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This paper uses the relationships between three basic, fundamental and proven concepts in manufacturing (resourcecommitment to improvement programs, flexibility to changes in operations, and customer delivery performance) as theempirical context for reviewing and comparing two casual modeling approaches (structural equation modeling andBayesian networks). Specifically, investments in total quality management (TQM), process analysis, and employeeparticipation programs are considered as resource commitments . The paper begins with the central issue of the re-quirements for a model of associations to be considered causal . This philosophical issue is addressed in reference toprobabilistic causation theory. Then, each method is reviewed in the context of a unified causal modeling frameworkconsistent with probabilistic causation theory and applied to a common dataset . The comparisons include conceptrepresentation, distribution and functional assumptions, sample size and model complexity considerations, measure-ment issues, specification search, model adequacy, theory testing and inference capabilities . The paper concludes with asummary of relative advantages and disadvantages of the methods and highlights the findings relevant to the literatureon TQM and on-time deliveries .© 2003 Elsevier B .V. All rights reserved.

Keywords: Manufacturing; TQM; Delivery performance ; Causal modeling; Structural equation modeling; Bayesian networks

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European Journal of Operational Research 156 (2004) 92-109

Production, Manufacturing and Logistics

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Causal modeling alternatives in operations research :Overview and application

Ronald D. Anderson a,1, Gyula Vastag b,*a Kelley School of Business, Indiana University, 801 West Michigan Street, BS4053, Indianapolis, IN 46202-5151, USAb Kelley School of Business, Indiana University, 801 West Michigan Street, BS4027, Indianapolis, IN 46202-5151, USA

Received 1 July 2002; accepted 26 November 2002

1. Introduction

those in the physical sciences . A fundamental ap-peal of causal modeling is the ability to combine

Interest in causal modeling methodologies in cause-effect information, based on theoreticalthe social sciences stems from the desire to estab- construction, with statistical data to provide alish patterns of regularities or laws analogous to

quantitative assessment of relationships among thestudied variables. The purposes for employingcausal modeling in the study of operations are todevelop an explanation of relationships and to`Corresponding author . Tel . : +1-317-278-3681 ; fax: +1-317-

provide a basis for inference . The portrayal, eval-274-3312/278-3312.E-mail addresses: randers@iupui .ed u (R.D . Anderson), uation and summarization of assumed causal re-

[email protected] (G. Vastag) .

lationships are the components of explanation .' Tel . : +1-317-274-2446; fax : +1-317-274-3312 . These relationships are then used to develop

0377-2217/$ - see front matter ® 2003 Elsevier B .V. All rights reserved .doi :10 .1016/50377-2217(02)009049

RD. Anderson, G. Vastag / European Journal of Operational Research 156 (2004) 92-109

93

inferences for diagnostic reasoning from effects tocauses and for the prediction of outcomes thatwould follow from a policy or procedure inter-vention. Available modeling methods offer differ-ing functional advantages and limitations .However, any method should have potentialmanagerial usefulness by providing outputs withclear interpretation and the capability to assess theimpact of potential changes in the modeled pro-cess .

Ideally, a causal study would take the form of arandomized controlled experiment conducted overan appropriate time period . Such a research designwould minimize construct, internal, external, andstatistical threats to validity (Cook and Campbell,1979), and allow the possibility of causal conclu-sions to be reached . Unfortunately, randomizedcontrolled experiments can seldom, if ever, beutilized to provide causal knowledge for strategyand policy issues . Thus, causal modeling methodsfor non-experimental data are of interest .

Bayesian networks and structural equationmodels (SEM) are the causal modeling methodsfor non-experimental data reviewed and comparedin this paper. The paper begins with the centralissue of the requirements for a model of associa-tions to be considered causal . This philosophicalissue is addressed in reference to probabilisticcausation theory . Then, each method is reviewedin the context of a unified causal modelingframework consistent with probabilistic causationtheory, and applied to a common dataset. Thecomparisons include concept representation, dis-tribution and functional assumptions, sample sizeand model complexity, measurement, specificationsearch, model adequacy, theory testing and infere-nce capabilities . The paper concludes with a sum-mary of the relative advantages and disadvantagesof the methods .

2. Probabilistic causation theory

The area of causation has been extremely activeover the past twenty years with numerous inter-actions between the fields of philosophy, statisticsand computer science. This activity has spawnspirited controversy on a wide variety of concep-

tual and methodological issues (McKim andTurner, 1997). Causality, as a theoretical postu-late, has been the subject of highly contested dis-cussions since the reductive account offered byHume (1969). Hume characterized causation bythe regularity of constantly conjoined pairs ofevents (Effect = f (Cause)), under conditions oftemporal priority (a cause must precede an effect),and contiguity (a cause is temporally adjacent toan effect). However, Hume's account does notprovide for imperfect regularities nor does it havethe ability to distinguish between a genuine causalrelation and a spurious association . These weak-nesses motivated development of theories of cau-sation that cast causal relationships betweengeneral events in terms of stochastic descriptions(Supper, 1970) .

The key feature of probabilistic causation is aparadigm switch from the absolute determinationof an effect due to the occurrence of a cause to theoccurrence of a cause increasing the probability ofan effect . An assumption underlying this perspec-tive is that incomplete knowledge of causes resultsin uncertain cause-effect relationships . This con-ceptualization, labeled as pseudo-indeterminism(Spirtes et al., 1993), assumes that specified causesdo not alone determine an effect, but do so inconjunction with unspecified unobserved causes .Thus, pseudo-indeterminism assumes that sets ofindependent specified causes and unspecified cau-ses are the direct causes (-+) of an effect: specifiedcauses -+ effect E- unspecified causes .

Cause-effect relationships, under the assump-tion of pseudo-ihdeterminism, may be encodedinto a graphical structure known as a directedacyclic graph or simply a DAG . Each arrow in aDAG depicts causal dependence and the absenceof a connecting arrow indicates causal indepen-dence. The encoded structure is characterized asdirected, since two-headed arrows depicting non-causal association are not allowed and as acyclic,since feedback loops (e.g ., X -+ Y ---+ X) are notallowed .

