0, γ25 < 0, γ35 < 0, γ45 < 0 and γ12 > 0indicating that the first four indicators are commonly correlated with indicator5 and that indicators 1 and 2 are, in addition, correlated. So, since the otherfour indicators are each correlated with indicator 5, all of the the indicators arejointly dependent (there is one h and all five indicators are in this set). That is,∏Hh=1 f(xhi |c ) = f(xi |c ) = f(x1i, x2i, x3i, x4i, x5i |c ), and one rejects the null

hypothesis that the the levels of the indicators are independent after one hasconditioned on cluster.The combined answers to 5, 2, 3 and 4 have decreased relevance (compared

to assuming them independent). For example, the answers to the statement,"I enjoy competing with others" and the "Number of races in the last twelve

14

months" do not have as much combined relevance as they would if the questionswere independent, and this decrease in relevance increases the more one hasraced, and the less one agrees with "I enjoy competing with others."Since γ12 > 0, the joint positive relevance of these two questions is minimized

if one definitely agrees that competition destroys friendships and that "gameswithout winners and losers are boring."12 Or, said the other way, the more onedisagrees with "competition destroys friendships" and the more one disagreeswith "games with no clear cut winners or losers are boring," the more relevantare these two questions in determining the composition of the clusters. Theanswers to questions 1 and 5 also have increased relevance, and their relevanceincreases the more one races and the more one disagrees with "competitiondestroys friendships."

The main parameters of interest, the µsq and the αq|c are diffi cult to directlyinterpret, so only reported online as Table A1.13 Easier to interpret are theestimated πsq |c , the probability that an individual chooses response category sto question q, conditional on being a member of cluster c (Table 3).14

Starting with the average response-levels by cluster for each indicator, the"means" in Table 3, one sees that competitiveness cluster2 is the highly com-petitive cluster, and cluster3 the not competitive. In explanation:

• cluster2 is least likely to agree that "Competition destroys friendships"(cluster3 most likely);

• cluster2 is most likely to agree that "Games with no clear cut winners orlosers are boring" (cluster3 the least likely);

• cluster2 are most likely to agree that "Competing is enjoyable" (cluster3least likely);

• cluster2 is more likely to agree that "Mountain bike rides are an opportu-nity to compete with others" (cluster3 least likely); and

• cluster2 is more likely to race (cluster3 least likely).

As expected, the majority of respondents are in cluster1 (62%), not extremein terms of competitiveness.That cluster2 is the cluster of highly competitive bikers is also apparent from

the estimated πsq |c in Table 3. For example, the estimated probability that an12γqq′ = γq′q . Recollect that γ(sq)(s′q′) = γqq′ (scoresq)(scores′q′ ); so for each response

pair (sq and s′q′), if γqq′ > 0, γ(sq)(s′q′) is monotically increasing in (scoresq)(scores′q′ ).And if γqq′ < 0, γ(sq)(s′q′) is montonically decreasing in (scoresq)(scores′q′ ). That is, aresponse pair (sq and s′q′) becomes more relevant (γ(sq)(s′q′) > 0) if the question pair (q andq′) has a positive γqq′ ; less relevant if it has a negative γqq′ And, this effect is increasing inthe multiplicative product of the two scores.13All of the online only tables are at

http://www.colorado.edu/economics/morey/papers/MtBikePsychPaperOnlineTables.pdf14Since the model has no covariates, these do not vary by i once one conditions on cluster.

15

individual in cluster2 answers "completely disagree" that "competition destroysfriendships" is 69%, for those in cluster3 it is 9%.

The estimated probability that an individual is in cluster c given that the in-dividual chooses response s to indicator q, πc|sq , also demonstrate that cluster2is the competitive cluster and cluster3 is the least competitive cluster. For ex-ample, the probability of being in cluster2 given that you "strongly agree" with"Games with no...winners...boring" is 43% whereas for cluster3 it is 5%. All ofthe πc|sq are reported online as Table A2.The probability that individual i is in cluster c conditional on his answers

the competitiveness questions, Pr(c : xi), assigns most individuals to a compet-itiveness cluster with high certainty.

