1 Introduction

Retaining public transport (PT) passengers or encouraging a mode shift to PT services is a strategy of many large cities that aims to reduce congestion, improve public health and decrease air and noise pollution. As passengers are the direct users of PT services, it is paramount to gain a deep understanding of service quality based on their perceptions (Eboli and Mazzulla 2015). Perception is an abstract and psychological term that plays a major role in governing behavior and making decisions (Habib et al. 2011).

To evaluate service quality, one should understand the factors affecting the formation of perceptions towards PT service quality. The significance of assessing service quality from the users’ perspective has been highlighted in many references including TCRP report 165 (2013) in which a service quality framework is defined. Subjective user perception is usually collected by a Customer Satisfaction Survey (CSS). It is prevalent in these surveys to have both questions about the customers’ overall satisfaction and detailed questions about specific attributes of the service. Moreover, obtaining the relative importance of these attributes is essential when an investment prioritization is needed (Cao and Cao 2017; Weinstein 2000).

In developing countries, it is more prevalent to use simple aggregate measurement tools, such as SERVQUAL, developed by Parasuraman et al. (1985), and there are few studies that have applied sophisticated models which can deal with users’ subjective perceptions (Irfan et al. 2012; Machado-León et al. 2017; Rahman et al. 2016). Therefore, the goal of this paper is to apply a methodology that takes the concept of perception and satisfaction into account. Thus, a structural equation model (SEM) is adapted to investigate the causal relationship between customer satisfaction and perceived service quality. The advantage of an SEM is that it permits the definition of latent variables, which can reflect the subjectivity of perceived satisfaction and service quality. It should be noted that using an SEM model with all its characteristics (e.g., latent structures and parameter values) from a previous study in a new case study is questionable and requires a meticulous investigation on how well they can be transferred. However, applying the SEM structure from previous studies can be considered as a way to accelerate model development in a new study when there are solid reasons to argue for it. On the other hand, what justifies the need for a new study is that by comparing the new model results with the previous ones, an opportunity will be provided for PT researchers, planners, and decision-makers to understand how each PT service works similar to/different from the other studies, and how passengers from various cities around the world perceive their PT service quality differently. These comparisons would enable PT planners to learn how to apply and/or modify the previous successful experiments according to their own region and society. Therefore, this study includes several latent structures for service quality that were considered in prior theories and previous studies (CEN 2002; de Oña et al. 2013; Eboli and Mazzulla 2015; Parasuraman et al. 1985). Furthermore, various SEM structures suggested in previous studies are examined on a locally collected dataset to confirm the model’s spatial transferability. In other words, the precession of detected relationships in previous studies is examined with a locally collected and consistent dataset. It is investigated how previously developed model structures of other cities would perform if they were directly applied to the new case study. After exploring various model alternatives, it is proposed that the SEM model should also undergo a rigorous model development exercise by conducting an exploratory factor analysis (EFA) first. A combination of EFA and prior knowledge about the nature of data can lead to an enhanced model.

The scope of this paper covers the analysis among different models and choosing the most proper one(s), but its results, as suggested in the literature, can be considered as a determinant in further studies to: (1) inform operators, transport managers, policymakers, and researchers about the specific impact of each attribute on customer satisfaction; (2) distinguish how resources should be allocated to these attributes to improve the overall PT service quality; and (3) analyze how PT service quality can affect the ridership’s spatial and temporal fluctuation (Boisjoly et al. 2018; Cao and Cao 2017; Chowdhury et al. 2018; Ingvardson and Nielsen 2019; Morfoulaki et al. 2015).

The remainder of this paper consists of the following sections: first, a literature review is provided, then the methodology is explained followed by a brief introduction to the case study. Then the data collection procedure and results are presented. The paper ends with conclusions and recommendations for future research.