The common cause principle states if two vari-ables in a population are associated and neither isa cause of the other, they must share a commoncause (Reichenbach, 1956) . The term association isused, in reference to probabilistic dependence

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R. D. Anderson, G. Vastag / European Journal of Operational Research 156 (2004) 92-109

p(X, Y) > p(X)p(Y), rather than the narrowerterm correlation that implies a measure of linear-ity. When an event C is a common cause of X andY, X i- C -+ Y, or is intermediate to X and Y,X - C -* Y, C is said to screen off values of Xfrom values of Y resulting in probabilistic inde-pendence p(X, YIC) = p(XIC)p(YIC) . Thus, acausal system with asymmetric relations is as-sumed to always exist in reference to populationassociations, but usually is not known with cer-tainty and must be inferred from sample data .

The common cause principle is the justificationfor the causal Markov condition that states everyeffect variable, conditional on its direct causes, isindependent of all variables that are not its effects(Spirtes et al ., 1993) . The causal Markov conditioncan also be expressed in probability statements : ifX does not cause Y, then p(X I Y & direct causes ofX) =p(XIdirect causes of X). The notion of anunderlying causal mechanism generating observa-tions implies the converse of the causal Markovcondition . That is, empirical regularities of con-ditional independence relations observed from apopulation are due to a causal structure not co-incidence (Scheines, 1997) . This assumption, la-beled as the stability condition (Pearl, 2000) or thefaithfulness condition (Spirtes et al ., 1993), statesprobabilistic independencies are a stable result ofcausal structure and not due to happenstance orspecific parameter values . Therefore, the jointpopulation probability distribution over a definedvariable set is assumed stable or faithful to theunderlying causal structure as specified in theDAG. Lastly, if the variable set includes all rele-vant common causes, it is said to be causally suf-ficient . Assertions portrayed by a DAG areassumed to be causal when combined with causalsufficiency, the causal Markov and faithfulnessconditions, and independence of specified andunspecified causes .

SEM and Bayesian networks are viewed ascausal models when the above conditions are sat-isfied. Druzdzel and Simon (1993) demonstrate aBayesian network can be represented by a simul-taneous equation model with hidden variables andaddress causal interpretation in the context of theunderlying principles of SEM . Pearl (1995) pro-vides a detailed exposition of causal diagrams in

empirical research and emphasizes inferences reston causal assumptions .

The above causation account is not universallyaccepted in the philosophy of science, even bythose that adopt a probabilistic viewpoint (Cart-wright, 1997) . There is an often-cited exception tothe common cause principle and the causal Mar-kov condition in the microscopic world of quan-tum mechanics (Hausman and Woodward, 1999) .At issue in this environment is the behavior ofcomplementary pairs of particles that are notprobabilistically dependent on one another or theeffects of a common cause. Yet under manipula-tion of one particle, the other instantly behaves inan identical manner. Various elements of thisparadox have been debated in physics and phi-losophy since publication of the Einstein-Podol-sky-Rosen thought experiment (Einstein et al .,1935). The implications of these debates are thatthe probabilistic behavior of some phenomena donot conform to the pseudo-indeterminism pers-pective, but is due to inherently stochastic prop-erties in Nature .

2.1. A causal model

A causal model may be expressed asM = {S, Os}, where S is the structure of the causalassertions of the variable set V portrayed by aDAG and Os is a set of parameters compatiblewith S. A DAG can always be translated into a setof recursive structural equations with independenterrors that satisfies the causal Markov condition(Kiiveri and Speed, 1982) . A set of recursivestructural equations that describe the data-gener-ating process of a DAG is specified byY = f(Parents(V), Ut )

( 1)

where Y is a consequence variable linked by afunction f to a configuration set of direct causes,Parents(V), and U;, an error term (Pearl, 2000) .Each V is represented by an individual equationthat corresponds to a distinct causal mechanismwhere the function f is invariant over a range ofvalues of Parents(V) and U; . The error terms areassumed to represent mutually independent un-observed variables, each with a probability distri-bution function p(U,). Eq. (1) reflects the view that


Nature possesses stable causal mechanisms des-cribed byf that are deterministic functional rela-tionships between variables, while p( U,) reflectsincomplete causal knowledge associated withpseudo-indeterminism : Parents(Y) -+ Y F- U; .The specification of Eq . (1) can accommodate non-linear relationships, expressed in terms of the es-timated probability of an effect, as well as thetypical linear specification.

The parameters in O s assign a function f toeach Y and a probability measure p(U,) to each U,.A structure S is taken to portray a set of condi-tional independence assertions among the m vari-ables under study, which permits the factorizationof the associated joint probability distribution as

p(V,, V, . . ., Vm ) = p(V,IParents(V,))px (V2IParents(V2)) . . .px (VmlParents(Vm))

(2)

The factorability condition follows from thecausal Markov condition (Hausman and Wood-ward, 1999) .

3 . Structural equation models (SEM)

The true score model (Spearman, 1904), com-mon factor analysis (Thurstone, 1935), and sta-tistical factor analysis (Lawley and Maxwell, 1963)provide the foundation to represent the within-concept measurement model in SEM . This repre-sentation assumes a measured variable MV ; iscaused by two unrelated latent variables ; a speci-fied common cause representing concept j, LV1 ,and an error term, e,, for unspecified causes :LV1 --p MV; E- ei . The general measurementequation of an indicator, a specialization of Eq .(1), is given byMV; = 2;1LV1 + ei

(3)

where Ai1 is a path coefficient linking commoncause j to measure variable i and e, is the mea-surement error .

Path analysis (Wright, 1934) is generally ac-knowledged as the common parent of SEM(Joreskog, 1973) and Bayesian networks (Pearl,1988). Wright's method of path coefficients con-

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lists of developing a graphical representation as-sumed to describe a causal process, thendecomposing the correlation coefficient for eachpair of variables (V,•, Y) into a sum of products ofpath coefficients and residual correlations . Theconcept equations are an application of pathanalysis that specializes Eq . (1) into the standardlinear equations :LV1 = EbjkLVk + u;

(4)where bbk is a path coefficient, uj is the disturbance,and the index k ranges over all parents of LV1 .Thus, the variable set for SEM contains a set ofmeasured variables and two sets of latent vari-ables, V = {MV, LV, U}, where U = {e;, of} .

The distribution assumption for SEM is a nor-mal probability density under maximum likelihoodestimation, which results in normal conditionalprobability densities for each L1; and a multivari-ate normal joint distribution for the measuredvariables. Estimation by generalized least-squaresor asymptotic distribution free methods are notconstrained by the normality assumption, but im-plementation problems has resulted in sparseusage. The set of matrix parameters consistentwith Eqs. (3) and (4) is Os = {A, B, Y',,, Oe }, whereA is a matrix of measurement coefficients, B is amatrix of concept path coefficients, 'I'„ is a co-variance matrix of concept disturbances, and Oe isa covariance matrix of measurement errors . Themeasured variable matrix equation is establishedby substituting Eq. (4) into Eq. (3),MV = A(I - B)u + e. The parameter matrices ofOs can be combined to form the covariance of themultivariate normal joint distribution of the mea-sured variables, E = E[MVMV'] = A(I - B)'I'„ (I -B')A' + Oe .

