Journal of Choice Modelling 38 (2021) 100267
Contents lists available at ScienceDirect
Journal of Choice Modelling
journal homepage: http://www.elsevier.com/locate/jocm
Activity participation, episode duration and stop-making behavior of pilgrims in a religious event: An exploratory analysis
Ashish Verma a,*, Meghna Verma b,**, Punyabeet Sarangi c,***, Vivek Yadav c,****, Manoj M d,***** a Department of Civil Engineering and Robert Bosch Centre for Cyber-Physical Systems, Indian Institute of Science (IISc), Bangalore, 560012, Karnataka, India b Ramaiah Institute of Management, Bangalore, 560012, Karnataka, India c Department of Civil Engineering, Indian Institute of Science, Bangalore, 560012, Karnataka, India d Department of Civil Engineering, Indian Institute of Technology, Delhi, 110016, Hauz Khas New Delhi, India
ARTICLE INFO ABSTRACT
Keywords: Activity travel pattern of pilgrims in a religious setting is a complex process. Extant literature on Activity participation religious tourism has taken minimal efforts in addressing such complexity, which has led to a Episode duration paucity of information on preferred activity participation destinations and trip chain sequences of Propensity of stops pilgrims. So, the present research objective is two-fold. First, to examine the causal effects of Kumbh mela socio-demographics and daily local temperature on activity participation, trip chain type, and Structural equation modeling (SEM) Ordered logit model (OL) time allocation of individuals using structural equation modeling (SEM) that can help identify the dominant activity patterns. Second is to explore the impact of socio-demographic variables and activity patterns on the propensity of stop-making behavior using an ordered logit (OL) frame work to better plan and manage the influx of flows. The primary data was collected using an activity-travel diary by taking the case study of the Kumbh Mela event, which is considered as the world’s largest mass religious gathering, held at Ujjain, India, in 2016. From the results, it is observed that Males have a lower tendency to take multiple stops for primary religious activities and have simple trip chains. An increase in the members of a family visiting Kumbh decreases their overall time spent across various activities. As the mercury (temperature) rises, it reduces tourist’s participation in recreational and discretionary activities. Individuals who participate in primary and secondary religious activities tend to spend more time at Kumbh as compared to individuals who primarily visit for recreational purposes. These empirical findings provide meaningful insights for managing large religious events.
* Corresponding author. ** Corresponding author., *** Corresponding author. **** Corresponding author. ***** Corresponding author. E-mail addresses: [email protected] (A. Verma), [email protected], [email protected] (M. Verma), punyabeet.sarangi287@gmail. com (P. Sarangi), [email protected] (V. Yadav), [email protected] (M. M). https://doi.org/10.1016/j.jocm.2021.100267 Received 3 August 2019; Received in revised form 13 November 2020; Accepted 5 January 2021 Available online 11 January 2021 1755-5345/© 2021 Elsevier Ltd. All rights reserved. A. Verma et al. Journal of Choice Modelling 38 (2021) 100267
1. Introduction
Religious tourism can be viewed as any travel that involves religious experience (Pus¸cas¸u, 2015; Raj and Griffin,2015 ). Given this definition,it can be said that all trips taken to religious sites and the activities that individuals engage themselves at these sites broadly define the religious tourism context from a transportation perspective. In fact, over the past few years, many researchers within the transportation field have explored the challenges faced by this sector. Firstly, any form of tourism (religious or recreational) is a perishable economic product due to the observed Spatio-temporal variances in the preference of travelers (Witt and Witt, 1995). These shifts in the behavior of travelers1 may have detrimental effects on the economic vitality of a country. Secondly, policymakers and transport planners face an arduous task of planning as well as maintaining a hassle-free religious event for visiting travelers as religious events are associated with trafficcongestions, freight movements, etc. (Ahmed and Memish, 2019). Knowing the socio-demographic profilingof travelers and their motivation to visit and participate in religious activities can help planners improve and expand services for a steady flow of travelers. To address these challenges, as well as to have a better understanding of the tourism behavior, re searchers have applied the well-defined activity-travel demand paradigm into the religious tourism sector. The popularity of these activity-based modeling frameworks can be attributed to the ease with which they incorporate the temporal and spatial constraints at the macro (household) and micro (individual) level of activity participation while providing a framework that is more viable and implementable in forecasting travel demand (Arentze and Timmermans, 2004; Bhat and Koppelman, 1999). Besides, these well-definedactivity mechanisms provide acceptable inferences and a better understanding of the travel behavior of people that helps transport planners in framing policies to regulate the travel demand management