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Electronic Journal of Applied Statistical Analysis: Decision Support Systems and Services EvaluationEJASA:DSS (2010). Vol 1, Issue 1, 66 – 78e-ISSN 2037-3627, DOI 10.1285/i2037-3627v1n1p66 2010 Università del Salento, SIBA http://siba-ese.unile.it/index.php/ejasa dssCONSTRUCTION OF THE BALANCED SCORECARDBY USINGSTRUCTURAL EQUATION MODELS WITH LATENT VARIABLESGiuseppe Boari*, Gabriele CantaluppiDipartimento di Scienze Statistiche,Università Cattolica del S. Cuore, ItalyReceived 30 April 2010. Accepted 19 October 2010Available online 17 December 2010Abstract: The Balanced Scorecard is one of the most important quantitative toolfor the business strategic planning. Its implementation usually concerns theconstruction and analysis of proper weighted averages of the so-called KeyPerformance Indicators (KPI); these are either objective or subjectiveevaluations of the performance levels attained by the various sub-systemsconstituting a business organization. Recent evolutions of the model areconsidered and a particular version of the Balanced Scorecard, based onStructural Equation Models with Latent Variables, is introduced.Keywords: Balanced scorecard, business scorecard, structural equation models,latent variables.1.IntroductionThe Balanced Scorecard (BSC), introduced by Kaplan and Norton [14], represents a valuableinstrument for measuring the performance of a business organization, with the main objective ofaligning business units to the leadership goals. Section 2 presents the BSC implementation byintroducing the so-called KPI (Key Performance Indicators) summarized into a compositiveindex. Section 3 considers the classical statistical latent factor approach from which Parasuramanet al. [19] and Cronin et al. [5] derived their paradigms for measuring service quality: theSERVQUAL and SERVPERF models. The natural evolution of these models, within theStrategy-Focused-Organization model and the Business Excellence model, gave rise ([11], [12])to the so-called Kanji Business Scorecard, which is implemented, see Section 4, by means of thestructural equation model with latent variables. Section 5 introduces a practical example ofevaluation of a business process, [22]; it represents a particular Business Scorecard devoted to*Corresponding Author. Email: [email protected]

Boari, G., Cantaluppi, G. (2010). EJASA:DSS, Vol 1, Issue 1, 66 – 78.measure the compliance of a quality system with the requests stated by the international ISO9000:2000 standards.2.The Balanced Scorecard and compositive modelsThe Balanced Scorecard (BSC), introduced by Kaplan and Norton [14], represents a valuableinstrument for measuring the performance of a business organization, with the main objective ofaligning business units to the leadership goals. The BSC approach had further developments,[15], [16], with the introduction of the Strategy-Focused-Organization model, aimed attranslating the top management strategy into operational actions, addressed to a continuousimprovement of the organization performance. The BSC implementation starts with themeasurement of all the dimensions influencing the future results of an organization; then, properanalyses are produced, in order to assess the continuous improvement toward the businessexcellence and consequently the fulfilment of the targets stated by the strategic planners. In thisperspective, the so-called KPI (Key Performance Indicators) are considered; their assessment isthe main activity of the top management. The direct measure of KPI may be combined withsubjective evaluations of those aspects by a sample of managers or experts; their evaluation ofthe degree to which those indicators meet the global target may be done by means of datacoming from interviews or questionnaires. A summary index of performance evaluation maythus help the final assessment by the top management.Let us examine, for example, the Financial aspect, which leads to Business Excellence; it islinked to the following financial and marketing aspects: X1 Cash flow level,X2 Profit margin,X3 Return on equity,X4 Assets turnover,X5 Customer demand,X6 Ability to recruit and maintain outstanding staff,X7 Goals achievement,X8 Short and long term strategy,X9 Comparison with best-in-class.Following the Fishbein [7] compositive approach, the BSC methodology suggests to produce aglobal performance index by first indicating a system of importance weights summing up to one.With regard to the previous example, once defined the subjective system of weights wi(i 1,2, ,9), the following statistic (Financial Performance Indicator) may be used9FPI(k) wi Xi ,(1)i 1giving a direct summary measure of the level of the financial prospects for the firm k.Furthermore, as a benchmark, one can properly summarize similar indices FPI(j), j 1,2, ,n,67

Construction of the balanced scorecard by using structural equation models with latent variablesobtained from analogous analyses realized over a sample of n competing firms, in order tocompare the specific position of the company k with the average performance or with the bestpractice. Observe that, due to the subjective nature of the evaluations and in order to properlydefine the benchmark, a fair referee board should establish the most objective weighting system.3.Non-observable variables and Factor analysis approachThe previous formulation of BSC considers only observable variables, whose levels are properlysummarized by means of a weighted linear combination. A first evolution of these models isrepresented by the adoption of a Factor Analysis (FA) approach, which typically considers thereconstruction of non-observable variables (factors and factor scores) starting from theobservation of a collection of manifest variables (proxies) assumed to be linear functions of thecorresponding latent variable. Two well-known examples are represented by the SERVQUALand the SERVPERF models, developed by Parasuraman et al. [19] and Cronin et al. [5]; theysuggest two distinct procedures, devoted to measure the level to which the users of servicebusinesses perceive quality or evaluate satisfaction/performance, with reference to severalaspects not directly measurable. The different use of the paradigm of the gap betweenexpectations and perceptions distinguishes these procedures. The refinement of the analysisallowed to identify a purified set of manifest variables, which may be used to evaluate thefollowing 5 key aspects, describing the customer-service nsiveness,assurance,empathy.According to the Factor Analysis procedure, one can evaluate the levels of the 5 latent variables(factor scores) and identify the aspects best satisfying the customers. Furthermore, in thisinstance, a global (quality or satisfaction) index may be defined as a linear combination of themean levels of the above 5 variables in a fashion similar to (1), by using a weight systempreviously specified, or obtained as a result of surveys over a sample of customers.4.The Business Scorecard and the Structural Equation Model approachThe Structural Equation Model with Latent Variables (SEM-LV) approach represents a furtherdevelopment in the measurement of the business performance. This method joins the attitude ofthe FA procedures, which are mainly addressed to obtain an estimate of the latent scores, withthe feature of evaluating the strength of the (linear) relationship among the non-observablevariables establishing the dimensions of the construct. The involved relationships may begraphically described by the so-called path diagram and may be interpreted as the representationof a linear multivariate multiple regression model with a causal or recursive structure. Observethat also FA models may consider solutions with correlated latent variables, but this ensues only68

Boari, G., Cantaluppi, G. (2010). EJASA:DSS, Vol 1, Issue 1, 66 – 78.in presence of oblique or non-orthogonal rotations; on the contrary, the SEM-LV approachassumes the existence of those relationships among the latent variables, which may bestatistically estimated and tested by using the experimental data. We recall briefly that SEM-LVmodels are defined by the following two sets of relationships: ,y Y and x X ,(2)(3)called, respectively, the inner and the outer model, where and are two arrays of endogenous(m 1) and exogenous (n 1) latent variables, and are matrices (m m) and (m n) of unknownparameters; y and X are the sets (p 1) and (q 1) of manifest variables, linearly dependent on therespective latent variables, through the matrices Y (p m) and X (q n), which are assumed tobe block diagonal. , and are the equation error components. In (3) the relationships amongmanifest and latent variables are formulated according to a so-called reflective measurementmodel. One can also encounter situations where the relationship between the set of manifestindicators and the respective latent variable i is of the formative type, say i ixi i (see [6],[4] and [8]). In model (2) the matrix B is assumed to be lower triangular with zero elements onthe main diagonal, so the resulting model is said to be of the recursive type.With reference to the BSC, in [12] and [13] an alternative version is proposed, which is calledKanji Business Scorecard and is formulated according to the SEM-LV approach. The modelconsists of two sections related to the measurement of the relationships of PerformanceExcellence with Leadership and Organizational Values respectively. 1 Process Excellence 1 OrganizationalValue 2 OrganizationExcellence 4 PerformanceExcellence 3 Delight theCustomersFigure 1: Organizational Values - Performance Excellence relationshipThe second section of the model is defined according to the path diagram in Figure 1. The latentvariables are measured by proper manifest indicators, which give the extent stakeholders feel thatthe organization satisfies the items shown in Table 1 (manifest variables are listed under thecorresponding latent variables).69