The objective of the parameter estimation,usually based on the maximum likelihood crite-rion, is to reproduce the sample covariance asclosely as possible with a covariance matrix im-plied by the structure of measurement and struc-tural assertions . The overall fit of the model isassessed by significance testing of the discrepancyfunction formed from the differences between theimplied covariance matrix and the sample covari-ance matrix, and by descriptive indexes. Also,unconstrained matrix elements of O s can be tested

96 R. D. Anderson, G. Vastag / European Journal of Operational Research 156 (2004) 92-109

for significance. Complete details are provided inBollen (1989) .

4. Bayesian networks

An influence diagram provides a graphicalscheme for representing conditional dependenciesin a decision-making framework (Shachter, 1986) .Such diagrams model uncertain knowledge, deci-sions and utilities to assess the actions that willyield the highest expected utility . Bayesian net-works are a subset of influence diagrams that focuson the uncertain knowledge component. A discreteBayesian network (Pearl, 1988) is a specializationofM = {S, Os}, where the structure S implies a setof conditional probability distributions

Os = {p(V, IParents(V, ), 6 1 ),p

x (V2IParents(V2),02 ), . . .,px (V,„IParents(V,n),0,„)} .

Each variable has c t discrete values or states,and each Bt is assumed to be a collection of mul-tinomial distributions, one for each parent con-figuration. The probability assignment may besubjective or based on frequency ratios froma database or a combination of both . The associ-ated joint probability distribution of the networkvariables follows Eq . (2) as the product of theconditional probabilities in Os, p(vi, . . . , v,„) =Ilnp( lj l Parents(Vt ), 6 . ) . Conceptually, the frame-work for Bayesian networks is applicable to con-tinuous or discrete variables or both . However,applications have been concerned with discreteBayesian networks where the vast majority ofcomputational work has been focused .

The Bayesian network methodology has beenclosely associated with causation in philosophy(McKim and Turner, 1997) artificial intelligence(Pearl, 1988) and knowledge discovery (Spirteset al., 1993) . In addition, applications have beenmade in agriculture, computer imaging, computersoftware, education, information retrieval, medi-cine, space research and weather forecasting (Jensen, 1996) . Cooper (1999) and Heckerman (1999)provide technical reviews of Bayesian networks .

Two approaches have been employed to evalu-ate the independencies and dependencies in thegraphical structure S : an independence-testingmethod (Spirtes et al ., 1993) and a Bayesianscoring method (Cooper and Herskovits, 1992) .The independence-testing approach is consistentwith traditional statistical methods utilizing like-lihood ratio significance tests and maximum like-lihood estimation constrained to satisfy toconditional independencies implied by the data.Whereas, the Bayesian approach employs a scor-ing metric based on the probability of S in thecontext of conjugate analysis (Bernardo andSmith, 2000). Both approaches allow incorpora-tion of prior knowledge with the search algorithmsto specify S .

4.1. Independence-testing approach

The frequentist viewpoint, where a parameter01 = p(U,) is assumed as an unknown fixed quan-tity and the estimator of 6 is a random variable,underlies the independence-testing approach . Ingeneral, classical test statistics can be utilizedunder the assumption the data results from mul-tinomial sampling . The validity of the claim that Xcauses Y, with no screening off a common cause orintermediate variable, implies the populationprobability statement p(YIX) # p(Y) . This causalassertion can be evaluated by sample tests of in-dependence employing the maximum likelihoodchi-square test statistic, G2. Rejection of the nullhypothesis of independence ofX and Y,

Ho : p(YIX) =p(Y),provides evidence that p(YIX) 54 p(Y) in supportof the causal claim that X --+ Y . When an commoncause or intermediate screening variable is postu-lated as a claim that X and Y are independentconditional on C, i.e ., C screens off X from Y, asample test of conditional independence of X andY given C will provide evidence for support orrejection of the claim .

The approach is a two-step procedure imple-mented by the PC algorithm of TETRAD II(Scheines et al ., 1994), which first tests conditionalindependence relationships in a saturated structureor a structure constrained by prior knowledge . A


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sequential testing procedure is employed to elimi-nate dependency linkages at a specified significancelevel. Thus, a reject or retain decision of condi-tional independence is obtained for each testedlinkage. The rejected independence relationshipsare taken as dependency linkages and assembled toprovide the graphical structure. The output of thisassessment is a pattern that represents a set ofequivalent DAGs, rather than a unique set of di-rectional dependencies, that entail the same inde-pendence relations consistent with user-providedbackground knowledge . Search algorithms otherthan the PC algorithm are available for evaluatingcausal assertions (Spirtes et al ., 1993) .

In the second step, maximum likelihood esti-mates of the conditional probabilities O s areconstrained to conform to the structure of the firststep. When a database is used for estimation, theconditional probabilities are relative frequencyratios that are calculated as the joint frequency ofY and its parents divided by the frequency of theparents .

4.2. Bayesian scoring approach

In the alternative Bayesian approach, the esti-mator of Oi is assumed fixed, conditional on thedata D, and the parameter 0; is viewed as a randomvariable. The prior probability distribution of 0,,p(O i), describes what is known about 0 i withoutknowledge of the data. The posterior probabilitydistribution of 0,, p(Oi ID), describes what is knownabout 0. with knowledge of the data . The rela-tionship between the posterior distribution and theprior distribution is provided by Bayes' theorem(Bayes, 1763), p(0;ID) = p(D10i)p(0i)/p(D), wherep(D10 i) is the likelihood of the data given 0; .

The Bayesian approach assumes that the struc-ture S and the conditional probabilities in O s arestochastic variables with prior probability distri-butions provided from prior knowledge . Bayes'theorem provides the mechanism to revise theprior distribution of a model M, given the data D,to the posterior distribution, p(MID) = p(M, D)/p(D) =p(M)p(D1M)/p(D) . The p(D) doesnot change over the values of M, and can beviewed as a normalizing constant needed to scalep(M)p(DIM) to sum to unity over all outcomes of

M. Thus, the posterior distribution of M isproportional to the product of the prior distribu-tion ofM and the likelihood of the data D givenM, i.e ., Posterior Distribution cc Prior Distribu-tion x Likelihood of the Data or p(MID) ocp(M)p(DI M) .

