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Prioritisation of the determinants of customer satisfaction: A simultaneous equation approach in ordinal endogenous set-up Indranil Mukhopadhyaya; Souvik Kumar Bandyopadhyayb; Aditya Chatterjeec a Human Genetics Unit, Indian Statistical Institute, Kolkata, India b Indian Institute of Public Health, Hyderabad, India c Department of Statistics, University of Calcutta, Kolkata, India Online publication date: 19 February 2011

To cite this Article Mukhopadhyay, Indranil , Bandyopadhyay, Souvik Kumar and Chatterjee, Aditya(2011) 'Prioritisation

of the determinants of customer satisfaction: A simultaneous equation approach in ordinal endogenous set-up', Total Quality Management & Business Excellence, 22: 1, 117 — 130 To link to this Article: DOI: 10.1080/14783363.2010.545558 URL: http://dx.doi.org/10.1080/14783363.2010.545558

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Total Quality Management Vol. 22, No. 1, January 2011, 117 –130

Prioritisation of the determinants of customer satisfaction: A simultaneous equation approach in ordinal endogenous set-up Indranil Mukhopadhyaya, Souvik Kumar Bandyopadhyayb and Aditya Chatterjeec∗ Human Genetics Unit, Indian Statistical Institute, Kolkata, India; bIndian Institute of Public Health, Hyderabad, India; cDepartment of Statistics, University of Calcutta, Kolkata, India

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a

The determination and ordering of the influencers of customer satisfaction are of paramount interest in various service industries. The theory of logistic regression may be exploited to relate customer satisfaction usually measured in an ordinal scale with possible covariates, measured in metrical, ordinal or binary scales. However, some of the confounders are themselves determined by other covariates under study. This necessitates the use of a simultaneous equation with ordinal endogenous variables. We propose one such approach and demonstrate its efficacy with a real life example. Keywords: exogenous; endogenous; satisfaction score; ordinal response; influencer; logistic regression; deviance; model validation

Introduction Simultaneous equation models, as familiar to econometricians, deal with two types of variables. Traditionally they are termed as endogenous variables that are determined by an economic model and exogenous variables that are treated as possible covariates determined from outside. According to Maddala (1992), endogenous variables are sometimes called ‘jointly determined’ whereas exogenous variables are usually known as ‘predetermined’. Such models are usually concerned with metrical variables. Schmidt and Strauss (1976) presented a two-equation model with both continuous and binary endogenous variables. They used the term mixed logit model to describe their approach. However, the exogenous variables are taken to be continuous. Later on Heckman (1976) and Schmidt (1978) considered the case with both continuous and qualitative endogenous variables. Schmidt (1978) claimed the model to be realistic in some situations and applied it quite effectively to the analysis of unionism and earning. Warren and Strauss (1979) also considered the mixed logit model and used it to analyse the extent of unionism and right to work legislation in the presence of several metrical exogenous variables. Rivers and Vuong (1988) proposed a two-step maximum likelihood procedure for estimating the parameters of simultaneous probit models. They explored the detailed properties of the estimators. In addition, a simple test for exogeneity has been proposed and some optimality properties of the proposed test have been studied in contrast to an alternative limited information estimator based test procedure. Greene (1998) attempted to use the simultaneous probit model in the presence of binary endogenous and metrical exogenous variables. This is a generalisation of an approach by Burnett (1997), using the cumulative distribution function of bivariate normal distribution. Greene (1998) proposed a maximum ∗