4.2 The estimated LC cluster model of sensation-seeking

There are eight Likert-scale questions about sensation-seeking– see Table 1.Three clusters are assumed.Based on p − values, all of the parameters are significant and for those

parameters that vary by cluster, the αq|c parameters, the estimates differ signif-icantly by cluster. The estimated cluster-membership probabilities for the threesensation clusters are 58%, 28% and 14% (Table 4)Five of the γqq′ parameters, the correlation parameters, are significantly

different from zero: γ16 < 0, γ56 < 0, γ57 > 0, γ38 < 0 and γ78 > 0. That is,for this aspect of personality,

∏H

h=1f(xhi |c ) =∏3

h=1f(xhi |c ) = f2(x2i |c )f4(x4i |c )f(x1i, x3i, x5i, x6i, x7i, x8i |c )

There are three independent subsets of indicators. "Liking to do things that area little frightening" and "I rarely spend much time on the details of planningahead" are both independent of all of the other indicators; Indicators 1, 3 plus5 − 8 form a third correlated subset. Within f(x1i, x3i, x5i, x6i, x7i, x8i |c ), thejoint responses to questions 1, 3, 5, 6 and 8 have less relevance in determiningthe cluster-membership probabilities than they would if the answers to thesequestions were all independent, and the joint responses to questions 5, 7 and 8have more relevance. The latter is not surprising because only questions 5, 7and 8 ask specifically about bad things that might happen on a ride.The estimated πsq |c are reported in Table 4 along with the average response-

levels implied by these estimated probabilities. The estimated πc|sq are availableas Table A3 online.The mean response levels in Table 4 demonstrate that, relatively speaking,

cluster2 are sensation seekers and cluster3 are cautious. In explanation,

• cluster2 is most likely to agree that "Unpredictably is what makes lifeenjoyable" (cluster3 least likely);

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• cluster2 is most likely to agree that "I like to do things that are a littlefrightening" (cluster3 is least likely);

• cluster2 is most likely to agree that "I like exploring new trails even if Iget lost" (cluster3 least likely);

• cluster2 is most likely to agree that "I rarely spend much time on thedetails of planning ahead" (cluster3 least likely);

• cluster2 is most likely to choose a "descent at the limits of your technicalability", cluster3 a "fast, smooth descent with little risk of falling";

• cluster2 is most likely to agree with "I love to go fast.." (cluster3 leastlikely)

• cluster2 is most likely to "worry about crashes or injuries" (cluster3 leastlikely). Members of cluster2 are riding in a way that makes crashes morelikely and they like it that way.

Most individuals are assigned with high certainty to a sensation cluster.

4.3 The estimated LC cluster model of extroversion/introv

There are five questions about extroversion: four Likert-scale questions, plus"How often do you socialize off the bike (parties, dinner, talk on the phone,have coffee or drinks, etc.)."Seven of the γqq′ parameters are significantly different from zero: γ14, γ15,

γ23,γ34, γ35 > 0 and γ25, γ45 < 0; so, like in the competition model, all of thethe indicators are jointly dependent (there is one h and all five indicators are inthis set).The estimated πsq |care reported in Table 5, along with the average response-

levels implied by these estimated probabilities. The estimated πc|sq are reportedas Table A4 online.Starting with mean response levels for cluster and indicator (Table 5), one

sees that, relatively speaking, cluster2 are extroverted and cluster3 are intro-verted. In explanation,

• cluster2 is least likely to agree with "One only needs a few dependablefriends" (cluster3 most likely);

• cluster2 is most likely to agree with "I have a wide circle of good friends"(cluster3 least likely);

• cluster2 is more likely to disagree with "I try to avoid arguments andconfrontations" than is cluster3;15

15Cluster 1 is the most likely to disagree.

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• cluster2 is most likely to agree that "rides are an opportunity to enjoyfriends" (cluster3 least likely); and

• cluster2 is most likely to socialize off the bike (cluster3 least likely)

Most individuals are assigned with high certainty to a extroversion/introversioncluster.

5 A LC model of ride choice with competitive-ness, sensation-seeking, and extroversion co-variates

5.1 Ride choice

Unlike the estimated LC cluster models, this model is quite standard. Assumethe utility to individual i if they do ride j and belong to behavioral class cb is

Uij|cb = Vij|cb + εij|cb (10)

where εij|cb is a draw from an Extreme Value distribution. The term ridedenotes a trail/companion combination. The notation |cb denotes conditionalon belonging to behavioral class cb. We assume three classes, cb = 1, 2, 3.16 Theprobability of individual i choosing alternative A given that they belong to cband given the choice pair A,B is, therefore

PiA|cb =eViA|cb

eViA|cb + eViB|cb

(11)

The deterministic component of utility, Vij|cb , is assumed a function of thefollowing trail and companion characteristics:

trailj ≡ the number of miles of trail on ride j

singlej ≡ the fraction of the trail on ride j that is singletrack

gradej ≡ the average grade on the climbs, expressed as a %. A grade of over10% is steep.

climbsj ≡ the number of climbs on ride j

expendi ≡ weekly expenditures by individual i on entertainment (in $)

feej ≡ the fee charged for ride j (in $)16Models with additional behavioral clases were estimated but did not add much in terms

of signficance or interest.