2 Literature review

In order to move towards a customer-oriented service, PT organizations must pay more attention to service quality measurement (Stuart et al. 2000). There are two methods of measuring service quality: (1) the objective method where service quality can be expressed by performance measures (e.g., capacity, speed, reliability, and frequency). These measures can be collected by different tools, including -but not limited to- terminal surveys, automated vehicle location (AVL), and automated passenger counter (APC) (Ma et al. 2014; Mesbah et al. 2015); and (2) the subjective method that only can be measured by means of customer perceptions (Mouwen and Rietveld 2013; Vitale et al. 2016). Customer satisfaction is, in fact, one of the key determinants of personal perceptions towards a service (Chen 2008; Hensher and Prioni 2002). There is an ongoing debate about how the two concepts of service quality and customer satisfaction are related and/or separated from each other. Although, service quality and customer satisfaction are often used interchangeably in PT studies (de Oña et al. 2013; Eboli and Mazzulla 2007, 2015; Irfan et al. 2012; Stuart et al. 2000), their differences have been considered in some parts of the literature (Hadiuzzaman et al. 2017; Lai and Chen 2011; Minser and Webb 2010). For example, service quality judgments are thought to be more detailed and cognitive while customer satisfaction judgments are considered more holistic and affective (Lai and Chen 2011; Oliver 2015). CSS is a regular tool used to collect passengers’ subjective perceptions in diverse ways (e.g., on-board, online, phone, social media) (Abenoza et al. 2017; Eboli and Mazzulla 2007; Grisé and El-Geneidy 2017; Haghighi et al. 2018). In a CSS, passengers express their level of satisfaction with service quality attributes and overall service based on a pre-defined scale of evaluation [usually a Likert scale (Likert 1932)]. In addition, the relative importance of these attributes is needed to identify the impact rate of each attribute on overall satisfaction.

There are two different methods to estimate the relative importance of these attributes: stated importance (asking customers to rate each attribute on an importance scale) and derived importance (deriving a measure of attribute importance by statistically testing the strength of the relationship of individual attributes with overall satisfaction) (de Oña et al. 2013; Weinstein 2000). Stated importance is the more intuitive and simpler of the two methods, but it extends the survey length, which can reduce response rate and precision of the survey. Also, stated importance can lead to deficient discrimination among importance ratings, with customers rating almost all of the measures near the top of the scale. For this reason, in recent years there has been a development in derived importance estimation based on CSS (Dell’Olio et al. 2010; Habib et al. 2011; Imaz et al. 2015; Joewono and Kubota 2007; Weinstein 2000). Several techniques such as bivariate correlations (Figler et al. 2011; Weinstein 2000), regression analysis (Cao and Cao 2017; Dell’Olio et al. 2010; Hensher et al. 2010; Weinstein 2000), factor analysis (Eboli and Mazzulla 2012; Javid et al. 2016; Lai and Chen 2011), and SEM (de Oña et al. 2013; Eboli and Mazzulla 2015; Joewono et al. 2012; Karlaftis et al. 2001; Lai and Chen 2011; Minser and Webb 2010; Stuart et al. 2000) have been used to investigate the relationship between service quality attributes and customer satisfaction.

Because of the complex and abstract concept of service quality (Parasuraman et al. 1985), SEM has become more frequently used in recent years than the other aforementioned techniques. SEM was adopted in several fields of research and generalized by Wiley (1973) and Jöreskog (1970). It depends on a series of underlying observed and latent variables. The latent variables, also known as factors, can provide a better understanding of how customers perceive service quality by grouping the attributes that behave similarly into a factor representing them (Hadiuzzaman et al. 2017; Wan et al. 2016). The process of considering an aggregation of observed variables into a factor has been carried out by different methods in the literature. Some of them are based on previous research. For instance, Aydin et al. (2015) proposed a nine-latent model based on Nathanail’s study (Nathanail 2008), and Shen et al. (2016) considered the TCRP report 165 (TCRP report 165 2013). Other studies adopted a general satisfaction theory to a passenger satisfaction study, for example, Irfan et al. (2012) and Celik et al. (2014) propounded models based on the SERVQUAL theory (Parasuraman et al. 1985). The last group of studies used heuristic methods such as principal component analysis (PCA), EFA, and confirmatory factor analysis (CFA) (de Oña et al. 2013, 2015; Eboli and Mazzulla 2012; Lai and Chen 2011; Minser and Webb 2010; Mouwen and Rietveld 2013). For further information on how to apply SEM for analyzing public transport service quality please refer to Eboli et al. (2018).