smoothly. Moreover, the interdependency between various keywords, namely joint travel, task and time allocation, episode frequency, trips, and tours, is well established in the extant literature on activity-travel demand modeling (Golob, 2003; Simma and Axhausen, 2001). This stream of literature is further enriched by various activity-based studies (Cheng et al., 2019; Liu et al., 2018; Manoj and Verma, 2015a) conducted in developing countries. These past studies based on activity paradigm have explored the interdependence between household demographics, individual attributes, in-home, and out-of-home activity participation, and travel behavior. However, only a handful of past studies in the activity domain have attempted to explicitly model the inherent relationship between pilgrim’s activity participation and time allocation behavior in a massive conglomeration of pilgrims at a religious destination. This has led to a paucity of information on destination choices & preferences; crowd movement & management; and prioritizing & planning activity partici pation due to temporal and spatial constraints in the context of events, festivals, and religious gatherings, etc. that are of global importance (Smallwood et al., 2012; Xia et al., 2011; Zoltan and McKercher, 2015). Notably, in a religious event, walking is the primary mode of movement for most of the between and within destination trips that are undertaken to participate in various activities inside the cordoned destination region2 for various religious fairs or festivals worldwide (Verma et al., 2018). With walking being a slow mode of travel, it induces both acceptable trip time and distance constraints. As a consequence, the choices and preferences of travelers in allocating time to various religious activities have to be carefully interpreted. Furthermore, the propensity of taking stops during a home-based or non-home based tour by an individual has also been exten sively researched in the past decade to understand the trip patterns and frequency of episodes undertaken by an individual (Chu, 2003; Timmermans et al., 2003). The findingsof these studies reveal that travel patterns are mainly independent of spatial settings though some exceptions exist. However, unlike the traditional activity travel-based analysis where home-to-home is considered as the anchor point for a trip chain, in case of festivals and religious events, they have designated entry and exit points that make the trip chaining pattern more interesting and exciting to study but has garnered limited attention. In a religious event setting, pilgrims/visitors desire to participate in several activities in a cordoned destination region forces them to link their activities, resulting in complex trip chains. This interlinking of trips exhibited by individuals is stemmed due to a variety of external and internal factors (Smallwood et al., 2012; Xia et al., 2011). The external factors include socio-demographic characteristics (sex, age, income), weather condition (temperature, humidity etc.), socio-cultural factors (language, religion, culture) and service quality attributes (access to transport facilities, atm, etc.) while the internal factors include psychological aspects, behavioral traits like motivation, level of satisfaction, and perception towards individual safety and security (Alejziak, 2013; LaMondia et al., 2008). Thus, it can be seen that unlike the traditional home-based activity setting, a multitude of variables impacts the activity participation, time spent, and stop-making behavior of travelers visiting religious destinations. However, the current work is mainly concerned with the causal effects of socio-demographic variables on activity participation, time spent, and the stop-making behavior of travelers visiting a religious site. Based on the above discussions, the present study has tried to address the existing gaps in the religious tourism sector with the following objectives: i) examine the interdependencies between socio-demographics, climatic conditions, religious activity partici pation, and travel pattern (that includes total time spent and trip chain type) of individuals using structural equation model (SEM). ii) exploring the impact of socio-demographic variables, climatic conditions, and religious activity participation on the propensity of stop- making behavior using an ordered logit (OL) model to identify the dominant activity patterns of tourists/pilgrims at a religious event. Here, both the proposed empirical approaches are estimated independently by taking the case study of Kumbh Mela, which was held at Ujjain, India, from April 22, 2016 to May 21, 2016. The reason behind carrying out the study at Kumbh Mela is that it is considered as the largest human congregation on Earth and experiences footfall from all over the world. The event represents a fascinating amalgam
1 For the ease of convenience, the terminologies ‘travelers’, ‘tourists’, ‘visitors’ and ‘pilgrims’ used in the present study are synonymous of each other and must not be interpreted differently. They refer to an individual visiting Kumbh Mela. 2 A cordoned destination region is perceived as an area encircled with discrete physical & management boundaries with closeness to resources (i. e., attraction or recreation sites) such that an individual can visit the entire area in a day’s time (WTO, 2007).