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118 I. Mukhopadhyay et al. likelihood estimate and applied the procedure successfully to study the relationship among various gender economics variables. Greenland and Brumback (2002) have made a cursory reference to simultaneous equation analysis as applicable to epidemiological research. Cheng et al. (2003) considered a modified simultaneous equation model to handle uneven data and used their result to assess the demand and price parameters in US automobile industries. They considered all the endogenous variables to be metrical and used dummy variables to exploit the effect of some of the metrical variables. Moreover, they introduced a log linear type model to explain market share and transaction prices through metrical influencers. The problem we consider in this study stems from a real life situation in the context of the assessment and ordering of the possible influencers of customer satisfaction. Customer satisfaction is a buzz word in today’s industry. Customers’ overall evaluation of a farm’s product or service may be distinct for a particular individual’s evaluation in connection with a specific transaction. Although customer satisfaction surveys are event specific, mainly for diagnostic purposes, they may serve as a good surrogate for overall customer satisfaction regarding the service, which might not be the case for goods. This is because overall customer satisfaction for service is expected to be guided by transaction specific satisfaction as measured from the survey. In many customer surveys apart from responses on transaction specific satisfaction, those on overall company satisfaction or brand satisfaction are also collected. It is generally found that the degree of association between such satisfaction scores (measured through Goodman – Kruskal gamma coefficient in case of categorised responses (Agresti, 2002)) is positive and significantly high. It has been established beyond any doubt that higher level of customer satisfaction leads to greater customer loyalty (Anderson & Sullivan, 1993; Bearden & Teel, 1983; Bolton & Drew, 1991; Fornell, 1992; LaBarbera & Mazursky, 1983; Oliver, 1980; Oliver & Swan, 1989; Yi, 1990). This in turn helps to secure future revenues (Fornell, 1992; Rust, Zahorik, & Keiningham, 1994; Rust & Keiningham, 1995), reduce the costs of future transactions (Reichheld & Sasser, 1990), decrease price elasticity (Anderson, 1996), and minimise the likelihood of customers defection in case of faltering quality (Anderson & Sullivan, 1993). Improvement in quality and customer satisfaction reduces costs associated with defective goods and services, such as costs associated with warranty, field service, re-working/replacment of defective goods, and handling/managing complaints (Crosby, 1979; Fornell & Wernerfelt, 1988; Garvin, 1988; Gilly & Gelb, 1982). There is a conflicting view of the effect of customer satisfaction on productivity (Huff, Fornell, & Anderson, 1996). One view suggests that the firms achieving a higher level of customer satisfaction devote less effort to handling returns/rework, warranties and complaint management, thus have lower costs and hence increase productivity (Crosby, 1979; Deming, 1982; Juran & Gryna, 1988). Reichheld and Sasser (1990) argued that reducing defects leads to greater loyalty, and increased loyalty leads to greater productivity via the lower costs of making future transactions and favourable word-of-mouth of customers. There is an equally convincing view of lowered productivity as a result of increased cost to derive enhanced customer satisfaction (Griliches, 1971; Lancaster, 1979). To moderate this dilemma, we quote Juran and Gryna (1988) who propose the dual concept of quality. The quality that meets a customer need is known as a ‘customisation quality’ and the quality that consists of freedom from deficiencies is known as a standardisation quality. In the context of the service industry, the way service is delivered falls under the purview of the first category and any variation encountered by customers with respect to service delivery is the second type of quality. Customisation and standardisation are independent and often mutually conflicting aspects of quality. The basic objective is to strike a


Total Quality Management 119 trade-off between customer satisfaction and productivity (Anderson, Fornell, & Rust, 1997). Manufacturing industries are usually dominated by standardisation quality whereas, for service sectors, the customisation aspect of quality plays the principal role (Anderson et al., 1997). The assessment of customers’ responses towards the evaluation of customer satisfaction for diagnostics of the underlying process is of paramount importance in telecommunication industries, power utilities, Business Process Outsourcing (BPO) or Knowledge Process Outsourcing (KPO) sectors and other service agencies. The performance of any service industry is mainly evaluated through various customer centric surveys, conducted internally or through external agencies. The American Customer Satisfaction Index (ACSI) or its predecessor, the Swedish Customer Satisfaction Barometer (SCSB) represents a new type of customer based measurement system for evaluating and enhancing the performance of firms, industries, economic sectors, and national economies. The ACSI measures the quality of goods and services as experienced by the consumers who consume them. An individual firm’s ACSI represents its customers’ overall evaluation of total purchase and consumption experience, both actual and anticipated (Anderson, 1996; Fornell, Johnson, Anderson, Cha, & Bryant, 1996). Analogously, an industry’s ACSI represents its customers’ overall evaluation of its market offering and so on for different sectors, nations etc. We have already noted that transaction specific satisfaction measures may provide specific diagnostic information about a particular product or service encountered, whereas overall customer satisfaction is a more fundamental indicator of the firm’s past, current and future performance (Anderson, 1996). It may be pointed out that customer value has a futuristic implication whereas customer satisfaction has a historical perspective. The service quality assessment indicators as developed in SERVQUAL models (Parasuraman, Zeithaml, & Berry, 1985, 1988, 1994a, 1994b; Zeithaml, Berry, & Parasuraman, 1993) try to assess the expectations and perceptions of customers with regard to several service dimensions. The appraisal of gaps between expectations and perceptions of service coupled with assessment on expectations may lead to prioritisation of the service parameters based on some well defined service prioritisation index (Chatterjee & Chatterjee, 2005). Recently Chatterjee, Ghosh, and Bandyopadhyay (2009) successfully applied similar methodology for the assessment of students’ evaluation reports for rating teachers and courses in the context of higher education. In the development of ACSI, the variables under consideration are generally metrical and hence amenable to the usual statistical analysis. Fornell et al. (1996) used a partial least square approach for the estimation of parameters involved in the model. However, this might not be the case in various customer centric surveys and SERVQUAL analysis, where the responses are usually ordinal or binary. Chatterjee and Chatterjee (2005) attempted a methodological improvement to implement SERVQUAL models for ordinal data. The present paper also addresses the methodological issues in connection with a simultaneous equation model and tries to implement innovative techniques of discrete data analysis. As an alternative to customer centric surveys, ACSI or SERVQUAL, customer dissatisfaction as opposed to customer satisfaction may be assessed through customer verbatim. Various text mining and data mining techniques are employed to extract information from customer verbatim, ultimately sentiment analysis is conducted on the basis of discrete data. This method is quite popular in automobile industries and used while delivering warranty services. In various behavioural and social science related research based on customer centric surveys, it has been found that all the response variables, both exogenous and endogenous, are categorical (ordinal, nominal, binary) in nature. Some of the endogenous variables may depend on a mixture of other endogenous and exogenous