There are some issues in each of these methods. Machado-León et al. (2017) pointed out the main reason SERVQUAL had lost popularity over the last few years. Tyrinopoulos and Antoniou (2008) suggested that “Factor analysis should not be blindly applied to a dataset with several variables hoping that some underlying patterns would be uncovered; instead, a theoretical motivation should drive factor analysis applications” (pp. 263). On the other hand, using proposed models of previous studies could be questionable due to the uniqueness of the initial dataset or differences in sample frames, time frames and community characteristics (Golob 2003; Trompet et al. 2013). Transferability tests can be applied to answer this negligence.

Transferability is an issue of applying a structured and/or estimated model of one context to another one across spatial, temporal, or cultural dimensions (Atherton and Ben-Akiva 1976; Koppelman and Wilmot 1982). It has been widely applied in disaggregate travel demand models (Agyemang-Duah and Hall 1997; Atherton and Ben-Akiva 1976; Ben-Akiva and Bolduc 1987). Although many studies consider transferability as the direct application of the exact parameter values to another context, the process of considering transferability has been suggested to have four different levels: (1) basic theory of travel behavior; (2) mathematical modeling; (3) empirical model characteristics; and (4) parameter values (Hansen 1981; Sikder et al. 2013). In SEM, model transferability has been commonly investigated under the concept of multigroup equivalence, which is defined as testing SEM equivalency across a variety of comparative groups (e.g., gender, age, culture, organizations) (Byrne 2010). Cultural diversity was among the most favored multigroup equivalence studies in the past two decades (Byrne 2015). “Culture” elucidates behavioral norms within a society and evidence suggests that customers’ requirements vary across cultures (Smith and Reynolds 2002). In psychological studies, it is believed that since each cultural context can comprise diverse attitudes, norms, and values, the people from different contexts may have different perceptions about the same set of evaluating questions. Therefore, they may be represented by a distinct structure in each context (Hui and Triandis 1985). A study by Malhotra et al. (1994) investigated differences in perceived service quality between developed and developing countries. The authors illustrated the importance of considering various aspects (e.g., environmental, economic, sociocultural) which may cause distinction cross-nationally, and how they might affect the service quality evaluation. In SEM cross-cultural studies, similar to transferability studies mentioned before, there are two levels of testing for equivalence: structural equivalence and measurement equivalence (Byrne 2010; Hui and Triandis 1985). Adapting the four transferability levels of demand modeling into the transferability of customer satisfaction by SEM, it can be noted that in level 1, one should confirm that customer satisfaction can be modelled by a well-grounded theory. At level 2, SEM can be applied to mathematically model this theory. Structural and measurement equivalence tests in SEM are, respectively, similar to level 3 and 4 (Byrne 2010; Van de Vijver and Leung 1997). Studies suggest that the process should be started by the more abstract cross-cultural equivalence (i.e., structural equivalence or level 3) and then, if passed the prior stage, one can go through the later stage (i.e., level 4 or measurement equivalence) (Smith and Reynolds 2002). Measurement equivalence is commonly investigated by a set of three tests namely, “metric equivalence”, “measurement unit equivalence”, and “scalar equivalence” (Van de Vijver and Leung 1997) while structural equivalence is investigated by a set of fit indices (Byrne and Van de Vijver 2010; Cheung and Rensvold 2002). A detailed discussion about cross-cultural equivalence has been provided by Berry et al. (2002) which is beyond the scope of this paper.