2 A. Verma et al. Journal of Choice Modelling 38 (2021) 100267 of religious and social activities, and recreational elements assembled in a short span with limited space (Maclean, 2008). The remaining paper is divided into six sections. Section 2 briefly describes the extant studies on activity participation, time allocation, and trip chaining behavior from a methodological perspective. Section 3 and 4 respectively discuss the specification and theoretical foundation behind the empirical frameworks undertaken in the present paper. This is followed by section 5, which contains a description of the study area and data (exploratory analysis of exogenous and endogenous variables). The penultimate section (Section 6) elaborately interprets the causal effects and empirical findingsof the models. The finalsection concludes with the salient findings and scope of future research.
2. Literature review
Understanding tourist/visitor’s time spent on various activities and trip-chain pattern at religious events have been gaining interest among researchers as it impacts the planning and regulation of policies at these events. Thus, section 2.1 presents a brief review of past studies that have explicitly used structural equation modeling (SEM) to model time spent by individuals in various religious activities, and section 2.2 discusses past studies that have used ordered logit (OL) model to study the stop-making propensity of individuals.
2.1. Modeling time allocation and trip chaining pattern of individuals using SEM framework
Contemporary studies on household travel behavior have established a firm relationship between activity participation, time allocation, trip chaining pattern, and socio-demographic (Golob, 2000; Golob and McNally, 1997; Lu and Pas, 1997; Simma and Axhausen, 2001). While, activity participation may be definedas the need to perform an activity that motivates an individual to take an out-of-home trip, distributed over space and time (Kitamura, 1988) trip chaining, on the other hand, may be definedas a tour with the home as the starting and ending point and consists of multiple out-of-home activities as anchor points (Primerano et al., 2008). In this regard, Golob and colleagues pioneered the SEM technique in transportation planning to understand the association between activity participation, trip chain, and time spent across socio-demographic categories. After which, in the last decade SEM models have been widely used to study the causal effect of individual characteristics and household structure on activity participation and travel pattern choices (Chen and Akar, 2017; Kuppam and Pendyala, 2001; Pitombo et al., 2011; Whitehead-Frei and Kockelman, 2010). Among these studies, Kuppam and Pendyala (2001) focused on understanding the structural relationships between commuter’s de mographics, activity patterns, trip generations, and trip chaining. The results of their study proved that there exists a strong rela tionship between demographics, activity engagement, and travel behavior. Besides, Whitehead-Frei and Kockelman (2010), in their study of American time use using SEM, focused mainly on the in-home and out-of-home activity-participation of children and women. Similar studies conducted by Pitombo et al. (2011) and Chen and Akar (2017) observed that family income, household head, gender as well as car ownership has a strong influence on activity participation, joint travel, and origin/destination choices. Further, in affir mation to the studies conducted in developed countries, studies conducted in developing nations such as research works by Cheng et al. (2019) in the Chinese context and works by Manoj and Verma (2017, 2015b) in the Indian context also concluded that the afore mentioned variables strongly influence the travel behavior and activity participation of household members. However, most of the extant literature that have modeled time allocation and trip chaining pattern of individuals using the SEM framework has primarily focused on the home-based tours. Besides, scholarly works in the field of religious destination or leisure tourism are either obsessed with eliciting the behavioral traits of visitors at a tourist/religious destination or are focused on under standing the decision-making process of a tourist in choosing a destination. As per the author’s knowledge, very few peer-reviewed studies have touched upon the activity participation and travel behavior of visitor’s at a religious destination from a transport planning perspective. Summarizing these studies, it can be said that the movement of visitors between various activity focal points at a religious/tourist destination can be complex (Xia et al., 2011). Such complexity stems from the numerous travel routes available to an individual (Gayathri et al., 2017), the spatial distribution of activity attractions (Lew and McKercher, 2002) and demographics of the visitors (Xia et al., 2011). Hence, these interesting observations, combined with the revival of religious sites/tourism destinations across the globe, presents a unique challenge of exploring the activity participation and travel behavior of visitors at these destinations.