120 I. Mukhopadhyay et al. variables. This has necessitated the development of an appropriate analysis of simultaneous equation models where all the exogenous and endogenous variables under consideration are categorical. To initiate the problem and for the sake of simplicity, we restrict our research to cases where all exogenous and endogenous variables are assumed to be binary. However, later on we consider ordinal (more than two categories) endogenous variables along with a mixture of binary (and/or ordinal) as well as metrical exogenous variables. The present discussion deals with responses obtained from customer surveys conducted just after rendering a service according to customers’ needs (transaction specific customer responses) and focuses on the assessment of customer satisfaction. Usually customers’ responses in any such survey are recorded in a 5-, 7-, 9- or 10-point scale and satisfaction and/or dissatisfaction respectively are measured by merging the top half and/or the bottom half of the responses. This is because mid-responses correspond to indifferent or confused customers whose opinions are not useful for either enhancing the quality of the service or initiating possible measures towards transforming dissatisfied customers to satisfied customers. However, in some surveys the responses of the indifferent customers might be of some importance to assess the positive or negative swings required to make them satisfied or dissatisfied. As discussed earlier, customer satisfaction and/or dissatisfaction depends on several service and product parameters or influencers. The objective of the present paper is to quantify and order them according to importance. The performances of such a simultaneous equation model in the presence of binary exogenous and endogenous variables need to be validated through real life data. Moreover, the method needs to be extended to a situation where both polytomus as well as binary endogenous variables might be accommodated in the presence of metrical, nominal, and ordinal exogenous variables. We have tried to implement an exhaustive study of the problems with regard to real life data taken from the telecommunication industry. However, for the sake of confidentiality and commercial reasons, the variables have been renamed in a convenient way. The paper is structured as follows. In section 2, the basic structural equations of the model are elaborated. The estimation of the parameters along with the computation of deviance, which is the difference of the value of the twice log-likelihood between the saturated model and the model under consideration, a simple approach involving percentages of explained variation attributable to various influencers are also discussed. The third section deals with computational aspect of both binary as well as ordinal simultaneous equation models. The models have been applied to disguised real life data and the estimates are compared with the corresponding usual logistic regression model. The corresponding percentage of deviance explained through each influencer, along with the apportionment of the percentages of explained variation of the study variable through these influencers are computed both for the usual logistic regression and the present set up. All computation has been implemented using R (R Development Core Team, 2008). The paper concludes with the discussion and scope for further generalisation in modelling and computation. Model specification and solution Let us consider the endogenous response variables Y and Z ¼ (Z1, Z2, . . . , Zs), being influenced by ‘k’ exogenous variables X ¼ (X1, X2, . . . , Xk). As mentioned earlier, we consider all the endogenous variables under consideration as ordinal. Moreover for the sake of simplicity we take s ¼ 1. Under this set up the logistic models for both Y and Z would be appropriate. We assume that Y depends on Z and the other exogenous variables X,

Total Quality Management 121 while Z depends only on X. The natural way to model the present situation is to use a ‘simultaneous logistic equation’, which explains the dependence of Y on other exogenous and endogenous variables. We propose the structural equation of the model as follows: logit(Y) = b′ X + gZ logit(Z) = d′ X

(1)


Here b ¼ (b0, b1, . . . , bk), where b0 stands for the intercept and b1, . . . , bk indicate the k-component regression parameters in the logistic regression of Y on k exogenous variables indicated by X while g stands for the regression parameter of Y on the other endogenous variable Z in the model. d ¼ (d0, d1,. . ., dk) have a similar interpretation with respect to the endogenous variable Z and exogenous variables X. Based on n observations, the representative equation of (1) may be written as: P(Y = 1|X, Z) = b′ X + gZ P(Y = 0|X, Z) P(Z = 1|X) = d′ X P(Z = 0|X)

(2)

Here the endogenous variable Z depends on the exogenous variables X, whereas the other endogenous variable Y depends on all the other variables X and Z. So, the exogenous variables X affect Y directly as well as through Z. As a result, the actual effect is being magnified and the coefficient of Z deviates from what it should be if only the effect of Z would have been considered after eliminating the effect of the exogenous variables. Thus if we fit a logistic regression of Z on X, the predicted residuals would contain the effects of Z not explained by X. The two-step logistic regression procedure may be summarised as: (a) Based on the logistic model of Z on X, we predict the residuals that are assumed to contain the unexplained information of the effect of Z after eliminating the effects of X. (b) Use another logistic regression of Y on X along with the predicted residuals as explanatory variables. The above observations may be symbolically depicted in the following three equations. First fit the Equation 3 below and use this to get the predicted values of the residuals as given in Equation 4. Finally fit another logistic equation given in Equation 5. logit(Z) = d′ X + 1

(3)

1ˆ = logit(Z) − dˆ ′ X

(4)

logit(Y) = b′ X + g1ˆ

(5)

In the study of logistic regression, the concept of ‘odds ratio’ computed as the exponentiation of the regression coefficient (Agresti, 2002) plays a dominant role. It represents the ratio of probability of success to failure in the response variables conditional to success and failure of covariates. In the binary set up containing only two values ‘1’ and ‘0’, the word ‘success’ means the value ‘1’ for the response variable as well as the covariates.


122 I. Mukhopadhyay et al. To study the extent of variation explained by the model, the deviance with respect to the saturated model is calculated. Considering several models by dropping the exogenous variables one by one according to their order of importance in explaining the response variable (might be determined by the relative magnitude of the p-values to indicate significance of the corresponding effect), provides us with the change in deviance values thus explaining the variation due to the effect of the exogenous variables present in the model. To see the influence of different exogenous variables, we drop them one by one starting with the least significant influencer as reflected from p-values or z-values and study the change in the deviances for each such model. These changes are represented as percentages of deviance of the full model from the intercept model. The degree of importance of several confounders to explain the response variable may be alternatively computed through measures of the proportion of variation of the binary response variable explained by the confounders and by measures of predictive precision with and without the confounders. Mittlbo¨ck and Schemper (1996, 2002) used multiple R2 for the general linear model along with some small sample adjustments of it. R2 or its quantifier given by 1 (SSE/SST) as a measure of explained variation that shows how much the prediction error is reduced when using covariates compared to when they are not used (Korn & Simon, 1991). The total sum of squares (SST) is the explained variation in the response variable computed for the intercept model, which is the same as the total variation present in the response variable. The sum of squares due to residuals (SSE) may be interpreted as the variation for the response variable explained by the full model. The magnitude of comparative increase in the SSE in comparison to SST, by dropping one variable at a time through the relative magnitude of the corresponding p-values may be computed stepwise to indicate the relative importance of the covariates. We have implemented both the approaches with regard to the first set up of the problem to identify the relative importance of the confounders as influencers of response variable under consideration. Application in customer satisfaction survey The present problem stems from a customer centric survey in a telecommunication industry where the objective was to evaluate, assess, and prioritise the possible determinants of customer satisfaction. The actual survey deals with responses from customers while obligatory services to the customers are being provided by the telecommunication company in the event of problems regarding billing, collection, connection, and facility for example. Customers were also asked to assess the present service provider against the backdrop of competitive service providers with respect to their requirements. The survey was quite exhaustive in nature and encompassed almost all determinants of customer satisfaction that the company felt were relevant. The objective was to prioritise the determinants, assess their level of influence and find possible measures in terms of those influencers to enhance customer satisfaction. For the sake of confidentiality and business reasons we considered a subset of customers whose responses were recorded. For the same reason we deleted the majority of the possible influencers from the list (around 25 in number) and renamed the retained influencers (only four in number). Therefore, for the sake of convenience we had to assume that customer satisfaction was dependent on only three influencers, while in the actual scenario, the number is quite large. The renamed influencers were: ‘Package type of the service under consideration’, ‘Effort level needed to solve a particular problem for which interventions from the service provider is required’, ‘The waiting time of the customer before getting attention from the service provider’ and ‘Whether the problem is actually been sorted out with such interventions’. For notational

Total Quality Management 123 simplicity, let us name the variables as follows: Customer satisfaction (Y), Package type (X1), Waiting time (X2), Effort level (X3), and Problem resolution (Z). We considered two set ups for the same data. In the first set up, for the sake of simplicity and exposition, we converted responses for all the parameters into binary variables. For customer satisfaction we considered binary variables ‘1’and ‘0’ respectively for ‘satisfaction’ and ‘dissatisfaction’. This is done by suitably combining the top half and bottom half of the customer rating scale. For the problem resolution variable as indicated by Z, we designate resolved cases as ‘1’ and non-resolved cases as ‘0’. For other variables the following rule was used: .


.

.

.

Package type, a nominal binary variable with a particular group of packages being designated as ‘1’ and its complementary group being designated as ‘0’. Waiting time, an ordinal binary variable ‘0’ is assigned for no or negligible waiting time, while ‘1’ indicates substantial waiting time. Effort level, an ordinal binary variable with amount of effort above the usual is designated as ‘1’ and efforts within the usual level is designated as ‘0’. Since the response variable is binary we used the usual logistic regression with binary covariates.

For the second set up we converted customer satisfaction into a three-category polytomus response variable where we inserted an additional category of moderately satisfied or indifferent customer in between satisfied and dissatisfied customers. This has been done by suitably combining the ordered values of the ordinal response variable Y. In the case of waiting time we retained the actual metrical set up of the variable. As such the first set up consists of binary exogenous as well as endogenous variables. However, the second set up is a generalisation of the first set up where both the binary as well as the polytomus endogenous variables are considered. At the same time the binary as well as the metrical exogenous variables have been retained. Since the response variable is polytomus (three categories under ordinal set up) we used a proportional odds form of logistic regression with a mixture of metrical and binary covariates. For a detailed discussion on logistic regression we refer to Agresti (2002) and McCullagh and Nelder (1989). The understanding of the telecommunication company regarding customer satisfaction being influenced by the chosen variables is as follows. Some of the packages are less problematic and require lesser interference from the service providers. These packages are expected to have enhanced customer satisfaction and have been grouped in one category and assigned the value ‘1’. The complementary group containing packages requiring continuous interference by the service providers but are otherwise profitable is attributed the value ‘0’. It is a general perception that customers are usually satisfied if they can convey the nature of the problem to the concerned representative of the service provider without much delay and with little waiting time. Better communication of the encountered problem to the designated authority is sometimes more important and satisfying than the actual solution of the problem, particularly when the problem is minor in nature. In the first set up, if the customer has a negligible waiting time before reaching a representative to discuss the problem, then the value of the variable is recorded as ‘0’. Otherwise, the value of the variable is recorded as ‘1’. In the second set up the actual waiting time is taken into account as the second exogenous variable. An enhanced effort level leads to an early solution of the problem with the least rework and negligible effect on the customer’s tolerance and patience, thus leading to an expected increase in customer satisfaction. As such, in both the set ups ‘0’ corresponding to the third exogenous variable indicates usual or ordinary effort level whereas ‘1’ corresponds to the enhanced effort level.


124 I. Mukhopadhyay et al. Since, for the sake of confidentiality, we are constrained to using a smaller set of data with a highly inadequate number of possible influencers; our intention is to judge whether the company’s perception regarding the direction and magnitude of the selected influencers are justified. Moreover, if that is so, is there any way to quantify and prioritise the effects of the selected influencers in a meaningful way? Once we can substantiate the methodological issues, dealing with much larger data set and accommodating the complete list of influencers will be an issue of enhanced computation time. A simple logistic regression with Y as the only response variable and X ¼ (X1, X2, X3) and Z as the possible covariates would reveal that the confounder indicating whether the problem has been resolved is controlling customer satisfaction to a great extent. This is because resolving the problem may be dependent on several issues and also dependent on X. The strong dependence of customer satisfaction on the actual resolution of the problem is quite evident from the high percentage of deviance or explained variation of response variable as well as the large value of the odds ratio for that variable. However, this finding is not very innovative nor enterprising from a management perspective, who may be interested to know how far the other actionable exogenous variables denoted as X are influencing customer satisfaction. One suggestion could be to exclude the variable indicating the actual solution of the problem, i.e. Z, from the list and conduct a logistic regression by considering Y as a response variable and other variables X as covariates. However, this modelling may not be adequate as the resolution of the problem might not be under management control but affects customer satisfaction to a great extent. At the same time, resolution of a problem itself is affected by the actionable exogenous variables. As a result there may be strong evidence of two-stage dependence. The first stage consists of the dependence of response variable Y on the part of endogenous variable Z not explained by other exogenous variables X; while the second part is the dependence of response variable Y on other exogenous variables X. This requires the consideration of the variables corresponding to customer satisfaction (Y) and problem resolution (Z) as the binary endogenous variables and the other three, namely, package type (X1), waiting time (X2), and effort level (X3) as exogenous variables. It may be noted that customer satisfaction is positively influenced if the problem is sorted out. However, resolution of any problem depends heavily on the effort level exerted and in no way can depend on customer satisfaction. In the subsequent computations we report the estimates of the parameters, corresponding odds, z-values, p-values, percentages of variation explained by a particular variable for the first as well as the second set up. Moreover, we have computed the percentages of explained variation of the response variables through various confounders only for the first set up. These computations deal with the results based on the three approaches, which are as follows: Approach (a): Consider endogenous Y as response variable but only X as only exogenous variables in usual Generalised Linear Model (GLM) or logistic regression framework. Approach (b): Consider endogenous Y as response variable and both Z and X as possible exogenous variables in GLM or logistic regression framework. Approach (c): Consider Y and Z as endogenous and X as exogenous variable in the simultaneous equation GLM or logistic regression framework, as proposed in the present work. For the sake of completeness, the nature of dependence of other endogenous variable Z on all the exogenous variables X is also studied. There is a strong dependence between customer satisfaction and the resolution of the problem as revealed by the Goodman – Kruskal

Total Quality Management 125 Table 1. Estimates of regression parameters, odds, z-value, p-value, percentages of deviance explained and percentage contributions to explained variation for the response variable by the covariates in case of binary response variable with binary covariates.

Estimates of parameter

Odds

z-value

p-value

Percentage of deviance explained for response variable

Percentage contribution to explained variation in response variable


Approach (a): Logistic regression of Y (Customer Satisfaction) on X (Package Type, Waiting Time, Effort Level) – 1.195 0.232 – – (Intercept): b0 ¼ 0.078 1.2687 4.137 0.00003 1.14 1.21 (Package Type): b1 ¼ 0.238 0.8737 22.686 0.007 2.73 2.39 (Waiting Time): b2 ¼ 20.135 4.6228 29.220 0 96.13 96.4 (Effort Level): b3 ¼1.531 Logistic regression of Z (Problem Resolution) on X (Package Type, Waiting Time, Effort Level) – 212.4 0 – – (Intercept): d0 ¼ 20.763 0.9204 21.711 0.087 0 0.05 (Package Type): d1 ¼ 20.083 3.3135 27.886 0 87.78 87.32 (Waiting Time): d2 ¼ 1.198 1.9523 13.35 0 12.22 12.63 (Effort Level): d3 ¼ 0.669 Approach (b): Logistic regression of Y (Customer Satisfaction) on (X, Z) (Package Type, Waiting Time, Effort Level, Problem Resolution) 29.119 0 52.46 50.92 (Problem Resolution): g ¼ 1.725 5.6125 – 26.135 0 – – (Intercept): b0 ¼2 0.439 1.3445 4.861 0 0.54 0.51 (Package Type): b1 ¼ 0.296 0.5205 211.465 0 1.3 1.26 (Waiting Time): b2 ¼ 20.653 4.2589 25.838 0 45.7 47.31 (Effort Level): b3 ¼ 1.449 Approach (c): Logistic regression in simultaneous equation set up of Y (Customer Satisfaction) on (X, Z) (Package Type, Waiting Time, Effort Level, Problem Resolution) and Z (Problem Resolution) on X (Package Type, Waiting Time, Effort Level) 29.174 0 52.49 50.95 (Problem Resolution): g ¼ 0.724 2.0627 – 2.757 0.006 – – (Intercept): b0 ¼ 0.193 1.3113 4.461 0.00001 0.54 0.51 (Package Type): b1 ¼ 0.271 0.7498 25.348 0 1.3 1.26 (Waiting Time): b2 ¼ 20.288 5.1810 28.946 0 45.67 47.28 (Effort Level): b3 ¼1.645

Gamma coefficient (the value of available data is 0.89). However, regarding actual resolution, the role of various influencers may not be similar in comparison to customer satisfaction. Table 1 is concerned with the first set up where all the endogenous as well as the exogenous variables are considered binary. Table 2 establishes the superiority of the proposed simultaneous equation framework in comparison to other simple logistic regression set ups through goodness of fit type criteria. Table 3 depicts the situation where a mixture of polytomus as well as binary endogenous variables, along with a combination of both binary and metrical exogenous variables are considered. Results and discussion We found the Goodman – Kruskal gamma coefficient between transaction specific satisfaction and over all brand satisfaction scores to be 0.93. Therefore, transaction specific satisfaction scores might be treated as an efficient surrogate for overall brand satisfaction scores. The direction and nature of dependence of the exogenous variables: package

126 I. Mukhopadhyay et al. Table 2. Assessing closeness between numbers of observed and expected satisfied customers in first set up (binary response variable with binary covariates). Approach Approach (a) Approach (b)


Approach (c)

Description of the Model Logistic regression of Y (Customer Satisfaction) on X (Package Type, Waiting Time, Effort Level) Logistic regression of Y (Customer Satisfaction) on (X, Z) (Package Type, Waiting Time, Effort Level, Problem Resolution) Logistic regression in simultaneous equation set up of Y (Customer Satisfaction) on (X, Z) (Package Type, Waiting Time, Effort Level, Problem Resolution) and Z (Problem Resolution) on X (Package Type, Waiting Time, Effort Level)

Absolute – measure

Square measure

0.3142

41.2949

0.3209

51.6398

0.2392

24.8731

Table 3. Estimates of regression parameters, odds, z-value, p-value, percentages of deviance explained for the response variable by the covariates in case of polytomus ordinal response variable with binary and metrical covariates.

Estimates of parameter

Odds

z-value

p-value

Percentage of deviance explained for response variable

Approach (a): Logistic regression of Y (Customer satisfaction) on X (Package Type, Waiting Time, Effort Level) – 219.278 0 – (First Intercept) b0|1 ¼ 21.224 – 21.137 0.128 – (Second Intercept): b0|2 ¼ 20.069 1.2725 4.281 0 1.13 (Package Type): b1 ¼0.241 0.9998 24.512 0 2.22 (Waiting Time): b2 ¼ 20.0002 4.6786 30.112 0 96.65 (Effort Level): b3 ¼ 1.543 Logistic regression of Z (Problem Resolution) on X (Package Type, Waiting Time, Effort Level) – 27.092 0 – (Intercept): d0 ¼ 20.408 0.9352 21.412 0.158 0 (Package Type): d1 ¼ 20.067 1.0010 20.068 0 80.87 (Waiting Time): d2 ¼ 0.001 1.7126 11.034 0 19.13 (Effort Level): d3 ¼ 0.538 Approach (b): Logistic regression of Y (Customer satisfaction) on (X, Z) (Package Type, Waiting Time, Effort Level, Problem Resolution) 5.4412 29.488 0 52.27 (Problem Resolution): g ¼ 1.694 – 210.05 0 – (First Intercept): b0|1 ¼ 20.678 – 8.877 0 – (Second Intercept): b0|2 ¼ 0.588 1.3418 5.01 0 0.54 (Package Type): b1 ¼ 0.294 .9995 211.224 0 1.06 (Waiting Time): b2 ¼ 20.0005 4.4862 27.967 0 46.13 (Effort Level): b3 ¼ 1.501 Approach (c): Logistic regression in simultaneous equation set up of Y (Customer Satisfaction) on (X, Z) (Package Type, Waiting Time, Effort Level, Problem Resolution) and Z (Problem Resolution) on X (Package Type, Waiting Time, Effort Level) 2.0421 29.684 0 49.95 (Problem Resolution): g ¼ 0.714 – 221.134 0 – (First Intercept): b0|1 ¼ 21.406 – 22.191 0.014 – (Second Intercept): b0|2 ¼ 20.139 1.3165 4.677 0 0.54 (Package Type): b1 ¼ 0.275 0.9997 26.079 0 1.06 (Waiting Time): b2 ¼ 20.0003 5.2436 30.566 0 48.45 (Effort Level): b3 ¼ 1.657


Total Quality Management 127 type (X1), waiting time (X2), effort level (X3) on endogenous customer satisfaction (Y) is consistent in both the set ups. In somewhat parallel to the telecommunication company’s general perception, the more customer friendly package group has only a marginal positive impact on customer satisfaction with values of odds ranging from 1.26 to 1.31 and 1.27 to 1.34 in the first and second set ups respectively. An increase in the waiting time to reach the concerned representative has a marginal negative impact on customer satisfaction with values of odds ranging from 0.52 to 0.87 in the first set up. However, the second set up indicates that waiting time and customer satisfaction are more or less independent traits with a value of odds close to unity. The percent variation as well as the percentage of explained variation through these two exogenous variables are negligibly small in both of the set ups. The most important finding in both of the set ups is the changing role of problem resolution and effort level towards the enhancement of customer satisfaction. Since in approach (a), no other endogenous variable has been conceived, the effort level is practically consuming an entire share of percentage of deviance explained as well as explained variation. Moreover, the effort level has a significant ‘beta’ coefficient coupled with odds for satisfaction to dissatisfaction with regard to high and low effort level having values ranging from 4.6228 to 4.6786 in the two set ups. This picture is not very appealing in the context of management perception. A comparison of logistic regression set up with both exogenous X and endogenous Z as possible covariates to explain Y and the present simultaneous equation set up with Y and Z as endogenous and X as exogenous variables reveal that both sorting out the problem and effort level contribute more or less equally towards the percentage of deviance explained as well as the percentage of explained variation for the response variable. The most appealing feature of the finding is that in usual logistic regression approach, the odds for resolution are exceptionally high which is quite misleading and serves no purpose as it is not under management control. This is because problem resolution is totally dependent on the nature of problem the customer has encountered over which the management might not have any control. However, the present simultaneous equation approach indicates that the actual influencer of customer satisfaction is effort level with the highest odds (5.1810 and 5.2436) followed by odds corresponding to the variable indicated by actual resolution of the problem (2.0627 and 2.0421) in the two set ups respectively. The proximity of the respective figures corresponding to the percentages of deviance explained and the percentages of explained variation for each variable in the first set up is noteworthy. In view of any one of percentage deviance explained or percentage contribution to explained variation of the response variables or odds; the present simultaneous equation approach yields the most realistic and actionable results that might be of great importance to management to first quantify, then prioritise and ultimately assess the actual impact of the possible determinants of customer satisfaction. The ordering of the influencers with regard to problem resolution is not at all similar to what has been found for customer satisfaction. In fact the second variable i.e. ‘waiting time’ being dominant to explain the actual resolution of the problem becomes somewhat misleading and may arise on account of spurious correlation. As our focus of the present study is to quantify and order the determinants of customer satisfaction, we prefer to skip this issue and provide a word of caution that it may be possible that the two endogenous variables, customer satisfaction and problem resolution, may not have exactly the same set of explanatory exogenous variables. We have tried to demonstrate the methodological aspect with the help of a small data set and relatively lesser number of covariates. The suggested method has been implemented quite successfully for the actual data set and the recommendations as


128 I. Mukhopadhyay et al. revealed from the solutions are found to be quite helpful to the telecommunication industry to determine and prioritise the determinants of transaction specific satisfaction and hence overall customer satisfaction. The estimation of the percentage of satisfied customers from the model and matching the figure with the actual data might be another way of model comparison and subsequent validation. While doing so it should be taken into account that in the first set up there are 16 classes for different combinations of X and Z. The observed frequency of the response variable, that is, satisfied customers in the present case, for these classes are different and hence any measure indicating the closeness between the observed and expected values of satisfied customers for a particular class should be expressed in relation to either observed or expected frequency for that class. As such we have suggested two measures to examine the closeness betweenobserved andexpected frequency taken together for all 1 nobs − nexp /nobs and 1 (nobs − nexp )2 /nobs , where the classes. The measures are 16 16 nobs and nexp are respectively observed and expected number of satisfied customers in each of the above 16 classes and the sum is extended over all the classes. It should be 1 , is the modified chi-square statnoted that the second measure, expect for the multiplier 16 istic. The results are given in Table 2 and here also the divergence from proximity between the observed and expected frequencies of the response variable corresponding to the simultaneous equation model in the logistic set up gives the minimum value with respect to both the measures. We have also attempted the computation of percentage contribution to explained variation of the response variable by the covariates and the above-mentioned divergence measure for the second set up. The results are quite similar to the first set up and are not discussed in detail. Concluding remarks In the present paper we have used the simultaneous equation approach where both the endogenous variables are ordinal while some or all of the exogenous variables are categorical/binary. The suggested procedure has been applied to real life disguised data. The approach has been found to be superior from an application perspective, since the findings are more realistic and appealing in comparison to the usual or common sense procedure. However, the classical simultaneous equation approach in GLM set up needs to be addressed more elaborately where each endogenous variable might depend on other endogenous variable(s) along with some or all exogenous variables. This situation is of paramount interest in various problems of business analytics and related areas. Moreover, an appropriate optimum estimation procedure in this set up needs to be developed. Unlike the present approach, standard software packages are not useful and separate computational techniques need to be evolved and addressed. References Agresti, A. (2002). Categorical data analysis (2nd ed.). New Jersey: Wiley InterScience. Anderson, E.W. (1996). Customer satisfaction and price tolerance. Marketing Letters, 7(3), 265–274. Anderson, E.W., Fornell, C., & Rust, R.T. (1997). Customer satisfaction, productivity, and profitability: Differences between goods and services. Marketing Science, 16(2), 129–145. Anderson, E.W., & Sullivan, M.W. (1993). The antecedents and consequences of customer satisfaction for firms. Marketing Science, 12(2), 125–143. Bearden, W.O., & Teel, J.E. (1983). Selected determinants of consumer satisfaction and complaint reports. Journal of Marketing Research, 20(1), 21–28.


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