This paper aims to test the different transferability levels of various service quality structures from cities in developed countries to another city in the context of a developing country. All four levels of transferability may be considered in a cross-cultural comparison. However, due to limited access to the original data of previous studies, their models have been redeveloped by locally collected data; thus, investigating level 1, 2, and 3 (i.e., basic theory, mathematical modeling, and model characteristics, respectively) is accomplished but assessing the fourth level of transferability is impractical by a common multigroup equivalence analysis (Byrne 2016). Finally, with the findings obtained from the structure of previous studies, an enhanced model is developed which can illustrate the service quality and its affecting factors with respect to the nature of locally collected data.

3 Methodology

3.1 Structural equation modeling

This approach permits modeling of a causal relationship by considering both observed and latent variables (i.e., indicators and factors, respectively). It comprises a series of statistical methods (e.g., factor analysis, path analysis, and regression models) to analyze the data.

SEM consists of two components: a measurement model reflecting the relationship between latent and observed variables, and a structural model assessing the strengths of causal relationships between latent variables. Moreover, latent variables can be defined as endogenous (dependent) or exogenous (independent). The basic equation of the structural model is defined as (Bollen 1989):

$$\eta = {\text{B}}\eta + \varGamma \xi + \zeta$$
(1)

where \(\eta\) (eta) is a \(m \times 1\) vector of endogenous latent variables, B (beta) is a \(m \times m\) coefficient matrix of the endogenous latent variables, \({{\varGamma }}\) (gamma) is a \(m \times n\) coefficient matrix of the exogenous latent variables, \(\xi\) (xi) is a \(n \times 1\) vector of exogenous latent variables, and \(\zeta\) (zeta) is a \(m \times 1\) vector of error terms associated with the endogenous latent variables.

The basic equations of the measurement model are:

$$x = \varLambda_{x} \xi + \delta ,$$
(2)
$$y = \varLambda_{y} \eta + \varepsilon ,$$
(3)

where \(x\) is a \(q \times 1\) vector of the independent observed variables, \(\varLambda_{x}\) (lambda) is a \(q \times n\) matrix of factor loadings for the effects of independent observed variables on exogenous latent variables, and \(\delta\) (delta) is a \(q \times 1\) vector of measurement error. Similarly, \(y\) is a \(p \times 1\) vector of dependent observed variables, \({{\varLambda }}_{y}\) is a \(p \times m\) matrix of factor loadings for the effects of dependent observed variables on endogenous latent variables, and \(\varepsilon\) (epsilon) is a \(p \times 1\) vector of measurement error.

There are various SEM estimation methods, most of which are based on covariance analysis. Covariance analysis works by finding model parameters in which the difference between the covariance implied by the model and the covariance of the sample is minimized (Golob 2003). The most commonly used SEM estimation method is Maximum Likelihood (ML). In addition, SEM parameters can be estimated by other methods, such as generalized least squares (GLS), asymptotically distribution-free weighted least squares (ADF-WLS) among others (Bollen 1989; Golob 2003). However, choosing the suitable estimation method depends on different assumptions (e.g., probability distribution, the scale of the variables, sample size) (Golob 2003).

3.2 Studied structures

This paper uses three classes of structures to achieve a structure which represents the factors affecting service quality appropriately. These structures are as follows.

3.2.1 Previous studies

As discussed in the literature review section, there have been many studies applying SEM with an exploratory and case-specific structure. de Oña et al. (2013) introduced a model with three exogenous latent variables, Service, Comfort, and Personnel and one endogenous latent variable, Overall service quality. This structure is referred to by S1 in this paper. Eboli and Mazzulla (2015) presented a latent structure which consists of seven exogenous latent variables, Safety, Cleanliness, Comfort, Service, Additional Services, Information, and Personnel; these latent variables are linked to an endogenous latent variable of Service Quality. This structure is referred to by S2 in this paper.