Prior knowledge of Os is usually very minimalor non-existent and the estimation of the condi-tional probability distributions relies primarily onavailable data. The Bayesian approach uses theproportionality relationship, Posterior Distribu-tion oc Prior Distribution x Likelihood of theData, to estimate the maximum posterior proba-bility for variable i in state k for parent configu-ration j. The estimation task is greatly simplifiedwhen the prior and posterior distributions have thesame functional form, which is termed as beingconjugate. The family of Dirichlet distributions isconjugate for multinomial sampling and providesthe basis for prior-to-posterior analysis in manycomputational programs (Cowell et al ., 1999, ap-pendix A). A Dirichlet prior distribution of 0iwhen combined with the data frequency countsyields a Dirichlet posterior distribution (Ramoniand Sebastiani, 1999) .

When the situation of initial ignorance exists,the prior probability of 0i is generally taken as auniform distribution (Geiger and Herkerman,1997). Parameter specification of the prior distri-bution provides a summary of prior experience,and is specified by a quantity called the prior dis-tribution precision . The value of the precisionnecessary for uniform priors is judgmental, andconceptually considered the number of cases rep-resenting prior experience, often termed as theequivalent sample size (Winkler, 1967) . An equiv-alent sample size of I indicates the lowest level ofconfidence in prior estimation .

4.3. Combining independence-testing and Bayesianscoring methods

Although the philosophical positions underly-ing the independence-testing and Bayesian scoringmethods are very different, there has been an effortto combine the two approaches in developingBayesian networks . The PC algorithm, with largesamples, will recover all causal relationship from

98 RD. Anderson, G. Vastag / European Journal of Operational Research 156 (2004) 92-109

observational data assuming the causal Markovand faithfulness conditions, causal sufficiency, in-dependent sources of variation, and valid statisti-cal testing (Cooper, 1999) . Scheines (1999)adopted a hybrid approach of first using inde-pendence-testing for construction of causal modelstructure S . Then he employed the Bayesian scor-ing method, using the multinomial-Dirichlet dis-tribution to estimate Os . This hybrid approach isadopted in the following application .

5 . A manufacturing application: Concepts, objec-tives and data

A study of the relationships between threeconcepts (resource commitment to improvementprograms, flexibility to changes in operations andcustomer delivery performance) provides the em-pirical context for reviewing and comparing theBayesian network and SEM methodologies . Thecomparison and tests of the two approaches useddata from the second round survey of the GlobalManufacturing Research Group (GMRG) . Why-bark and Vastag (1993) have the questionnaireused in the survey and it provides details of thisglobal data gathering effort primarily focusing ontwo industries: small machine tools and non-fashion textile manufacturing. A brief overview ofthis project is provided in Appendix A .

The variables associated with resource com-mitment are programs in which the respondingcompany had invested money, time and humanresources in the past two years . Three specificprograms were measured on five-point scales(1 = none to 5 =a large amount) : Total qualitymanagement (labeled TQM), process analysis (la-beled Analysis) and employee participation (la-beled Involve). The concept flexibility to changewas measured by flexibility to change product(labeled Product) and flexibility to change outputvolume (labeled Volume) . Customer delivery per-formance was measured by delivery speed (labeledSpeed) and delivery as promised (labeled On-Time). The flexibility and performance variableswere measured on five-point scales in reference tocompetitors (1 = far worse than competitors to3 = about the same as competitors to 5 = far

better than competitors) . However, scale responses1 and 2 were combined due to extreme sparsenessin the lowest scale category .

The general goals of causal modeling, explana-tion and inference, are translated into three ob-jectives specific to the application . The firstobjective is to provide an adequate explanation ofhow resource allocation for performance im-provement influences flexibility and delivery per-formances . The concepts are assumed to have thefollowing temporal ordering: resource commit-ment precedes flexibility to change and deliveryperformance, and flexibility to change precedesdelivery performance. Potential explanations, atthe concept level, include a common effect modelwhere resource commitment is a direct cause offlexibility to change and delivery performance, andflexibility to change is a direct cause of deliveryperformance. An alternative is a mediation modelwhere flexibility to change is a mediating variablebetween resource commitment and delivery per-formance .

The second objective is to utilize the selectedmodel to develop predictions of observable per-formance outcomes given assumed resource allo-cation levels in the TQM program . The finalobjective is to provide diagnostics from the se-lected model for assessment of relative changesin variables when an intervention manipulatesthe state of the On-Time variable to certainty . Thelast two objectives require a modeling methodto have the capability to translate the explana-tory content at the conceptual level to inferentialcontent at the empirical level . The methods ofSEM and Bayesian networks are applied below todata .

5 .1. Structural equation model

The concepts of resource commitment, flexibil-ity to change and delivery performance are repre-sented by the latent variables labeled asPROGRAMS, FLEXIBLE and DELIVERY. Theset of model variables for the SEM application isdefined by V = {PROGRAMS, FLEXIBLE, DE-LIVERY, TQM, Analysis, Involve, Product, Vol-ume, Speed, On-time} and U={uj,u2,u3,e,,e2,e3, e4, e5, e6, e7} . The hypothesized within-concept


99

structures are the basis for the following mea-surement equations :

TQM = .,PROGRAMS + e l ,Analysis = A2PROGRAMS + e2,Involve =1 3PROGRAMS + e3,Product = .i4FLEXIBLE + e4 ,Volume =1SFLEXIBLE + e5,Speed = 26DELIVERY + e6,On-time = 27DELIVERY + e7-

5.1 .1. Distribution assumptionsThe analysis began by testing the assump-

tion that the joint probability distribution of themeasured variables is multivariate normal . Exces-sive kurtosis is known to yield a maximum likeli-hood test statistic that is a poor approximationof a chi-square variate (Babakus et al ., 1987 ;Johnson and Creech, 1983) . If multivariate kur-tosis is extreme, the Satorra-Bentler scaled chi-square can be used to adjust the inflated chi-squaregoodness-of-fit statistic, with robust standarderror estimates for model parameters (Bentler,1995). However, the Mardia standardized coeffi-cient of multivariate kurtosis (Mardia, 1970) in-dicated that deviation from multivariate normalitywas minor (Z = 3 .29) .