2.2. Ordered logit model
The number of stops taken by an individual during a tour is generally modeled as an ordered variable in the literature (Daisy et al., 2018). Therefore, ordered logit (OL) models have been utilized to not only understand the travel behavior of people through household surveys (Bhat and Srinivasan, 2005; Nurul Habib and Miller, 2007; Daisy et al., 2018) but also tourist behavior at religious even ts/festival destinations (Kemperman et al., 2003; Yang et al., 2011). The OL approach predicts the preferences of persons in under taking an ordered number of stops in a temporally constrained activity set up (Nurul Habib and Miller, 2007). In the context of home-based tour, frequency of activity episodes rather than total stops during a tour is given as the input in the ordered set up (Bhat and Zhao, 2002; Bhat and Srinivasan, 2005; Nurul Habib and Miller, 2007; Arentze et al., 2011). Many researchers have found a variety of factors, including socio-demographics, land use density, work schedule, availability of transportation services, work duration, activity levels etc., affecting the propensity of making stops. Bhat (1997) formulated a joint model of work mode choice and non-work stops for commutes to work. The model identified socio-demographic variables, work duration and overall activity at the household level to be significantly affecting the stop making propensity of workers. In a similar study, Bhat (1999) also found that socio-demographics, retail employment density and work-related characteristics significantly impacts the evening commute stop making behavior of workers using the 1990 San Francisco Bay Area Household Survey data. Krizek (2003) looked at the effect of
3 A. Verma et al. Journal of Choice Modelling 38 (2021) 100267 accessibility in neighborhood of Central Puget Sound regions (Seattle, Washington) on tour types and stops and found that households in neighborhoods with higher level of access are prone to make few stops for work and maintenance tours as residents tend to make much simple tours (leave and back home). Among research works on similar lines in European context, Maat and Timmermans (2006) found that high density areas cause more complex trip chains resulting in a greater number of stops per tour. Apart from socio-demographics and built environment in the previous studies, Cao et al. (2008) also identified that attitudes and work-related attributes influence the stop making behavior of workers. Kun et al. (2009) used land use density, work schedule, transportation services and socio-demographics of workers in Beijing to predict the number of stops at fivedifferent time periods of the day using stop frequency models. Doherty and Mohammadian (2011) used ordered response choice models in predicting the activity schedules of out-of-home tours as function of activity types and its characteristics. However, despite all these methodological advancements to model the stop making propensity in the home-based setup, very few of these advanced models have seen an application in reli gious/tourism activities. Moreover, from the handful of studies (Kemperman et al., 2003; Yang et al., 2011), which the authors could gather, on modeling tourism activity stops, the findings revealed that waiting time in queues, activity distance locations, visitor characteristics affect their stop making behavior. However, these studies analyzed tourism set up, and none of the existing literature has tried to explore it in a religious context, which makes it more appalling to model the religious activity episodes of pilgrims. The above literature is not comprehensive and exhaustive. As can be inferred from the above paragraphs of section 2, most of the past studies have limited themselves to formulate empirical approaches to study the out-of-home activity participation and travel behavior of individuals using household-level surveys in developed countries. However, there is a lack of literature on the travel behavior of tourists in a religious gathering. Evidence from past studies have also indicated that the travel behavior of pilgrims in a religious setting is entirely different from that of contemporary household travel behavior. For example, an empirical study conducted by Masiero and Zoltan (2013) found that young people mostly travel to participate in recreational and cultural activity hotspots and are more likely to move widely through a destination. On the other hand, families traveling to these destinations show restricted but more intense movement patterns. Hence, a better understanding of the travel patterns of the heterogeneous participants at a religious event like Kumbh Mela helps in formulating effective transportation policies and adequately manage the logistics issues.