3.2.2 Established customer satisfaction theories

Apart from the above studies which apply a case-specific latent structure, available general theories about assessing customer satisfaction in which factors affecting service quality are identified. Parasuraman et al. (1988) introduced the SERVQUAL instrument, which consists of five dimensions, Tangibles, Reliability, Responsiveness, Assurance, and Empathy, to assess customer satisfaction. The European Committee for Standardization recommended a Quality Criteria system of eight factors, Availability, Accessibility, Information, Time, Customer Care, Comfort, Security, and Environmental Impact, to evaluate customers’ perceptions (CEN 2002). In this paper, structures S3 and S4 are based on these two theories, respectively.

3.2.3 Exploratory approach

When using models and theories proposed in previous studies, there is a critical consideration that originates from the nature of data. In fact, it can cause ambiguity due to the uniqueness of the initial dataset or differences in community characteristics (Golob 2003; Trompet et al. 2013). As a result, in this study, another structure (S5) is considered based on an EFA which leads to the formation of five exogenous latent variables namely Comfort, Security, Major Services, Cleanliness, and Personnel accompanied by one endogenous latent variable named Customer Satisfaction.

As discussed in Sect. 2, applying factor analysis to a dataset without taking the context into account may result in relations in which their causality can not be easily justified. Instead, a cause-and-effect theoretical basis should lead the application of factor analysis. In this paper, structure S6 is developed by a constrained EFA with respect to prior knowledge about the nature of data. Four exogenous latent variables are formed in this approach, Major Services (i.e., main attributes related to the performance of service), Comfort (i.e., attributes associated with feeling comfortable during a trip) (Duarte et al. 2010), Security (i.e., attributes associated with feeling safe and secure), and Minor Services (i.e., attributes generally related to staff performance). Moreover, in S6, the conceptual differences between service quality and customer satisfaction, also discussed in Sect. 2, is acknowledged in order to investigate the debate about their uniformity/discrepancy. As a result, a second-order latent variable of Service Quality is considered which is reflected by the four exogenous latent variables (Major Services, Comfort, Security, and Minor Services). This Service Quality is the latent variable which has a direct causal relationship with the endogenous latent variable of Customer Satisfaction.

3.3 Applied data and modeling procedure

Since the data of each previous study was collected independently, there was neither a unified framework of data collection nor a unique list of attributes among them. Furthermore, access to the original data of all previous studies was not possible. Therefore, those models were redeveloped by the locally collected data. The attributes were matched as much as possible and their factor loadings are estimated by means of a CFA, the details of which is given in Table 2. The reliability and validity of every six structures have been checked and compared with each other. Afterwards, an SEM model is developed for each of the six structures in order to make them also comparable by their goodness-of-fit indices. Figure 1 shows a conceptual formation of S1, S5, and S6. For the sake of consistency, the endogenous latent variable is named “customer satisfaction” in all the six models (in order to occupy less space, observed variables are not drawn).

Fig. 1
figure 1

Conceptual formation of S1 (a), S2 (b), and S6 (c)

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4 Survey

4.1 Case study

Tehran, the capital of Iran, is the most populous city in the country and the second-most populated metropolitan area in the Middle East. It has a population of approximately 8.9 million in the central city and 15.1 million in the metropolitan area. Its area is about 700 km2 (270.2 mi2) (Habibian and Rezaei 2017). There are 18.3 million daily vehicle trips in Tehran showing 23% growth in the past decade. The private vehicle share is about 40% while common public transport modes including minibus, bus, and rail carry 38% of the trips and the rest of the motorized trips are made by a shared taxi mode (also called jitney). The mass rail transport system (also called Metro) consists of five lines with about 135 km (84 mi) of double tracks and more than 100 stations connecting four corners of the city. Another major line is being constructed and two others are planned. The Metro system carries 18% of total motorized trips (Tehran Municipality 2016).

Tehran Metro Line 3 is one of the newest lines opened in 2012. It is the second longest rail transport in Tehran, connecting the northeast to the southwest, with 37 km (23 mi) of double tracks containing 23 stations. It provides about 350,000 daily trips over 18 h a day (Tehran Municipality 2016; Tehran Traffic and Transportation Organization 2013). Figure 2 depicts a schematic map of Line 3 (blue line—starting from upper rightmost).