5.1.2. Unidimensionality, convergent validity anddiscriminant validity

Confirmatory factor analysis was applied toassess the measurement properties of unidimensi-onality, convergent validity and discriminant va-lidity . Unidimensionality, which assumes each setof indicators reflect a single concept, was evaluatedby the goodness-of-fit of the congeneric factormodel (Joreskog, 1971) and was supported(x2 = 13.45, df = 11, p = 0 .27) . The congenericfactor model was also employed to evaluate con-vergent validity, the degree of agreement amongindicators used to measure the same concept . Theminimum requirement for convergent validity isevidence of significant link coefficients betweeneach indicator and the common factor (Pedhazurand Schmelkin, 1991). The ratio of the coefficientestimate to the estimated standard error, which is

approximately distributed as a normal variate,provides the test statistic for the null hypothesisthe coefficient is equal to zero . Each A-coefficient inthe congeneric model was at least fifteen standarderrors from the hypothesized value of zero, pro-viding evidence of convergent validity .

Discriminant validity, the degree to which alatent variable and its indicators differ from otherlatent variables and their indicators, was assessedby fixing the correlation between each pair ofconcepts to 1 .0, then estimating the constrainedmodel, and comparing the resulting value of chi-square with the unconstrained model chi-square(Pedhazur and Schmelkin, 1991) . The null hy-pothesis of a unit (perfect) correlation between twoconcepts was rejected each of the pairs of latentvariables, at the 0.05 significance level, thus pro-viding evidence of discriminant validity .

5.1.3. Tau-equivalent measures and reliabilitySince the congeneric model was acceptable, tau-

equivalent confirmatory factor analyses wasapplied to determine if the within-concept 2-coef-ficients are equal (Joreskog and Sorbom, 1993) . Thetau-equivalent model was found to have an ac-ceptable fit (x2 = 20.82, df = 15, p = 0.14). Fur-ther, in comparison with the congeneric model, thecomposite hypothesis that (A, =12 = 23, 24 = 2s,26 = 2 7 ) was supported (0x2 = 7.37, idf = 4,p = 0.12). Thus, each LVI was assumed to con-tribute equally to each measured variable withineach concept and the three models of concept re-lationships were constrained to tau-equivalentmeasurement.

Tau-equivalent or parallel measures are re-quired for appropriate assessment of internalconsistency by Cronbach's alpha coefficient of re-liability (Bollen, 1989, p . 217) . The construct reli-abilities for PROGRAMS, FLEXIBLE andDELIVERY are 0.75, 0.71, and 0.81, respectively,and are in the acceptable range .

5.1.4. Structural modelsThe common effect model and the mediation

model are potential explanations of the relation-ships between the assumed latent variables . Thesestructures are specified as

100

Common Effect Model :

PROGRAMS = u l

FLEXIBLE = b iPROGRAMS + u2

DELIVERY = b 2PROGRAMS

+ b3FLEXIBLE + U3 ;

Mediation Model :

PROGRAMS = u,

FLEXIBLE = b,PROGRAMS + u2

DELIVERY = b 3 FLEXIBLE + u3 .

The common effect model assumes that FLEX-IBLE and DELIVERY are the common effects ofPROGRAMS. The model had an adequate statis-tical fit (X2 = 20.82, df = 15,p = 0.14) and excel-lent descriptive fit indexes (CFI = 0 .99, AGFI =0.98, RMSEA = 0 .03) . The mediation model alsoshowed an acceptable statistical fit (X 2 = 21 .36,df = 16, p = 0 .16) and descriptive fit (CFI =0.99, AGFI = 0.98, RMSEA = 0 .02). The differ-ence chi-square comparing the common effectmodel to the mediated model and evaluating thehypothesis b2 = 0 was not significant (X2 = 0.54,df = l, p = 0 .46) . Each concept equation coeffi-cient for the mediation model was significant (b, =0.31, s .e . = 0 .04 ; b3 = 0.63, s .e . = 0 .05). Thus, themore complex common effect model was rejectedin favor of the parsimonious mediation model,PROGRAMS FLEXIBLE DELIVERY.

The standardized parameters for the mediationmodel are displayed in Fig . 1 .

R. D . Anderson, G. Vastag / European Journal of Operational Research 156 (2004) 92-109

Fig. 1 . SEM mediation model: standardized parameter esti-mates.

Each set of standardized measurement coeffi-cients show the relative influence of a conceptvariable and an error variable on a measuredvariable. The square of a standardized coefficientshows the proportion of observed variance at-tributed to specified causes, the LV variable, andunspecified causes, the error term. For example,PROGRAMS contributes 49% (0.702 ) of the unitvariance of TQM and the unspecified causes at-tribute 51% (0.71 2 ) . The standardized concept co-efficients similarly show the relative influence of aspecified concept variable cause and unspecifiedcauses, the u-variables. Thus, PROGRAMS vari-ance is entirely due to unspecified causes, 15%(0.38 2) of the FLEXIBLE variance is attributed toPROGRAMS and 85% (0 .922 ) to unspecifiedcauses, and 36% (0.60 2) of the DELIVERY vari-ables is accounted for by FLEXIBLE, with 64%(0.802 ) assigned to unspecified -causes . The pathmodel interpretation of Fig . 1 shows a one stan-dard deviation change in FLEXIBLE is expectedto result in a 0.60 standard deviation change inDELIVERY. A one standard deviation change inPROGRAMS is expected to result in a 0 .38 stan-dard deviation change in FLEXIBLE, and a 0 .23(= 0.38 x 0 .60) standard deviation change in DE-LIVERY.

The prediction of the impacts of changes inTQM or On-Time on other observed variables isnot possible unless the latent variables can bemeasured. However, measurement of latent vari-ables is indeterminate (Acito and Anderson, 1986) .Thus, prediction and diagnostics of measuredvariables is not a capability of SEM .

5.2. A Bayesian network

The set of model variables for the Bayesiannetwork application is defined by V = {TQM,Analysis, Involve, Product, Volume, Speed,On-Time} and U = {u,, u2 i u3, u4, u5, u6, u'7} . Ahybrid combination of the independence testingand Bayesian approaches, as discussed above, wasadopted for developing the network structure andestimating the conditional probabilities. Indepen-dence testing was employed to build the structureand a Dirichlet distribution conjugate analysis wasused for probability estimation .

RD. Anderson, G. Vastag /European Journal of Operational Research 156 (2004) 92-109

5.2.1. Building the network structureThe process of constructing the graphical

structure started with a within-concept temporalordering. The TQM is the most general improve-ment program, and is assumed to be a commoncause of process analysis and employee involve-ment programs (Analysis 4- TQM --> Involve).Further, a process analysis program is assumed tobe a cause of employee involvement programs(Analysis --* Involve) . In terms of flexibility,product flexibility is assumed to be a direct causeof volume flexibility (Product -4 Volume). Fordelivery, speed of delivery is viewed as a directcause of on-time delivery (Speed -+ On-Time) .

The PC algorithm, which permits the incorpo-ration of variable order specification and restric-tion of the parent relationships, was used forconformation of the within-concept structure andto search for between-concept relationships . Thewithin-concept structure was confirmed by rejec-tion of the hypothesis of independence for eachrelationship (p < 0 .001). Additionally, four be-tween-concept relationships were deemed to besignificant. Independence between TQM andproduct flexibility was rejected (p < 0.001), andindependence between employee involvementprograms and product flexibility was rejected(p < 0.005). These results imply dependencies ofTQM -+ Product and Involve --+ Product. Fur-ther, the independence testing results implied thedependencies of Product --* On-Time andVolume -+ Speed (p < 0.001) .

The complete structure of the Bayesian networkis shown in Fig. 2 .

Fig . 2 . Bayesian network structure .

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The structure implies the following equations :

TQM = ft(ui),Analysis = f2(TQM, u2),

Involve= f3(TQM, Analysis, u3),

Product= f4 (TQM, Involve, u4),

Volume = f5(Product, u 5 ),

Speed = f6 (Volume, U6),

On-Time = f7(Product, Speed, U7)-

5.2.2. Conditional probability estimationThe Bayesian approach was used to estimate

the conditional probabilities for the network . Eachp( U,) = 0, was assumed to be a collection of mul-tinomial distributions, one for each parent con-figuration . The precision of the prior estimationwas set at an equivalent sample size of 1 . TheKnowledge Discoverer program (Sebastiani andRamoni, 2000) was used to estimate the posteriorprobabilities for the sets of parents of each con-sequence variable .

5.2.3. Probabilistic inferenceProbabilistic inference is concerned with revis-

ing probabilities for a variable or set of variables,called the query, when an intervention fixes thevalues of another variable or set of variables,called the evidence . Any of the variables in theBayesian network can serve as a query or as evi-dence, thus allowing forward inference from cau-ses to effects (prediction) or backward inferencefrom effects to causes (diagnostics) . The simplesttype of intervention is one where a single variableis forced to take on a fixed value . The interventionreplaces the functional mechanism for the evidencevariable, Ei = f(pail , u i ) with a fixed value, E, = ei ,assumed known with certainty, in all equations .This creates a new model by removal of the net-work arrows from the parent set of the instanti-ated variable, which represents the system'sbehavior under the intervention . The relativemagnitude of an influence from an interventionmay be measured as the percent change from pre-intervention probabilities to post-interventionprobabilities of the query for evidence in differentstates .

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R D. Anderson, G. Vastag / European Journal of Operational Research 156 (2004) 92-109

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5.2.4. PredictionThe objective of predicting the impact of po-

tential changes in TQM allocation levels on flexi-bility and delivery variables was accomplished byTQM interventions as the evidence . The magni-tude of the impacts of the interventions wasgreatest on the direct effects of Involve, Analysis,and Product, as would be expected from theBayesian network. The indirect influences onVolume, Speed and On-Time were relatively small .

The distributions resulting from the TQM in-terventions can be summarized by expected valuesand compared to the expected values of pre-inter-vention distributions . Fig. 3 provides a summary ofexpected changes given TQM interventions .

Fig. 3 follows the basic principles of Trellisdisplays (Cleveland, 1993) . The variables from theleft to the right show an increasing impact of TQMintervention . The level of TQM intervention ran-ges from 1 = None (at the bottom of the graphs)to 5 = Large Amount (at the top) . Over this rangeof interventions, the customer delivery perfor-mance measures (Speed and On-Time) show theleast variation . Investments in employee partici-pation and process analysis (Involve and Analysis)show the greatest variation . The pre-interventionexpected value of Involve was 2 .72 (where 1 = noallocation and 5 = large allocation) . The expectedvalue of Involve with the TQM intervention set tono allocation was 1 .64 or an expected decrease of39.7%, as displayed in Fig . 3. In a similar fashion,the TQM intervention at the largest allocation

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These results are consistent with our currentunderstanding of TQM programs and systems .There is a saying attributed to Kaoru Ishikawathat summarizes the people aspect of this programsuccinctly: "TQM starts with education and endswith education." Furthermore, process improve-ments and continuous improvement programshave always been essential parts of quality mana-gement philosophies .

The expected changes in the delivery variableswere small. The range of expected changes inSpeed of delivery was from -3 .4% for no TQMallocations to 1 .5% for the highest TQM allocationlevel. The On-Time delivery variable also dis-played a narrow range of expected percent changesover the TQM interventions . Similar small impactswould be obtained from interventions on Analysisand Involve since the influences are mediated bythe flexibility variables .

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"backward" probabilistic inference with interven-tions of On-Time delivery . The expected percentchanges in the causes of On-Time delivery result-ing from On-Time interventions are summarized inFig. 4. As with Fig . 3, the expected changes arebased on comparing pre-intervention and post-intervention expected values .

SAnalysis

RD. Anderson, G. Vastag I European Journal of Operational Research 156 (2004) 92-109

Involve TQM Product

The expected changes in Fig . 4 may be viewedas measures of diagnostic importance for On-Timedelivery. The highest level of Speed of delivery isthe most important cause of improvement in On-Time delivery. The indirect cause of Volume flexi-bility is second in importance, followed by thedirect cause of Product flexibility. Expected chan-ges in the allocation levels of the improvementprograms were minor .

These findings are consistent with the literatureon JIT systems, including papers on the linkagesbetween quick set-ups (and thus increased manu-facturing flexibility), manufacturing lead-time re-duction, and delivery speed improvements(Schmenner, 1988; Vastag and Whybark, 1993 ;Vastag and Montabon, 2001) .

5.3. Specific comparisons

Both the Bayesian network and SEM, based onthe results of traditional significance testing, sup-ported the model of flexibility of change mediatingresource commitment programs and delivery per-formance. However, SEM provided the moreparsimonious explanation of the mediation modelat the concept level. SEM relationships, describedin the dimensionless regression metric of stan-dardized values, are appropriate since the latentvariables are not measured, and thus have noempirical metric . Although the latent variables arenot measured, a great deal of emphasis is placedon the measurement sub-model relating observed

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variables to the hypothetical latent variables . Thestrength of measurement by tau-equivalent evalu-ations and alpha reliability coefficients of internalconsistency play a central role in the SEM analy-sis. However, the measurement evaluations andthe fit of relationships between latent variablesprovide only an abstract causal description, sinceprediction and diagnostics are not possible . Thus,SEM could only achieve the explanation objectiveof the application .

The Bayesian network approach, using onlymeasured variables, allows interventions on theTQM and On-Time network variables that resultsin predictions and diagnostics . The distributionchanges from pre-intervention to post-interventionwere summarized to expected values and then des-cribed by expected percent changes, as shown inFigs. 3 and 4. Probabilistic Inference could also beconducted with interventions on other networkvariables.

In summary, SEM provides a parsimoniousdescription of observed and hypothetical variablesrich in support by psychometric indexes . Whereas,the Bayesian network provides predictions de-scribed in terms of probabilities and percents . Ifthe objective were only a description of theoreticalconstructs with no interest in current or futureinference to observable variables, then SEM islikely be the preferred method . If objectives in-cluded prediction and diagnostics of observedvariables, then the Bayesian network approachshould be selected .

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6. General comparisons

Both SEM and Bayesian networks are specifiedby Eq . (1), and each coveys the causal assertions ofa model M = {S, Os} using a DAG to portray thestructure of assumed functional relationships .However, fundamental differences exist betweenmethods for the structure S and the set of param-eters Os compatible with S . Concept representa-tion, distribution and functional assumptions,sample size, model complexity, measurement,specification search, model adequacy, theory test-ing and inference capabilities are the characteristicsdiscussed below for each of reviewed methods .Table 1 provides a generalized summary of thesecomparisons .

6.1. Concept representation

Bayesian networks are often labeled as Baye-sian belief networks . However, SEM also portraysa belief structure based on a conceptualization ofperceived reality derived from existing theory,empirical evidence and speculation . The primarybelief in SEM is an observable variable MV t iscaused by two unrelated unobservable hypotheti-cal variables .

The level of abstraction entailed by the modelstructure varies across the methods in relation tothe form of within-concept representation . Con-

cept representation in SEM is highly abstract andparsimonious; with the simple methodologicallyform of linear regression . SEM portrays covaria-tions between measured variables as the result of acommon cause, LVi , which results in the mea-surement model of e t -* MV t f- LV;. Finally,SEM greatly simplifies the DAG since only theLV; variables require temporal ordering .

6.2. Function, distribution and measurement as-sumptions

The functional form for discrete Bayesian net-works is non-parametric and non-linear. Dirichletdistributions are assumed to result from multino-mial sampling, and a subjective estimate of preci-sion is required for the prior distributions . SEMmethods are parametric in function and distribu-tion, assuming normality and linearity . Althoughmultivariate normality is usually assumed in SEM,the assumption is often not tested (Breckler, 1990)nor supported in applications (Micceri, 1989) .

Continuous measurement is generally assumedfor SEM due to the normality assumption . How-ever, SEM offers considerable flexibility in han-dling non-normal continuous variables (Westet al., 1995), ordinal data (Coenders et al ., 1997)and categorical data (Muthen and Muthen, 1998) .Bayesian networks currently require categoricalmeasurement . Scale compression, such as imple-

104


Table ISummary of model comparisons

Comparison SEM Bayesian network

Concept representationParsimony High LowMeasurement assumption Continuous DiscreteRelationship assumption Common cause and causally sufficient Causally sufficient

Operating characteristicsFunctional form Linear Non-linearDistribution assumption Normal MultinomialConcept network structure Parsimonious ComplexProcess modeling capability Limited Large

Assessment of adequacyGoodness-of-fit Global statistical tests Tests of independence

Model and measurement fit indexesSignificance tests for measurement andconcept coefficients

Inference Latent variable prediction Observed variable prediction


mented in the above application, will result insome loss of information in a Bayesian network .The tradeoff is parsimonious intuitive measure-ment, which is consistent with an emphasis on theanalysis of actions, versus full measurement utili-zation of SEM. If the tenuous assumption ofnormality for quasi-continuous scales holds inSEM, statistical testing will have greater powerthan significance testing in a discrete Bayesiannetwork. However, the magnitude of power dif-ferences is not known .

6.3. Sample size and model complexity

There is some general agreement that the mini-mum sample size for SEM should at least 100(Guadognoli and Velicer, 1988) . Minimum samplesize requirement for a Bayesian network is an openissue, but we speculate that 100 cases would be areasonable minimum requirement. However, theissue of minimum sample size for a Bayesian net-work would seem to be highly related to thenumber of states in the categorical variables andthe maximum number of parents of the variablesin the modeled system .

In general, SEM is best suited for modelingrather small processes, as Bentler and Chou (1987)have recommended an analysis be limited to 20 orfewer measured variables. This recommendation isnot too restrictive when item parcels employingsingle indicator SEM are used to represent con-cepts (Little et al ., 2002). Although SEM assumesa linear process, SEM can handle latent variableinteractions and quadratic effects (Ping, 1996) .However, branching patterns in modeled processthat create missing values require separate groupsbe formed for analysis. Bayesian networks havethe capability to be applied to very large processes,with potentially thousands of variables (Spiegel-halter et al ., 1993) . Further, Bayesian network canaccommodate a non-linear process, resulting frombranching patterns .

6.4. Specification search

Specification search in causal models is a pri-mary area of algorithm research, as well as asource of philosophical controversy (McKim and

105

Turner, 1997). The controversy centers on ac-ceptable ways of knowledge building and thepossibility of inferring causation from association(Glymour and Cooper, 1999, part 3) . The magni-tude of a search effort for a DAG without tem-poral order specification is enormous . Forexample, given the objective to identify the "true"model of relationships between ten unorderedvariables, 4, 175, 098, 976, 430, 596, 143 DAGsshould be searched and evaluated in reference toan appropriate fit criterion. When the backgroundknowledge gives complete variable order for aBayesian network, casual direction will availablein the pattern . However in applications, estab-lishing variable order is often an issue . Geneticalgorithms based on permutation assessmentshave been developed to assist in with this problem(Larranaga et al ., 1996) .

