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LISRELLISREL

Under Guidance Of Submitted ByDr. Vikas Daryal Naveen ChopraDirector MBA F S2TIMT 1106.12

LISRELLISREL

Linear Structural Relationship

LISRELLISRELA LISREL is defined by a hypothesized

pattern of linear relationships among a set of measured and latent variables.

Such a pattern of linear relationships can be represented mathematically in a variety of ways.

There exist alternative ways of organizing variables and defining parameter matrices, which yield alternative mathematical frameworks for representing data models and covariance structure models.

Tools AppliedTools AppliedPCA (Principle Component

Analysis)SEM (Structural Equation Model)

Principle Component Principle Component AnalysisAnalysisPrincipal component analysis (PCA) is a

mathematical procedure uses orthogonal transformation to convert a set of observations of possibly correlated variables into a set of values of linearly uncorrelated variables called principal components.

The number of principal components is less than or equal to the number of original variables.

Principal components are guaranteed to be independent if the data set is jointly normally distributed.

PCA is sensitive to the relative scaling of the original variables.

Variance ContributionVariance Contribution

PCA AnalysisPCA AnalysisThis Variance analysis shows that

the “Layout” variable having the most impact on “Repurchase Link” in PC3 i.e. 0.722.

Structural Equation Model Structural Equation Model Structural equation modeling (SEM) is

a statistical technique for testing and estimating causal relations using a combination of statistical data and qualitative causal assumptions.

This definition of SEM was articulated by the geneticist Sewall Wright (1921), the economist Trygve Haavelmo (1943) and the cognitive scientist Herbert A. Simon(1953), and formally defined by Judea Pearl (2000) using a calculus of counterfactuals.

Structural equation models (SEM) allow both confirmatory and exploratory modeling, meaning they are suited to both theory testing and theory development.

Structural Equation ModelStructural Equation ModelThe concepts used in the model must

then be operationalized to allow testing of the relationships between the concepts in the model.

The model is tested against the obtained measurement data to determine how well the model fits the data.

The causal assumptions embedded in the model often have falsifiable implications which can be tested against the data.

InterpretationInterpretationGFI (Goodness of Fit Index)NFI(Normed Fit Index)CFI (Comparative Fit Index)

Goodness of Fit IndexGoodness of Fit IndexThe goodness of fit index (GFI) is

a measure of fit between the hypothesized model and the observed covariance matrix. The GFI ranges between 0 and 1, with a cutoff value of .9 generally indicating acceptable model fit.

Normed Fit IndexNormed Fit IndexThe normed fit index (NFI) analyzes

the discrepancy between the chi-squared value of the hypothesized model and the chi-squared value of the null model.  However, this NFI was found to be very susceptible to sample size. Value for the NFI should range between 0 and 1, with a cutoff of .95 or greater indicating a good model fit.

Comparative Fit IndexComparative Fit IndexThe comparative fit index (CFI)

analyzes the model fit by examining the discrepancy between the data and the hypothesized model, while adjusting for the issues of sample size inherent in the chi-squared test of model fit, and the normed fit index. CFI values range from 0 to 1, with larger values indicating better fit; a CFI value of .90 or larger is generally considered to indicate acceptable model fit.

Path DiagramPath Diagram

InterpretationInterpretationThis Path Diagram also shows the

value 1.06, which is also highest in all variables and having the high impact on the “Repurchase Link”

ConclusionConclusionAt last, it concludes that, both

PCA & SEM shows the same results, so data gathered by researcher is consistent and the model is fit.

Thank Thank YouYou

Any Query?Any Query?