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Dli ≡ 1 if individual i spends on himself for entertainment less than $25 aweek, and zero otherwise

Dmi ≡ 1 if i spends on himself for entertainment between $25 and $100 a week,and zero otherwise

Dhi ≡ 1 if i spends on himself for entertainment more than $100 a week, andzero otherwise

soloj ≡ 1 if i is alone on ride j, and zero otherwise

backXj ≡ 1, if there is a companion, and at normal effort levels i would be Xminutes behind at each wait point, zero otherwise. X is 10, 5, or 2.

frontXj ≡ 1, if there is a companion, and at normal effort levels i would beX minutes ahead at each wait point, zero otherwise.

The intent is to estimate and predict ride choice, by behavioral class. Specif-ically assume

Vij |cb = (βel|cbDli + βem|cbDmi + βeh|cbDmi)(expendi − feej) (12)

+βs|cb (singlej) + βt|cb (trailj) + βc|cb (climbsj) + βg|cb (gradej)

+βsolo|cb (soloj)

+βb10|cb (back10j) + βb5|cb (back5j) + βb2|cb (back2j)

+βf2|cb (front2j) + βf5|cb (front5j) + βf10|cb (front10j)

with the restriction climbsj = 0 ⇐⇒ gradej = 0.

The first line of Equation 12 is the utility individual i gets from other en-tertainment, conditional on belonging to cb. It depends on his budget for en-tertainment minus the fee for ride j, and the individual’s marginal utility fromexpenditures on entertainment. βel|cb is, for example, the marginal utility ofexpenditures for those who spend less than $25 a week and belong to cb. (Thesubscripts l, m and h denote low, medium, and high budgets for entertainment.)There are step-income effects, a simple way to incorporate the common obser-vation that willingness-to-pay is a function of available income. Income effectsare allowed to vary by class.The next line in 12 represents, conditional on class, the baseline utility one

gets from the site’s characteristics, independent of whether one is riding solo orone has a companion.The last three lines determine how the utility of the ride is affected by the

presence of a companion and the companion’s ability. If one is riding alone(soloj = 1 implying frontXj = backX

j= 0 ∀X) the expected utility from the

ride shifts from the baseline by βsolo|cbIf one has a companion (soloj = 0), utility shifts from the baseline by

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Vcompanionj|cb= βb10|cb (back10j) + βb5|cb (back5j) + βb2|cb (back2j)

+βf2|cb (front2j) + βf5|cb (front5j) + βf10|cb (front10j)

This expression is zero if the companion is of your ability (frontXj = backXj =0 ∀X), the default. So, if a companion of one’s ability is preferred to riding aloneβsolo|cb < 0; if a companion of one’s ability is preferred to a companion of adifferent ability, Vcompanionj|cb < 0, and if a companion of another ability ispreferred to a companion of one’s ability, Vcompanionj|cb > 0. The specificationallows for companion effects to vary by class, a possibility we want to investigate.

5.1.1 The personality covariates

Now consider the dimensions of personality (competitiveness, sensation-seekingand extroversion) as possible probabilistic determinants of the class member-ships.17 Let, HCompi = 1 (zero otherwise) if his probability of being in com-petitiveness cluster2 is ≥ 80% given his answers to the five competitivenessquestions. In contrast, Individual i is non-competitive (NCompi = 1) if hisprobability of being in competitiveness cluster3 is ≥ 80%).Using the 80% cutoff, if individual i is sensation-seeking, SensSeeki = 1

(zero otherwise) )and if the individual is cautious, Causi = 1. If individual i isan extrovert, Extroi = 1 (zero otherwise) )and if the individual is an introvert,Introvi = 1.Let Pr(cb : HCompi, NCompi, SensSeeki, Causi, Introvi, Extrovi) denote

the probability that individual i belongs to cb given his likely personality. Specif-ically assume,

Pr(cb : HCompi, NCompi, SensSeeki, Causi, Introvi, Extrovi) (13)

= exp(ϕcb + λHC|cbHCompi + λHC|cbNCompi + λTH|cb SensSeeki

+λCS|cb Causi + λI|cb Introvi + λE|cbExtrovi)

÷3∑

n=1

[exp(ϕcn + λHC|cnHCompi + λHC|cnNCompi

+λTH|cn SensSeeki + λCS|cn Causi (14)

+λI|cn Introvi + λE|cnExtrovi)] (15)

17We have found only one latent-class model that considers the explanatory power of per-sonality traits. Doeven-Eggens et al. (2008) estimate a standard/restrictive LC cluster modelof personal network type that identifed three clusters: family-orientated, peer orientated, andmixed. The model has no covariates. Separately, the clusters were then regressed on per-sonality traits using a LC logistic regression, so there was no attempt to model the networkclusters as a function of personality.