3. Model specification
This section describes the formation of empirical frameworks used in the present study.
3.1. SEM specification
Based on the activity-travel behavior theory and literature review, a structural equation modeling (SEM) framework was laid out, as shown in Fig. 1. Based on the firstobjective and as shown in the figure,it was hypothesized that socio-demographic characteristics and external climatic conditions (Temperature expressed in degree Celsius) influencetravel patterns (includes the total time spent and trip chain type) of travelers visiting Kumbh Mela mediated by activity participation. In doing so, the indirect effects of socio- demographics and climatic conditions on travel patterns occur as well channeled via activity participation. The total effects are then calculated by adding up the direct and indirect effects. Here, activity participation is captured by dummy variables with ‘1’ indicating an individual’s decision to participate in an activity, namely Primary Religious, Secondary Religious, and Recreational activities, and ‘0’ indicates non-participation. As can be seen, all the variables that are of concern in the present study are directly observed (manifest variables). Hence, the results are based on a series of simultaneously estimated structural (linear regression) equations. A brief description of the list of sub-activities included under each main activity type in a religious setting is shown in Table 1. Classificationof sub-activities into these four main types of activity is done based on the review of earlier studies (Buzinde et al., 2014; Raj and Griffin, 2015) and to the best understanding of the authors about a religious event. Here, discretionary activities were not considered as a mediation variable in the SEM framework as discretionary activities are something individuals must perform out of simple necessity, that is, an individual would probably not participate in Kumbh Mela just to perform discretionary activities. Primary religious activities include offering prayer, taking a holy dip, visiting temples, and visiting camps/akharas. These activities are the primary reasons for the pilgrims to attend Kumbh Mela. The other religious activities like listening to preaching, reading the holy book, meeting Naga sadhus (saints), etc. are believed to be a consequence of participating in primary religious activity and hence are considered as secondary religious activities. Performing Yoga, Shopping at Kumbh Mela, Cleaning ghats3, etc. are the activities that are included under recreational activities. Discretionary activities include eating, using comfort stations, resting due to fatigue etc. These activities are secondary in nature but part and parcel of any pilgrim’s travel. The travel pattern of visitors is defined by total time spent by an individual in various activities (Primary Religious, Secondary Religious, and Recreational) at Kumbh on the day of the survey and his/her trip chain type. Here, total time spent is taken as a continuous variable and is entered into the model in natural logarithm units (base 10) while trip chain type is a binary outcome ′ ′ variable with ‘0 indicating ‘Simple Chain’ and ‘1 indicating ‘Complex Chain’. As the objective of trip-chain classification was to identify complicated and uncomplicated tours, those trip-chains that have a single religious or recreational activity were grouped as ‘Simple’ (or Uncomplicated), and ‘Complex’ (or Complicated) trip-chains were those with multiple religious or recreational activities.
3 a flight of steps leading down to a river.
4 A. Verma et al. Journal of Choice Modelling 38 (2021) 100267
Fig. 1. Overview of SEM framework (Indirect Effect: = a*b, Direct Effect: = c, Total Effect: = c + a*b).
Table 1 Activity types and their description.