SEM methods also generally employ modelspecification searches in applications . Joreskogand Sorbom (1993) describe three approaches forSEM construction and development : strictly con-firmatory, model generation and model compari-son. MacCallum (1995) observes that the strictlyconfirmatory approach in SEM is very rare inapplications, with model modification being verycommon. Model revisions in 'SEM are usuallybased on a local modification index, such as theLagrange multiplier test, to assess the improve-ment in fit if a selected subset of fixed parameterswere converted into free parameters . Model com-parison posits a small number of feasible repre-sentations and selects the most acceptable model,based on evidence from nested significance testingor fit indexes . The SEM application in this paperprovides an example of specification search bymodel comparison .

6.5. Model adequacy

Bayesian networks employ significance tests ofconditional independence for a statistical assess-ment of structure adequacy. A maximum scoringapproach is also available, where log likelihoodscores for various parent sets are computed foreach measured variable . SEM uses a global sta-tistical test of goodness-fit, significance tests ofmeasurement and concept coefficients, and

106

descriptive model and equation indexes to supportthe adequacy of a given model .

6.6. Theory testing

The qualitative tasks of concept definition,concept representation, temporal ordering andspecification of causal relationships provide themajor explanations of an investigated theorywhether the concepts are portrayed by latentvariables or data-dependent composites or directmeasured variables. The explanation contributionsof a quantitative method, regardless whether aregression or probability metric is employed, arelimited to assessment of the model's adequacy re-flected by significance testing, descriptive fit in-dexes, and estimation of the magnitude of causalinfluences .

Neither a Bayesian network, nor a SEM offers aunique model of reality; rather a class of observ-ationally equivalent models is portrayed thatcannot be distinguished by statistical analysis(Verma and Pearl, 1990 ; MacCallum et al ., 1993).Further, Cooper (1999) points out that the inter-pretation of a Bayesian network must be maderelative to the categorical variables represented bythe nodes in the DAG . The existence of equivalentmodels is similar to confounding in experimentaldesign, where different parameterizations cannotbe distinguished in reference to fit to the data(Stelzl, 1986) .

6.7. Inference

Science typically views theory validation ascoming from predictive verification of expectedtheoretical results based on empirical evidence . Acausal model should provide an explanatory des-cription of causal relationships, plus manipulationcapabilities for diagnosing the key changes neces-sary for system improvement and for predictingthe impacts of potential change actions. Since eachequation, implied by a structure S, represents adistinct causal mechanism, it is conceptually pos-sible to set any represented variable to a specificvalue, i .e ., impose an intervention .

Bayesian networks permit both forward andbackward inference, allowing diagnostics and

R D. Anderson, G. Vastag / European Journal of Operational Research 156 (2004) 92-109

prediction based on any set of selected measuredvariables as illustrated in the above application . Asnoted above, SEM has prediction capabilities onlyat the hypothetical variable level . Even when allaspects of a SEM representation are completelysupported, prediction of observable consequencesfrom potential managerial action is not attainable .Simply, the model assumes that every observablevariable is a function of two unobservable vari-ables, a common cause and an unspecified causethat cannot be subject to managerial interventions .The inability to translate knowledge gained fromthe theoretical model evaluation into a basis formanagerial actions is the major weakness SEM .

7. Summary

The focus of this paper is on methods that viewcausation from a graphical viewpoint . The notionof a DAG is utilized to represent the conditionalindependence between any two variables, whichimplies the absence of a direct causal relationship .Further, assuming the nodes of a DAG representrandom variables, the joint probability distribu-tion of these variables can be factored in a causalmeaningful manner. These general results aresummarized in the specification of a causal modelas a structure S conforming to a DAG and a set ofassociated parameters O s consistent with thestructure. SEM and Bayesian networks are por-trayed as specializations of the general causalmodel specification, M = {S, Os } .

The emphasis of causal modeling applied inoperations management has been primarily con-centrated on providing increased process under-standing by emphasizing psychometric andstatistical support for theory-based explanations .SEM have been the most frequently used methodfor quantifying and evaluating an assumed causalprocess. The primary objective, under this ap-proach, is to assess whether a postulated theoret-ical network is a reasonable approximation of theprocess that generated the study data . Indexessupporting construct validity, measurement reli-ability, parameter significance, model fit, andcausal effects tend to dominate the reported re-sults. Since the analysis is usually based on a high


level of theoretical and knowledge domain sup-port, the confirmatory findings typically supportthe large majority of hypothesized relationships .Thus, conclusions tend to provide value by incre-mental extension of existing conceptualizationsthat cannot be extended to prediction of observedoutcomes .

Bayesian networks, in contrast to SEM, assumethe main role of causal modeling is to facilitate theanalysis of potential and actual actions, ratherthan focus on theory confirmation . Indeed, Baye-sian networks offer the capabilities to explain sys-tem relationships and to predict the impacts ofpotential actions as alternative structures that canbe evaluated by traditional tests of significance orby posterior probabilities or both, as demon-strated in the above application . The probabilitymetric provides non-linear detailed relationshipinformation that should be easily consumable bythe managers as well as academics . The modelingeffort is concerned with observable variables, nothypothetical concepts . Thus, it is possible to in-troduce a conceptual intervention and evaluate theexpected observable changes . More specifically,the posterior probabilities resulting from the in-tervention can be compared to the pre-interven-tion probabilities to provide a quantitativemeasure of expected change .

Appendix A. Description of the global manufactur-ing research group survey

In the late 1980s and in the mid 1990s, theGlobal Manufacturing Research Group carriedout two worldwide surveys focusing on smallmachine tools and no-fashion textile manufactur-ing. Data were collected in about 30 countriesrepresenting market, transitional and plannedeconomies .

In each country, directories of trade associationmembers were used to select a random sample offirms. A manufacturing executive from each of theselected companies was contacted by telephone .The executive was presented evidence of the tradeassociation support and was invited to participatein the study . As an incentive, firms were told that ifthey participated in the survey, the average res-

ponses for firms in their industry would be pro-vided to them. Follow-up telephone calls weremade to solicit responses and remind the partici-pants to complete and return the questionnaires . Ifnecessary, a second round of mailing was done toincrease the sample size. In this paper, we selecteda subset of the GMRG database, countries withlarge number of responses .

In the subset of data we used in this paper, wehad 588 respondents from the second survey . Therespondents were from Canada (88), Japan (77),Mexico (93), Russia (92) and the United States(238). Industry representation was classified asmachine tool (209), textile (207) and others (172) .

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