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# Structural Equation Modelling

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Structural Equation Modelling

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### Structural Equation Modelling

1. 1. Structural Equation 1 Structural Equation Modeling Edgardo DonovanRES 610 – Dr. Joshua Shackman Module 3 – Case Analysis Monday, August 22, 2011
2. 2. Structural Equation 2 Structural Equation Modeling Structural Equation Modeling (SEM) is a statistical technique for estimatingcausal relations using statistical data and qualitative assumptions allowing it to be usedboth for theory testing and theory development. Structural Equation Modeling is apowerful yet complex analytical technique. The use of SEM to examine strategicmanagement phenomena has increased dramatically in recent years (Shook 2004, p. 397).In its most general form SEM consists of a set of linear equations that simultaneously testtwo or more relationships among directly observable and/or unmeasured latent variables.While SEM serve purposes similar to multiple regression, differences exist between thesetechniques. SEM has a unique ability to simultaneously examine a series of dependencerelationships while also analyzing multiple dependent variables. (Shook 2004, p. 398).Given SEMs ability to map and assess a web of relationships it offers vast potential as atool to diagnose key links. SEMs ability to tap intangible latent variables might helpunveil the unobservable constructs that are central to the resource-based view,transactions, costs economics and agency theory. (Shook 2004, p. 403). Structural equation modeling grows out of and serves purposes similar tomultiple regression, but in a more powerful way which takes into account multiple latentindependents each measured by multiple indicators, one or more latent dependents alsoeach with multiple indicators, the modeling of mediators as both causes and effects,modeling of interactions, nonlinearities, correlated independents, measurement error, andcorrelated error terms. SEM may be used as a more powerful alternative to multipleregression, path analysis, factor analysis, time series analysis, and analysis of covariance.Advantages of SEM compared to multiple regression include more flexible assumptions,
3. 3. Structural Equation 3particularly allowing interpretation even in the face of multicollinearity; use ofconfirmatory factor analysis to reduce measurement error by having multiple indicatorsper latent variable; the attraction of SEMs graphical modeling interface; the desirabilityof testing models overall rather than coefficients individually; the ability to test modelswith multiple dependents; the ability to model mediating variables rather than berestricted to an additive model; the ability to model error terms; the ability to testcoefficients across multiple between-subjects groups; and ability to handle difficult datasuch as time series with auto correlated error, non-normal data, and incomplete data.Moreover, where regression is highly susceptible to error of interpretation due tomisspecification, the SEM strategy of comparing alternative models to assess relativemodel fit makes it more robust (Garson 2008, p. 1). SEM is usually viewed as a confirmatory rather than exploratory procedure, usingeither a confirmatory, alternative models, or model development approach. In aconfirmatory approach a model is tested using SEM goodness-of-fit tests to determine ifthe pattern of variances and covariances in the data is consistent with a structural (path)model specified by the researcher. However as other unexamined models may fit the dataas well or better, an accepted model is only a not-disconfirmed model. In an alternativemodels approach one may test two or more causal models to determine which has thebest fit. There are many goodness-of-fit measures, reflecting different considerations, andusually three or four are reported by the researcher. Although desirable in principle, thisapproach runs into the real-world problem that in specific research areas, the researchermay not find in the literature two well-developed alternative models to test.
4. 4. Structural Equation 4In model development approach the model is developed using a calibration data sampleand then confirmed using an independent validation sample. In practice, much SEMresearch combines confirmatory and exploratory purposes: a model is tested using SEMprocedures, found to be deficient, and an alternative model is then tested based onchanges suggested by SEM modification indexes. This is the most common approachfound in the literature. The problem with the model development approach is that modelsconfirmed in this manner are post-hoc ones which may not be stable (may not fit newdata, having been created based on the uniqueness of an initial dataset). Researchers mayattempt to overcome this problem by using a cross-validation strategy under which themodel is developed using a calibration data sample and then confirmed using anindependent validation sample (Garson 2008, p. 2). Figure 1. Sample Use of SEM for Exploratory Model Analysis (Morgan 1994, p. 27).
5. 5. Structural Equation 5I believe that SEM may become useful in my studies provided that the data will fit themodel of my future study. If so perhaps SEM will be helpful in confirming the series ofrelationships my hypotheses proposes. SEM may also be useful in the exploratory phaseof my research provided that I despite apparent correlations that causal interpretationshould to be applied given that many SEM applications interprets the final model as thecausal model. Structural Equation Modeling (SEM) is a statistical technique for estimatingcausal relations using statistical data and qualitative assumptions allowing it to be usedboth for theory testing and theory development. Structural Equation Modeling is apowerful yet complex analytical technique.‘
6. 6. Structural Equation 6 BibliographyGarson, D. (2008). Structural equation modeling. StatNotes. North Carolina StateUniversity. Retrieved March 2, 2008, fromhttp://www2.chass.ncsu.edu/garson/pa765/structur.htmMcallister, DJ and Bigley, GS (2002). Work context and the definition of self: howorganizational care influences organization-based self-esteem. Academy of ManagementJournal. 45(5): 894-904.Morgan, RM and Hunt, SD (1994). The commitment-trust theory of relationshipmarketing. Journal of Marketing. 58(3):20-38Shook, CL, Ketchen, DJ Jr, Tomas, G, Hult, M, and Kacmar, KM (2004). An assessmentof the use of structural equation modeling in strategic management research. StrategicManagement Journal. 25(4)397-410 Retrieved August 24, 2008, fromhttp://proquest.umi.com/pqdweb?index=0&did=572905761&SrchMode=3&sid=1&Fmt=3&VInst=PROD&VType=PQD&RQT=309&VName=PQD&TS=1219960510&clientId=29440&aid=1