Fig. 2
figure 2

Tehran Metro Line 3 (blue line) (color figure online)

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4.2 Data collection

A paper-based questionnaire was designed for this study. The questionnaire included 47 questions divided into three sections: (1) satisfaction and importance level; (2) trip characteristics; and (3) demographic data. In the first section, passengers stated their perceived satisfaction and perceived importance for 22 service quality attributes (see Table 1) based on a 5-point Likert scale. Afterward, their current trip satisfaction and all Metro trips satisfaction were questioned separately. The second section asked questions about the passengers’ travel characteristics, such as their access mode, egress mode, the reason for using Metro. The last section, demographic data, included information about the passengers’ age, gender, household income, household size, etc. (Soltanpour et al. 2018).

Table 1 Mean and standard deviation of the collected attributes
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The data were collected through face-to-face interviews conducted on-board the Tehran Metro Line 3. Interviewers were graduate students of the transportation group. Not only their independence from the operator company made passengers more comfortable to express personal explicit judgment, but also their familiarity with transport issues has led them to easily explain any ambiguity in the questionnaire to the respondents with plain and clear examples (e.g., difference between safety and security, definition of attributes’ satisfaction and importance). Data collection lasted about 14 weekdays in January and February 2017 (all normal working days). Eventually, after eliminating 37 incomplete questionnaires, there were 300 validated responses for use in the modeling procedure. Table 1 shows the list of collected attributes, the mean and standard deviation of their satisfaction and importance scores stated by the passengers.

4.3 Sample characteristics

Following data collection, the first step is to analyze the respondents. Some information about the sample is provided as follows. The sample comprised more males (59%), most were aged below 40 (74.3%), and many had an academic degree (a university graduate) (69.7%) conforming census data in most districts Line 3 passes through which are amongst the most educated districts in Tehran (Atlas of Tehran metropolis 2011). Figure 3 illustrates summarized information about the respondents’ demographic and their travel habits.

Fig. 3
figure 3

Sample characteristics

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5 Results

Three classes of model characteristics, totally include six distinct SEM structures as explained in the methodology (S1–S6), are applied in this study. Four levels of the transferability test, which includes structural and measurement equivalence tests, are investigated in this section. The measurement and structural models are evaluated by criteria defined for each. Factor loadings and reliability are checked to evaluate structures’ validity and reliability. In the structural model evaluation, a number of goodness-of-fit indices are checked. These models are calibrated using AMOS software (Arbuckle and Wothke 1999).

5.1 Transferability at various levels

5.1.1 Basic theory

All the structures have been developed to assess the relationship between PT service quality and customer satisfaction, and to find service quality attributes and their related weights (importance) in Tehran Metro line 3. Therefore, all the structures are theoretically equivalent.

5.1.2 Mathematical models

A Structural Equation Model is the common theme for modeling all the structures. Also, it is confirmed that SEM is an applicable methodology in this case study, since S1 and S2 have relatively acceptable goodness-of-fit indices in comparison with their original models (i.e., de Oña et al. (2013) and Eboli and Mazzulla (2015) studies) (see Table 4). Thus, all the structures are equivalent in terms of mathematical modeling.

5.1.3 Empirical structural characteristics

Confirmatory factor analysis was conducted in order to examine structural characteristics and cross-cultural equivalence of previous structures (S1, S2, S3, and S4).

In the first structure (S1), three exogenous latent variables were considered, Service, Comfort, and Personnel. There are eight factor loadings out of 22 which are less than 0.40, the cut-off suggested by Stevens (1992) and Hair et al. (2009), showing that 36% (> 20%) of observed variables should be dropped from the model, which is not acceptable (Hair et al. 2009) (see Table 2). The Composite Reliability (CR) for each latent variable is greater than 0.6, the cut-off suggested by Bagozzi and Yi (1988); thus S1 passes the reliability test (see Table 3).

Table 2 Factor Loading of the Six Structures
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Table 3 Reliability of the six structures
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In structure 2 (S2), six exogenous latent variables were used, Safety, Cleanliness, Comfort, Service, Information, and Personnel. The latent variable of Personnel has a CR less than 0.6 which shows a reliability problem and one factor loading is below the cut-off point of 0.40.

In structure 3 (S3), five exogenous latent variables were considered, Tangibles, Reliability, Responsiveness, Assurance, and Empathy. Latent variables of Reliability and Responsiveness have a reliability issue with a CR of 0.4 and 0.5, respectively. Also, five factor loading values are below the cut-off of 0.4.

Structure 4 (S4) has six exogenous latent variables, Accessibility, Information, Time, Customer Care, Comfort, and Security. Only three latent variables have a CR greater than 0.6 indicating a reliability issue in the structure. Factor loadings of three observed variables are less than 0.40.

Due to the drawbacks of these first four structures, it is indicated that the latent constructs of previous studies and theories are not perfectly transferable to this case study. Thus, an EFA is conducted based on eigenvalues greater than 1, with the maximum likelihood method, and the Promax method of rotation to investigate whether an improvement could be achieved. This constitutes Structure 5 (S5). It categorizes 19 service quality attributes (three attributes are dropped) into five factors, Comfort, Security, Major Services, Cleanliness, and Personnel. Factor loadings and construct reliability are tested by running a CFA which depicts that the latent factor of Personnel is not reliable (CR = 0.5) and there are two factor loadings less than 0.40. These issues indicate that the structure may still be improved.

Thereafter, a constrained EFA with a fixed number of four factors is conducted for S6. It categorizes 21 service quality attributes (only one attribute is dropped) into four factors, Major Services, Comfort, Security, and Minor Services. Results indicate that there is no construct reliability issue, but two factor loadings are less than the cut-off point. The results of measurement models of all six structures are presented in Tables 2 and 3.

Six different SEMs based on the proposed structures (S1–S6) are developed. A number of goodness-of-fit indices are used for comparing models and then choosing the best one. Chi squared (CMIN), degrees of freedom (DF), goodness-of-fit index (GFI), Tucker–Lewis index (TLI), comparative fit index (CFI), and root mean square error of approximation (RMSEA) are common fit indices used to investigate how well a model fits the sample data. Akaike information criterion (AIC) is a fit index for comparing models; the closer its value to zero, the better the model fits the data (Akaike 1987). Chi squared is exceedingly sensitive to sample size, so the Chi squared to degrees of freedom ratio (CMIN/DF) is used instead. Ratios less than 5 are indicative of an acceptable fit (the lower, the better) (Marsh and Hocevar 1985). The GFI, TLI, and CFI greater than 0.90, and the RMSEA less than 0.08 indicate a close fit of the model to the data (Browne and Cudeck 1993; Hair et al. 2009; Jöreskog and Sörbom 1984).

The values of these indices for the six models are shown in Table 4. Also, GFI, RMSEA, and CFI which are reported in the studies of de Oña et al. (2013) and Eboli and Mazzulla (2015) are listed in the table to facilitate comparing S1 and S2, respectively, with their original models. Among the six structures, three structures (S2, S5, and S6) fit the data in a better way. Between these three, S2 has a reliability issue mentioned above (i.e., having a latent variable with low CR). Comparing S5 and S6, S6 passes all of the criteria confirming that the modifications made to S5 have remarkably enhanced the proposed structure.

Table 4 Fit Indices for Proposed Models
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5.1.4 Estimated parameters

Testing transferability of parameters (i.e., measurement equivalence) requires access to previous studies’ data. For S3 and S4, as they are developed based on a general theory, there is no previous data to make this level of transferability test happen. Also, there are some mode-specific and case-specific attributes in de Oña et al. (2013) and Eboli and Mazzulla (2015) studies which make it impractical to test the transferability of the structures in this level. Generally, as the previously studied structures (S1–S4) do not pass the prior level of the transferability test, leaving the test in the previous level is inevitable.

5.2 Results of the proposed model (S6)

From the analysis and comparisons made in previous sections, it is seen that S6 is the best model for this study’s data. This final model consists of four latent variables defining the second-order latent variable of Service Quality namely Major Services, Comfort, Security, and Minor Services. Major Services and Comfort have the largest effect on service quality (standardized weights of 0.94 and 0.88, respectively) (Table 5). The latent variable of Customer Satisfaction consists of two observed variables, All trips satisfaction and Current trip satisfaction, and is chiefly reflected by the latter (standardized weight of 0.88) which is an important finding here showing that perceptions about the trip that passengers are doing at the moment better describe their satisfaction level. Table 5 includes non-standardized weights (Non-st. W), standard errors (S.E.), critical ratios (C.R. = Non-st. W/S.E.), significance test of weights (P), and standardized weights (St. W) of the final model.

Table 5 Estimated weights of model (S6)
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The total effect of each service quality attribute on customer satisfaction is calculated. These are the values which can be defined as the derived importance of service quality attributes. Comparison between derived importance and perceived importance as stated by passengers in the survey shows significant differences. Among the top 3 important attributes ranked based on these two methods, there is only one shared attribute (Security in station). The comparison of attributes based on derived and stated importance is shown in Fig. 4. It provides another evidence that the derived and stated importance values can be very different.

Fig. 4
figure 4

Comparison of stated and derived importance

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6 Conclusions

This study presents experimental results on developing a customer satisfaction model for an urban public transport case study in a developing country. In addition, this study focuses on two topics: (1) examining various levels of model transferability i.e. from previous studies or fundamental theories into locally collected data, and (2) investigating the impact of service quality attributes on overall customer satisfaction. A comprehensive literature review on previous studies indicates that SEM is a strong method to be used for exploring a latent structure that can define service quality. Although, a new structure may be statistically better than borrowing it from the previous studies, it is worthwhile to examine previous structures if there is a solid reason to argue for them. Accordingly, it is important to confirm the transferability of previous models when they are used in any case study apart from their origin. In order to evaluate the customer satisfaction in the case study of Tehran Metro, a number of credible proposed structures and theories have been taken into account. However, findings of this paper demonstrate that previously proposed SEM structures show a weaker fit when applied to the present case study compared to an SEM structure that is developed based on an exploratory analysis. The main idea of the transferability test in this paper is on structural characteristics, which is suggested to be checked before a transferability test of estimated parameters.

The best structure of the latent variables is found after analyzing six distinct structures in terms of different levels of transferability test. The final model identifies four latent variables to describe service quality: Major Services (i.e., main attributes related to the performance of service), Comfort (i.e., attributes associated with feeling comfortable during a trip), Security (i.e., attributes associated with feeling safe and secure), and Minor Services (i.e., attributes generally related to staff performance). Among them, Major Services is the most influential latent variable on service quality, while Minor Services is the least influential latent variable.

Furthermore, this paper determines that the observed variable of “Current trip satisfaction” is a better indicator of the latent variable of Customer Satisfaction compared to “All trips satisfaction”. Therefore, on-board surveys should be given more attention, in order to obtain accurate perceptions about the trip passengers are doing at that moment, for better evaluation of service quality and customer satisfaction.

With the determination of the importance of service quality attributes, this paper confirms previous findings about the difference between stated and derived importance, and also helps PT operators and managers to justify and plan for PT improvement with a prioritization on how to invest the limited resources. In fact, attributes can be divided into four quadrants and an importance-performance analysis (IPA) can be undertaken to help operators better understand each attribute’s contribution to customer satisfaction. For instance, in the case of Tehran, attributes associated with train frequency (e.g., crowdedness, security, seat availability) require the highest attention. Allocating limited resources more efficiently can improve PT services, which can retain current users while encouraging new ones to use PT.

For future research, segmentation of trips into several sections (e.g., access, waiting, in-vehicle, transfer, and egress) and evaluation of service quality for each section separately could be considered. Also, other PT modes of the case study area could be considered for a more comprehensive evaluation with a larger sample size.