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where n in the denominator indexes the three behavioral classes. In words, theindividual’s most likely personality enters into the choice model as a covariatethat influences the individual’s class-membership probabilities.

The ln likelihood function for the sample is

lnL =

4583∑i=1

mi∑k=1

3∑cb=1

Pr (cb : HCompi, ..., Extrovi) (16)

∗[siAk

(lnPiAk|cb ) + (1− siAk)(1− lnPiAk|cb )

]where mi is the number of choice pairs answered by individual i (mi ≤ 5), andsiAk

= 1 if individual i selects alternative A in pair k and zero otherwise. 22, 685choice pairs were answered. The maximum likelihood β (Eq. 12 ) and λ (Eq.13) estimates are those that maximize Eq. 16.

5.2 The choice-model maximum-likelihood estimates

The covariate Extrovi was not significant, so λE|cb was set to zero– this sepa-rates us from the studies that find extroversion to be a significant determinantof exercise and recreational activity.One cannot reject the null hypothesis that the β parameter on solo is equal

for classes 1 and 2, so they were constrained to be equal. The choice modelwith the five significant personality covariates statistically dominates the choicemodel without these covariates. Based on the estimated p − values, all ofthe specified explanatory variables are significant determinants of the choicepairs, and for each explanatory variable its influence varies significantly by class.Overall R2 is .37 (.51 for Classb1, .12 for Classb2 and .67 for Classb3).The parameter estimates are reported in Table 6; for example, the β para-

meter on gradej is 16.28 for Classb1, −1.45 for Classb2 and 286.26 for Classb3–Classb3 likes steep trails. The unconditional class-membership probabilities are.27, .58 and .15 respectively.

Marginal utility of expenditures step decreases for Class1 and 2, but increasesfor Class3.Table 7 reports the probability of choosing, ceteris paribus, each level or

each ride attribute; for example the probability of choosing a 35 miles trail is.83 for Classb1, .26 for Classb2, and .30 for Classb3 (each column sums to one).The estimated probabilities of belonging to class cb if one, ceteris paribus,

chooses level k of a ride attribute are online as Table A5. For example, theprobability of being in Classb3 if one chooses a grade between 9% and 13% is.26. (26% might seem small given how much Classb3 likes steep, but note thatonly 15% of the population is in Classb3)Figure 2 shows the utility shifts relative to a companion of one’s own ability.

Negative bars indicate that the alternative is inferior; positive bars indicatepreferred. For all three classes, riding with someone of your own ability ispreferred to riding alone (solo = 1).

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5.2.1 Summarizing the effect on ride choice of trail attributes and

companion’s ability

Members of Classb3 want rides that are anaerobically challenging, technicallyexciting, and where they are challenged by a rider whose ability is close to theirs,

but, ideally, not equal– they want a challenging ride. WTP estimates reflectthis, they would pay, depending on how much they spend on entertainment,between $5 and $9 to have a companion that is two minutes faster rather thanthe same ability. As compared to the other two classes, more of Classb3 wouldprefer to ride alone (challenging themselves) than to ride with something whois substantially faster or slower (they don’t want to ride with the doped Lance,or with grandma). Members of Classb1 want to ride with someone of theirown ability on a long and endurance-challenging ride. Members of Classb2,the largest class, have more uniform preferences over trail characters, want acompanion, and the closer their companion is to their ability, the better.Expressing preference in terms of money, Table 8 reports WTP, for riding

with a companion of one’s own ability rather than a companion who is twominutes faster.

Table 8: WTP per-trip for a companionthat is same ability rather than two minutes faster

Classb1 Classb2 Classb3low entert. expend. $3.62 $5.52 −$8.62med. entert. expend. $4.58 $7.30 −$7.67high enter. expend. $4.70 $13.81 −$4.69

These estimated WTP are negative for Classb3 because they prefer a com-panion that is two minutes faster. Its absolute value is their WTA a companionof their exact ability. Recollect that the marginal utility of money is increasingfor those in Classb3; this is why WTP per-trip declines in absolute terms asweekly expenditures on entertainment increases.

5.2.2 The influence of each personality trait on class membership

Table 9 reports the class-memberships probabilities as a function of each person-ality trait. Recollect that the class-membership probabilities with no personalityinformation are 27%, 58% and 15% respectively

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Table 9: Prob. of class membership as a function of the 10 personality typesComp trait Sensation trait Introv trait Classb1 Classb2 Classb3Hcomp SensSeek Introv 47% 17% 36%Hcomp SensSeek Not Introv 32% 42% 26%Hcomp Caus Introv 40% 37% 23%Hcomp Caus Not Introv 20% 67% 13%Ncomp SensSeek Introv 56% 29% 15%Ncomp SensSeek Not Introv 31% 60% 9%Ncomp Caus Introv 40% 52% 8%Ncomp Caus Not Intov 17% 79% 4%Not extreme Not extreme Not Introv 26% 60% 13%

Knowing an individual’s personality type (set of the three personality traits)substantially, and significantly, allows one to identify that individual’s most-likely class. For example, whereas 15% of respondents are in Classb3, mountainbikers who are non-competitive, cautious and who are not introverts have onlya 4% probability of being in Classb3, whereas mountain bikers who are highlycompetitive, sensation seekers and introverts have a 36% probability of being inClassb3. We expected that being competitive and sensation-seeking would makeit more likely one is in Classb3, but did not anticipate that being an introvertwould do the same, the opposite of what some of the earlier research found.Table 10 shows how personality changes the odds of being in each class. For

example, the first set reports the odds of being in each class if one is highlycompetitive as compared to non-competitive. In general, being of an extremepersonality trait pushes one out of Classb2, toward both Classb1 and 3. Beinghighly competitive rather than non-competitive pushes mountain bikers moretowards Classb3 than toward Classb1 . Being a sensation seeker rather thanbeing cautious does the same, but the relative push toward Classb3 is not asstrong. Being an introvert pushes a little more toward Classb1 than Classb3.

Table 11 report the WTP per-trip by personality type for having a compan-ion of one’s own ability rather than a companion that is two minutes faster.These are the WTP per-trip by class (Table 8) weighted by the probabilitiesthat a personality trait is in each class.

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Table 11: WTP per-trip by personality type for having a companionthat is of one’s ability rather than two minutes fasterPersonality type weekly expend on entertComp trait Sensation trait Introv trait low medium highHcomp SensSeek Introv −$0.49 $0.61 $2.53Hcomp SensSeek Not Introv $1.23 $2.53 $5.26Hcomp Caus Introv $1.45 $2.70 $5.10Hcomp Caus Not Introv $3.35 $4.85 $5.64Ncomp SensSeek Introv $2.32 $3.51 $5.36Ncomp SensSeek Not Introv $3.64 $5.09 $8.08Ncomp Caus Introv $3.60 $4, 98 $7.62Ncomp Caus Not Intov $4.67 $6.28 $9.99Not extreme Not extreme Not Introv $3.14 $4.59 $7.75No information about personality $2.86 $4.32 $8.58

Only one of the WTP estimates by personality type is negative (a highlycompetitive, sensation-seeking, introvert with low weekly expenditure on enter-tainment). This is because only Classb3 has a negative per-trip WTP (see Table8) and only 15% of the mountain bikers are in Classb3. Within each weekly ex-penditure category, WTP per trip varies between four-fold and ten-fold as afunction of personality type.

6 Summary, thoughts and relevance

Our results indicate that a companion and her ability can be as important assite characteristics in determining one’s site choice. And show that hetero-geneity in site and companion choice varies probabilisticly as a function of threedimensions of personality (competitiveness, extroversion/introversion and thrill-seeking). Recreational preferences are based, at least in part, on whether oneprefers to seek thrills or caution, whether one prefers to compete against othersor against oneself, and whether on prefers to be an introvert. Making personalitya covariate is a step towards incorporating results from psychology and behav-ioral economics into environmental valuation. The tendency amongst environ-mental economists, including us, has been to say that behavior varies simplybecause preferences vary, and stopping there, but this stopping rule should bequestioned. In the words of Stigler and Becker (1977) “No significant behaviorhas been illuminated by assumptions of differences in tastes.”– something thatcan explain everything explains nothing.Recently there has been considerable research in environmental economics

that segments individuals into latent classes based on indicators (observedchoices and/or answers to attitudinal and stated-preference questions). Themodel typically used is a latent-class cluster model that imposes two restrictiveassumptions: (1): All of the indicators are of the same type (typically discrete,nominal random variables). And (2) once one has conditioned on class, theresponses are statistically independent. With respect to (1), indicator data is

24

often not all of one type, so one is forced, for example, to treat both a normally-distributed indicator and an ordinal discrete indicator as a discrete nominalindicator, or to ignore those indicators that are not of the specified type. Withrespect to (2), there is no way to test whether indicators are independent afteronce has conditioned on class. Ignoring dependence leads to one to concludethere are more classes that there actually are.We present and estimate a LC cluster model that relaxes both of these as-

sumptions, a model that embeds the standard model as a special case. While weutilized this generalized model and answers to personality questions to estimatepersonality clusters, one can use it for any type of indicator data.

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Table : 1 Likert-scale questions on competitiveness, sensation-seeking, and extroversion

How strongly do you agree or disagree with the following statement?*, **

Comp1 Competition destroyes friendships (1% , 9% , 25% ,32% ,32% )

Comp2 Games with no clear cut winners or losers are boring (3% ,7% ,15% ,21% ,53% )

Comp3 I enjoy competing with others (26% ,46% ,15% ,9% ,3% )

Comp4 Mountain bike rides are an opportunity to compete with others (10% ,32% ,26% ,20% ,12% )

Comp5 Number of races done in the last 12 months (1=never raced, 2= 1 race, 3= 2-3 races, 4= 4-5, 5= 6 or more races) (62% ,8% ,11% ,5% ,14% )

Sensation1 Unpredictability is what makes life enjoyable (28% ,49% ,15% ,6% ,1% )

Sensation2 I like to do things that are a little frightening (32% ,51% ,10% ,6% ,1% )

Sensation3 I like exploring new trails even if I get lost (48% ,39% ,6% ,5% ,1% )

Sensation4 I rarely spend much time on the details of planning ahead (9% ,23% ,17% ,35% ,15% )

Sensation5 If you had to choose between a fast, smooth descent with little risk of falling or a descent at the limits of your technical ability,

which would you choose?( 0=Smooth, fast, and little risk of falling ; 1=at my limit of my ability) (45% ,55%,)

Sensation6 To what extent do you agree with the statement "I love to go fast on my mountain bike." (52% ,32% ,10% ,5% )

Sensation7 To what extent do you agree with the statement, "I worry about crashes or injuries." (15% ,43% ,20% ,16% ,6% )Sensation7 To what extent do you agree with the statement, "I worry about crashes or injuries." (15% ,43% ,20% ,16% ,6% )

Sensation8 To what extent do you agree with the statement "Riding alone frightens me." (2% ,14% ,15% ,24% ,44% )

Extroversion1 One only needs a few dependable friends (16% ,35% ,21% ,17% ,11% )

Extroversion2 I have a wide circle of good friends (22% ,33% ,19% ,20% ,6% )

Extroversion3 I try to avoid arguments and confrontations (23% ,41% ,18% ,14% ,4% )

Extroversion4 Mountain bike rides are an opportunity to be with and enjoy my friends (50% ,31% ,13% ,4% ,1% )

Extroversion5 How often do you socialize off the bike (parties, dinner, talk on the phone, have coffee or drinks, etc.) with your mountain-bike partners?

(0=never, 1=occasionally, every few months; 2=a moderate amount, 1-2 a month; 3=quite often, on average 1 a week) (6% ,31% ,31% ,32% )

* Unless otherwise indicated, each question is scored: 1=definitely agree, 2=somewhat agree, 3=neither agree nor disagree

4=somewhat disagree, 5=definitely disagree

**Probabilities of responses to scores are reported In brackets

Table 3 Latent-class cluster model of competitiveness -

Estimated probabilities for each level of each question, by cluster*

Comp Cl1 Comp Cl2 Comp Cl3

Highly Not

competitive competitive

Cluster Size 62% 20% 18%

Competition

Comp1 "Competition destroyes friendships"

1** 1% 0% 4%

2 8% 0% 21%

3 28% 5% 40%

4 37% 25% 26%

5 27% 69% 9%

Mean 3.81 4.63 3.16

Comp2 "Games with no … winners ... boring"

1 3% 6% 0%

2 7% 11% 2%

3 15% 20% 7%

4 22% 22% 17%

5 52% 41% 73%

Mean 4.13 3.80 4.61

Comp3 "I enjoy competing with others"

1 17% 76% 3%

2 59% 23% 29%

3 17% 1% 26%

4 6% 0% 29%

5 1% 0% 13%

Mean 2.15 1.24 3.20

Comp4 "… rides ... opportunity to compete ..."

1 5% 33% 0%

2 33% 53% 4%

3 33% 12% 15%

4 22% 2% 35%

5 7% 0% 45%

Mean 2.93 1.84 4.21

Comp5

never raced 64% 52% 69%

1 race 8% 8% 7%

2-3 races 10% 13% 9%

4-5 races 5% 7% 4%

6 or more 13% 20% 11%

Mean 0.96 1.35 0.82

*For each class, for each question, response categories, by cluster sum to one

** 1=definitely agree, 2=somewhat agree, 3=nether agree nor disagree,

4=somewhat disagree, 5=definitely disagree

Table 4 Latent-class cluster model of sensation-seeking

Estimated probabilities for each level of each question, by cluster*

Sensation Cl1 Sensation Cl2 Sensation Cl3 Sensation Cl1 Sensation Cl2 Sensation Cl3

Sensation- Cautious Sensation- Cautious

seekers seekers

Cluster Size 58% 28% 14% Cluster Size 58% 28% 14%

Sensation Sensation

Sensation1 "Unpredictability ... life enjoy." Sensation5 "… smooth descent... or at limits..."

1** 14% 70% 2% 0 49% 23% 76%

2 63% 29% 33% 1 51% 77% 24%

3 18% 1% 31% Mean 0.51 0.77 0.24

4 5% 0% 27%

5 0% 0% 6%

Mean 2.14 1.30 3.03

Sensation2 "I like... frightening" Sensation6 "I love to go fast..."

1 11% 90% 0% 1 48% 74% 24%

2 77% 10% 27% 2 36% 23% 35%

3 10% 0% 28% 3 11% 3% 21%

4 2% 0% 36% 4 4% 0% 15%

5 0% 0% 9% 5 1% 0% 5%

Mean 2.03 1.10 3.26 Mean 1.74 1.30 2.43

Sensation3 "I like... even if I get lost" Sensation7 "I worry about crashes or injuries"

1 38% 88% 11% 1 16% 9% 26%

2 52% 12% 42% 2 45% 36% 50%

3 7% 0% 17% 3 20% 22% 15%

4 3% 0% 22% 4 15% 23% 7%

5 0% 0% 9% 5 5% 10% 2%

Mean 1.77 1.12 2.75 Mean 2.47 2.88 2.08

Sensation4 "I rarely… time… planning ..." Sensation8 "Riding alone frightens me"

1 8% 15% 4% 1 3% 1% 4%

2 22% 30% 14% 2 15% 9% 19%

3 18% 18% 15% 3 16% 13% 18%

4 37% 28% 42% 4 24% 24% 24%

5 16% 9% 25% 5 42% 52% 36%

Mean 3.30 2.87 3.71 Mean 3.89 4.17 3.68

*For each class, for each question, response categories sum to one

** 1=definitely agree, 2=somewhat agree, 3=nether agree nor disagree,

4=somewhat disagree, 5=definitely disagree

Table 5 Latent-class cluster model of extroversion/introversion

Estimated probabilities for each level of each question, by cluster*

Extrov Cl1 Extrov Cl2 Extrov Cl3

Extraverts Introverts

Cluster Size 76% 14% 11%

Extroversion

Extroversion1 "One only needs a few ... friends"

1 14% 0% 58%

2 40% 3% 36%

3 25% 11% 5%

4 16% 35% 1%

5 5% 51% 0%

Mean 2.59 4.33 1.48

Extroversion2 "I have a wide circle of ... friends"

1 15% 78% 1%

2 39% 21% 8%

3 22% 1% 15%

4 20% 0% 48%

5 4% 0% 28%

Mean 2.59 1.24 3.94

Extroversion3 "I try to avoid arguments and ..."

1 22% 25% 30%

2 40% 42% 43%

3 19% 18% 16%

4 15% 13% 10%

5 4% 3% 2%

Mean 2.40 2.28 2.12

Extroversion4 "... rides ... opp. enjoy ... friends"

1 49% 73% 26%

2 33% 22% 33%

3 13% 4% 24%

4 3% 0% 11%

5 1% 0% 5%

Mean 1.74 1.32 2.37

Extroversion5 "How often do you socialize off the bike"

Never 6% 2% 10%

Occasionally 32% 21% 40%

Moderately 31% 32% 28%

Quite often 31% 45% 22%

Mean 1.88 2.20 1.61

*For each class, for each question, response categories sum to one

** 1=definitely agree, 2=somewhat agree, 3=nether agree nor disagree,

4=somewhat disagree, 5=definitely disagree

Table 6: Parameter estimates for the behavioral ride-choice model

Variables Class_b1 Class_b2 Class_b3 p-value p-diff

low expenditure -0.38 -0.08 -0.11 0.000 0.000

medium expenditure -0.30 -0.06 -0.12 0.000 0.000

high expenditure -0.29 -0.04 -0.20 0.000 0.000

single 0.02 0.01 0.03 0.000 0.002

trail 0.14 0.00 0.01 0.000 0.000

climbs 0.36 0.19 0.01 0.000 0.001

grade 16.28 -1.45 286.26 0.000 0.000

solo -1.32 -1.32 -0.85 0.000 0.037

back10 -1.30 -0.77 -0.07 0.000 0.001

back5 -0.61 -0.53 -0.09 0.000 0.270

back2 -0.33 -0.55 0.95 0.000 0.000

front2 -1.37 -0.45 0.93 0.000 0.000

front5 -0.11 -0.66 0.01 0.000 0.003

front10 -1.32 -0.94 0.20 0.000 0.000

Intercept 0.00 0.83 -0.68 0.000

Covariates

Most competitive 0.00 -0.23 0.20 0.068

Not competitive 0.00 0.12 -0.85 0.028

Introverted 0.00 -1.28 -0.06 0.001

Sensation-seekers 0.00 -0.31 0.30 0.000

Cautious 0.00 0.59 0.01 0.030

Table 7: Estimated probability of choosing each level of each attribute, by behavioral class*

Class Size Class_b1 Class_b2 Class_b3 Class Size Class_b1 Class_b2 Class_b3

27% 58% 15% 27% 58% 15%

single (%) solo

0-17 13% 19% 7% no 79% 79% 70%

20-40 26% 32% 17% yes 21% 21% 30%

50 10% 10% 8%

60-66 25% 23% 26% back10

100 26% 17% 42% no 79% 68% 52%

Mean 55.80 47.63 68.65 yes 21% 32% 48%

trail (miles)

7 2% 24% 21% back5

14 4% 25% 23% no 65% 63% 52%

21 11% 25% 25% yes 35% 37% 48%

35 83% 26% 30%

Mean 32.07 19.56 20.61 back2

climbs (n) no 58% 63% 28%

0 11% 17% 25% yes 42% 37% 72%

1 16% 21% 25%

2 24% 25% 25% front2

4 49% 37% 25% no 80% 61% 28%

Mean 2.59 2.18 1.76 yes 20% 39% 72%

grade (%)

0 8% 17% 0% front5

0.9-1.3 13% 26% 0% no 53% 66% 50%

1.8-3.6 22% 34% 0% yes 47% 34% 50%

5.4 9% 8% 0% front10

9.0-13.0 48% 15% 100% no 79% 72% 45%

Mean 0.07 0.03 0.14 yes 21% 28% 55%

*For each class, for each attribute, attribute levels sum to one

0

0.5

1

1.5

back10 back5 back2 front2 front5 front10 solo

Figure 2: Utility as a function of the gap, by behavioral class

Class_b1

Class_b2

Class_b3

-1.5

-1

-0.5

back10 back5 back2 front2 front5 front10 solo

Table 10 - Odds ratio of being in each behavioural class

Class_b1 Class_b2 Class_b3

Thrill/Introv 0.84 0.59 2.39

Thrill/NotIntrov 1.01 0.71 2.88

Cautious/Introv 1.00 0.70 2.86

Cautious/NonIntrov 1.20 0.84 3.42

Class_b1 Class_b2 Class_b3

Hcomp/Introv 1.16 0.47 1.55

Hcomp/NotIntrov 1.55 0.63 2.07

Ncomp/Introv 1.39 0.57 1.85

Ncomp/NotIntrov 1.85 0.75 2.46

Class_b1 Class_b2 Class_b3

Hcomp/Thrill 1.47 0.41 1.39

Hcomp/Cautious 1.96 0.55 1.86

Ncomp/Thrill 1.77 0.49 1.67

Ncomp/Cautious 2.35 0.65 2.22

Only change Hcomp vs Ncomp

ODDS ratios

ODDS ratios

Only change SenSeek vs Caut

ODDS ratios

Only change Introv vs NonIntrov