Primary Activity Secondary Activity Type Brief Description
PRIMARY RELIGIOUS Offering Prayer/ To offer prayer or worship idols inside Temple (Prim_Rel) Worshipping Holy Dip To take holy bath at one of the Ghats of Kshipra river Check-in at Temple Visiting inside premises of the Temple Check out at Temple Visiting outside premises of the Temple Visiting Camp To visit Camp/Akhara and attend spiritual/religious sermons Listening to Bhajans Listening to Bhajans (religious songs/chanting) at Temple/Akhara Listening to Preaching To listen to the preaching of holy men/spiritual gurus at Akhara or from pundits/priests at Temple
SECONDARY RELIGIOUS Reading Holy Book To read a holy book near temple premises (Sec_Rel) Meeting Naga Sadhu To meet Naga Sadhu (Holy men who have given up all worldly pleasures including clothing) (Saints) Making Shiva Lingaa Molding the idol of Lord Shiva from mud Serving Food in Temple Serving food to pilgrims/devotees at the Temple
RECREATIONAL (REC) Yoga Performing yogaa Shopping Shopping from nearby local markets Discussing Discussing and gathering in between pilgrims Visiting Garden Visiting Garden Taking Photos Taking Selfies/photos Watching TV Watching TV at Akhara Fun Rides Taking fun rides at a circus in Kumbh area Cleaning Ghats Cleaning Ghats as a voluntary service & for fun
DISCRETIONARY (DIS) Using Comfort Stations Using toilets Sleeping Sleeping at hotel/Akhara Keeping Footwear Keeping footwear outside Temple Changing clothes Changing clothes before/after a holy dip in Kshipra river Using ATM Using ATM to withdraw cash Eating Food Having snacks/meals Drinking Drinking water/soft drinks or having tea Waiting for Food Waiting for food/Ordering food Smoking Smoking weed/hukkah Resting Resting at Temple premises in the Kumbh Mela area other than their place of accommodation due to exhaustion
a Yoga is a Sanskrit word meaning union. It combines physical exercises, mental meditation, and breathing techniques to relieve stress and strengthen muscles.
5 A. Verma et al. Journal of Choice Modelling 38 (2021) 100267
This classificationmore clearly reflectedthe complexity of individuals’ trip chain in a religious setting. The SEM model as specifiedin the present study is estimated using ‘lavaan’ package (Rosseel, 2012) in R software (R Core Team, 2020).
3.2. Ordered logit (OL) specification
To achieve the second objective of the present paper, individual-level OL models for each activity type were estimated. The main attractions of Kumbh Mela are temples, religious camps (Akhadas), holy saints (Naga sadhus), and Ghats for taking a holy dip in the river. These locations are not concentrated but spatially dispersed throughout the cordoned region of a city where the Kumbh Mela event is carried out. Other temporary arrangements of drinking water, comfort stations are also spread throughout the city. This forces the visitors/pilgrims to make multiple stops in order to participate in various activities. Hence, the number of stops taken by an in dividual for each activity type (primary religious, secondary religious, recreational, and discretionary) is an ordered outcome and therefore modeled as a dependent variable in the OL regression. As evident from the past studies discussed in subsection 2.2, explanatory variables such as socio-demographic profile, activity participation, and externalities such as temperature significantly influencean individual’s stop-making propensities and hence considered in the present study. The OL models were estimated using the ‘Apollo’ package (Hess and Palma, 2019) in R software (R Core Team, 2020).
4. Methodology
The methodological formulation behind the SEM and OL approaches is presented in detail in the following subsections.