Construction of the balanced scorecard by using structural equation models with latent variablesTable 1. Latent variables and corresponding proxy variables 1X1X2X3X4ORGANIZATIONAL VALUEhas a missionhas values reflecting concerns with all stakeholdersstrategy and policy are consistent with the stated aims and purposesvalues foster cooperation among the stakeholders 1Y11Y12Y13Y14PROCESS EXCELLENCEproducts have no defects or other non-conformities and exhibit the stated characteristicsservices run smoothly and as advertiseddisseminates accurate and reliable performance indicatorsuses benchmarking to improve its processes 2Y21Y22Y23ORGANIZATION EXCELLENCEregularly introduces new and innovative products and servicesworks in partnership with themhas a culture of continuous improvement and a learning attitude 3Y31Y32Y33Y34DELIGHT THE CUSTOMERSactively listens to their needs and requirementseffectively deals with complaintsprovides relevant and reliable information to themhas an ethical conduct 4Y41Y42Y43Y44PERFORMANCE EXCELLENCEprovides good value for moneyhas a healthy financial situationhas a good overall imagehas a good quality reputationThe first section of the model considers the relationship between Leadership and PerformanceExcellence (see e.g. [3]). The path diagram represented in Figure 2 corresponds to the final partof this section of the model proposed by Kanji and Wallace [13] and applied to a specificmanufacturing company: the estimates of the mean levels of the latent variables (in the ellipses,on a centesimal scale) and of the path coefficients (near the corresponding arrows) are reported.70

Boari, G., Cantaluppi, G. (2010). EJASA:DSS, Vol 1, Issue 1, 66 – 78.Customer Focus89Process Improvement890.3190.29271People Performance85Continuous Improvement Culture89Business Excellence0.2320.144Figure 2. Final section of the Path Model for Leadership-Performance Excellence relationshipThe values of the preceding estimates can also be represented into the Strategic SatisfactionMatrix, [6], which reports, see Figure 3, the impact levels or opportunities (regressioncoefficients) along the vertical axis and the performance mean levels (computed with theestimated latent scores) on the horizontal axis.Figure 3: Strategic Satisfaction Matrix for the analyzed companyBy considering this matrix one can identify the aspects on which interventions are more usefuland effective, in order to improve the final performance of the process. Observe that the People71

Construction of the balanced scorecard by using structural equation models with latent variablesPerformance (PP) aspect is clearly the one on which to concentrate the most improving actions.Another interesting example, developed in the sanitary context, is given in [9]. This represents anevolution of the SERVPERF model, since the model includes also the latent variable OverallPatient Satisfaction (measured by using four judgements regarding the quality level perceptionon the medical and surgery personnel and on the whole Hospital). The following graph shows theestimates of the impact of the five aspects considered in the SERVPERF model (see §2) on thePatient Satisfaction, together with the mean levels of the 5 above aspects, also using the StrategicSatisfaction Matrix technique. Observe that it is advisable to intervene on the aspect a) tangibles,while the aspect c) responsiveness had probably received more attention than 56065707580Figure 4. Strategic Satisfaction Matrix for Patient Satisfaction5.A case studyIn order to present a practical implementation of a SEM-LV to the evaluation of a businessprocess we want to recall an example reported in [22] referring to an analysis for assessing thedegree of compliance of the Quality Management System of a firm with the requirements of thestandard ISO 9000:2000.Data were collected by mea