Structural. Equation Modeling Using AMOS: An Introduction, The university of ... structural equation analysis, Fifth edition, Taylor and Francis Group,. New York.
Structural Equation Modeling (SEM) Dhofar University Dr. Omar Durrah Spring 2018 Durrah 2018
Presentation Outline SEM in a nutshell
SEM Advantages Major Applications of SEM Sample Size for SEM
SEM Jargon SEM Language Indices of Goodness of Fit
Exploratory Factor Analysis (EFA) Confirmatory Factor Analysis (CFA) Steps of SEM Analysis
SEM Software Packages Practical Application Durrah 2018
SEM in a nutshell SEM:
is very general, very powerful multivariate technique. SEM is an extension of the general linear model that enables a researcher to test a set of regression equations together. SEM can test traditional models, but it also permits examination of more complex relationships and models, such as confirmatory factor analysis (CFA). Source: Division of Statistics + Scientific Computation, (2012) Source: (Sudano & Perzynski, 2013) Durrah 2018
SEM in a nutshell SEM serves purposes similar to multiple
regression, but in a more powerful way which takes into account the modeling of interactions, nonlinearities, correlated independents, measurement error, correlated error items, multiple latent independents. SEM is combination of factor analysis and regression, Direct link between Path Diagrams and equations and fit statistics. Source: http://slideplayer.com/slide/8500105/ Source: (Ainsworth, 2006) Durrah 2018
SEM Advantages Advantages of SEM compared to multiple regression include more flexible assumptions use
of confirmatory factor analysis to reduce
measurement error by having multiple indicators per latent variable the attraction of SEM’s graphical modeling interface, Source: (Barbara, 2012) Durrah 2018
SEM Advantages the ability to test models with multiple dependents, the ability to model mediating variables,
the ability to model error terms, the ability to test coefficients across multiple
between-subjects groups, the ability to handle difficult data, non-normal data,
incomplete data. Source: http://slideplayer.com/slide/8500105/ Durrah 2018
Major Applications of SEM Confirmatory factor analysis (CFA). Path analysis. Second order factor analysis. Covariance structure models. Correlation structure models. Source: (Sudano & Perzynski, 2013) Durrah 2018
What Sample Size is Enough for SEM?
It needs to be large to get stable estimates of the covariances/correlations
200 subjects for small to medium sized model
A minimum of 10 subjects per estimated parameter
Source: (Ainsworth, 2006) Durrah 2018
SEM Jargon
Latent Variables: are the unobserved variables or
constructs or factors which are measured by their respective indicators. Latent variables include both independent, mediating, and dependent variables.
Indicators: are observed variables, sometimes called manifest variables or reference variables, such as items in a survey instrument.
Source: http://slideplayer.com/slide/8500105/ Durrah 2018
Error
Error:
An error term refers to the measurement
error factor associated with a given indicator.
Whereas regression models implicitly assume zero measurement error.
Error terms are explicitly modeled in SEM and as a result path coefficients modeled in SEM are unbiased
by
error
terms,
coefficients are not. Durrah 2018
Source: http://slideplayer.com/slide/8500105/
whereas
regression
Variables of SEM
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SEM Language Latent variables, factors, constructs
Observed variables, measures, indicators, manifest variables
Direct effects Correlation Source: http://slideplayer.com/slide/3387957/
Indices of Goodness of Fit Indices
Symbol
Criteria
X2
Insignificant
CMIN/DF
0.9
Tucker Lewis Index
TLI
> 0.9
Incremental Fit Index
IFI
> 0.9
Normed Fit Index
NFI
> 0.9
Goodness-of-Fit Index
GFI
> 0.9
Parsimony Normed Fit Index
PNFI
> 0.5
Parsimony Goodness-of-Fit Index
PGFI
> 0.5
Chi-Square Chi-Square/Degree of Freedom Root Mean Square Error of Approximation Root Mean Square Residual
Source: (Kline,1998)
Durrah 2018
Exploratory Factor Analysis (EFA): Exploratory
factor
analysis
is
a
statistical technique that is used to reduce data to a smaller set of summary
variables and to explore the underlining theoretical structure of the phenomena. Source: http://www.statisticssolutions.com/factor-analysis-sem-exploratory-factoranalysis/ Durrah 2018
Confirmatory Factor Analysis (CFA): (CFA) is a multivariate statistical procedure that is used to test how well the measured variables represent the number of constructs.
It plays an important role in structural equation
modeling.
Source: http://slideplayer.com/slide/8500105/ Durrah 2018
Steps of SEM Analysis 1.
Development of hypothesis / theory
2.
Construction of path diagram
3.
Model specification
4.
Model identification
5.
Parameter estimation
6.
Model evaluation
7.
Model modification
Source: (Loehlin & Beaujean, 2017) Durrah 2018
SEM Software Packages 1.
AMOS (Is used in case of a sample is enough)
2.
LISREL (It is considered one of the oldest programs)
3.
EQS (Is used in case of a sample is small)
4.
Mplus (Is used in case of a sample is not enough)
5.
R
6.
Mx
7.
SEPATH
8.
CALIS
Source: http://slideplayer.com/slide/3306961/ Durrah 2018
References
Ainsworth, A. (2006). Ghost Chasing”: Demystifying Latent Variables and SEM, University of California, Los Angeles. Barbara M. Byrne (2012): Structural Equation Modeling with Mplus, Routledge Press Division of Statistics + Scientific Computation, (2012). Structural Equation Modeling Using AMOS: An Introduction, The university of Texas at Austin Kline, R. B. (1998). Principles and Practice of Structural Equation Modeling. New York: The Guilford Press. Loehlin, J. & Beaujean, A. (2017). An introduction to factor, path, and structural equation analysis, Fifth edition, Taylor and Francis Group, New York. Sudano, J. & Perzynski, A. (2013). Applied Structural Equation Modeling for Dummies, by Dummies, Indiana University, Bloomington. Durrah 2018
Websites http://slideplayer.com/slide/3306961/ http://slideplayer.com/slide/3387957/
http://slideplayer.com/slide/8500105/ http://www.statisticssolutions.com/factor-analysis-sem-
exploratory-factor-analysis/ https://www.facebook.com/groups/723695840982530/sear
ch/?query=%20Nasser%20Alareqe (Data)
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Thank You Durrah 2018