4.1. Structural equation modeling
SEM framework is suitable to capture the posited relationship between socio-demographic, activity participation, and travel pattern as hypothesized in the present study. Here as specifiedin section 3.1, total time spent is a continuous variable while trip chain type and activity participation variables are binary coded. Hence, the observed binary (dichotomous) response can be specified as: { } * 0 if yi ≤ τ yi = * (1) 1 if yi > τ
* where yi is the response propensity, and τ is the threshold. The response propensity is then expressed in the form of a standard structural equation model without latent factors (Golob, 2003; Kuppam and Pendyala, 2001):
* * yi = α + Byi + Γxi + εi (2)
* where yi represents the column vector of p while xi represents the column vector of q. α represents the threshold values in case of categorical outcomes (for binary and ordinal data) and intercepts for continuous dependent variables, B represents the direct effect coefficientsand consists of a matrix of (p ×p) pairs of p endogenous variables. Γ represents the indirect effect coefficientsand consists of a matrix of (p ×q) pairs where q is the exogenous variables used in the model. Here, as can be seen from Fig. 1, exogenous variables are those variables from which the paths (symbolized by arrows) will only depart towards endogenous variables pointed by arrow heads. Thus, exogenous variables, either directly or indirectly influencethe endogenous variables (Golob, 2003). The error terms are denoted by εi whose dimension is p × I, where I denotes an identity matrix of rank p. Assuming a probit link function for error term, εi ̃ ( , 2). * is expressed as εi N 0 1 σi Here, yi is a response propensity (not directly observed) variable and does not have an inherent scale, hence, the variance in the error term εi cannot be directly estimated (Muth´en, 1984). Consequently, for model identificationpurposes, parametrization of the error term is considered. Among the two widely used parametrization techniques, the present study considers the ‘Delta’ method, which is the default parametrization while using ‘lavaan’ package. The model parameters are then estimated using a 2-stage procedure. The first step involves the estimation of thresholds and tet rachoric correlation matrix (for binary endogenous variables). In the second stage, the estimated threshold values and tetrachoric correlation matrix obtained from the data are fittedto the hypothesized SEM model used in the present study using various estimation methods (Olsson, 1979). The present study uses the ‘Diagonally Weighted Least Square’ (DWLS) fitfunction for estimation. The reason behind using DWLS is that the continuity property of ‘Maximum Likelihood’ (ML) function does not hold for ordinal and binary endogenous variables (Muth´en, 1984). The fitfunction for DWLS method is given by (Li, 2016; Muthen,´ 1984; Xia and Yang, 2019):
′ 1 FDWLS = (s σ(ω)) WDWLS(s σ(ω)) (3)
In Eq. iii, s = (s1,s2), where s1 is threshold vector and s2 represents the unstructured tetrachoric correlation matrix. σ(ω) = (σ1(ω),
σ2(ω)), where ω is a vector of model parameters (coefficients), σ1(ω), σ2(ω) respectively represent the model implied thresholds and tetrachoric correlation matrix. W is the weight matrix for the DWLS estimation method and is given as WDWLS = N*diag(θ) where N is the sample size and diag(θ) represents all the diagonal elements of the asymptotic variance-covariance matrix of thresholds and tet rachoric correlations (Li, 2016). For further details regarding the SEM methodology with categorical endogenous variables, the readers are referred to Muth´en (1984).
6 A. Verma et al. Journal of Choice Modelling 38 (2021) 100267
4.2. Ordered logit model (OL)
The econometric details of the standard ordered logit model (McKelvey and Zavoina, 1975) is described as follows. Let the observed dependent variable, i.e., the numbers of stops taken for each activity type is denoted by yi, where, i (i = 1, 2, ………, N) represents the ( = , , , ) number of observations. Let j j 1 2 ……… J and ψj denote the no of stops generated for each activity purpose and the thresholds associated with these stops, respectively. These unknown thresholds partition the propensity to undertake stops into J 1 intervals and < < < = = + are in ascending order such that ψ0 ψ1 ………… ψJ where ψ0 ∞ and ψJ ∞. * In traditional ordered logit model, it is assumed that yi is associated with a continuous, latent variable yi (representing the latent stop making propensities of tourists) and ψj with a response mechanism of the following form:
* yi = j if and only if ψ j 1 < yi < ψ j j = 1, 2………, J (4)
* The ordered regression equation for yi is typically a linear function and is given by:
′ * yi = xiβ + εi for i = 1, 2, ………, N (5)
′ where, xi is a list of independent variables, β is a set of independent vectors to be estimated, εi is the random error term and is assumed to be independent and identically distributed (iid) across individuals following a standard logistic distribution. Based on this assumption of the distribution of error terms, the probability expression of the ordered logit model takes the form as: