### Structural Equation Modeling (SEM)

```Using AMOSE Software
What Is Structural Equation Modeling?
 Structural Equation Modeling (SEM) is a multivariate
technique that combining aspects of (a) multiple regression
(examining dependence relationships) and (b) factor analysis
(representing unmeasured concepts – factors – with multiple
variables) to estimate a series of interrelated dependence
relationships simultaneously (Hair, Anderson et al. 1995).
 It is a statistical technique that allows the analyst to examine a
series of dependence relationships between
exogenous
variables and endogenous variables simultaneously.
 SEM is an extension of the general linear model (GLM) that
enables a researcher to test a set of regression equations
simultaneously.
Why SEM?
The usefulness of SEM in research is distinguished by following
characteristics:
 SEM programs provide overall tests of model fit and individual
parameter estimate tests simultaneously
 Regression coefficients, means, and variances may be compared
simultaneously, even across multiple between-subjects groups.
 It improves statistical estimation by accounting for measurement
error in the estimation process.
 It is able to represent unobserved (latent) concepts in the analysis
of dependence relationships.
The basic approach to performing a SEM analysis is as follows:
Theory
Model
Construction
Instrument
Construction
Interpretation
Data Collection
Model Testing
The
researcher
first
specifies a model based
on
theory,
then
determines
how
to
measure
constructs,
collects data, and then
inputs the data into the
SEM software package.
The package fits the data
to the specified model
and produces the results,
which include overall
model fit statistics and
parameter estimates.
Results
http://ssc.utexas.edu/consulting/
AMOS
 Stands for Analysis of MOment Structures
 Moment structures refer to:
:: Mean
:: Variance
:: Covariance
 A computer application under SPSS
 Use graphical interface
SEM Terminologies
 Manifest or Observed variables: it is a variable that
directly measured by researchers
 Latent or Unobserved variables: it is a variable not
directly measured, but are inferred by the relationships or
correlations among measured variables in the analysis.
Examples: Quality, perception, attitude, values, image
SEM Terminologies
 Exogenous (IV): an exogenous variable is one whose
variability is assumed to be determined by causes outside
the causal model under consideration(Pedhazur,1997) .
 Endogenous (Dependent and Mediating variables): is one
whose variation is to be explained by exogenous and other
endogenous variables in the causal model
SEM Terminologies
 Measurement Model: The measurement model
speciﬁes the rules governing how the latent
variables are measured in terms of the observed
variables, (Decide which manifest variables define
each latent variable) and it describes the
measurement properties of the observed variables.
That is, measurement models are concerned with
the relations between observed and latent
variables. (Ho, 2006).
SEM Terminologies
Structural Equation Model: is a flexible, comprehensive model that
specifies the pattern of relationships among independent and
dependent variables, either observed or latent. It incorporates the
strengths of multiple regression analysis, factor analysis, and
multivariate ANOVA (MANOVA) in a single model that can be
evaluated statistically. Moreover, it permits directional predictions
among a set of independent or a set of dependent variables, and it
permits modeling of indirect effects (Ho, 2006).
Checklist of Requirements in SEM
 Reasonable Sample Size:
“sample size is sufficiently large”
Ho (2006)The most appropriate minimum ratio is ten respondents per parameter
Kline (2005, 2010)
- N <100 small; N between 150 and 200 medium; N >200 large; but perhaps
even 200 case is insufficient to analyze more complex models.
- Thus 20 cases for every estimated parameter is ideal although 10 subject per
variable is less ideal, but may suffice(Kline, 2005).
James Stevens’(2002) a good general rule for sample size is 15 cases per
predictor
Schumacher and Lomax (2010) cited from Costello and Osborne (2005) 20
subjects per variables is recommended for best practices in factor analysis.
 Number of indicator variables: As a practical matter, three is the preferred
minimum number of indicators, and in most cases, five to seven indicators
should represent most constructs (Hair et al., 2006).
Assumptions in SEM
 Observations are independent of each other.
 Random sampling of respondents.
 Linearity of relationships between exogenous
and endogenous variables.
 Distribution of observed variables
multivariate normal (Ho, 2006).
is
Normality
 As a rule of thumb, discrete data (categorical data, ordinal
data with < 15 values) may be assumed to be normal if
skew and kurtosis is within the range of +/- 1.0 (some say
+/- 1.5 or even 2.0) (Schumacker & Lomax, 2004: 69).
In fact, residuals from a SEM analysis are not only expected
to be univariate normally
distributed, their joint
distribution is expected to be joint multivariate normal
(JMVN) as well. However, this assumption is never
completely met in practice.
Goodness-of-Fit Criteria
 Goodness-of-Fit measures can be classified into three types (Ho, 2006):
(1) Absolute fit measures: These measures determine the degree to which the
proposed model predicts (Fits) the observed covariance matrix. Some commonly
used measures of absolute fit such as:
a) Chi-square: In SEM, the researcher is looking for significant differences between
the actual and predicted matrices. As such, the researcher does not wish to reject
the null hypothesis and, accordingly, the smaller the chi-square value, the better fit
of the model.
b) Normed Chi-square/df: Values close to 1.0 indicate good fit. values between 2.0
and 3.0 indicate reasonable fit.
c) Goodness-of-Fit Index(GFI): value > 0.90
d) Root Mean Square Error of Approximation(RMSEA); Hair, et al., (2006; p748)
recommended RAMSEA between .03 and .08. Kline (2011, p 206 and 2005, p139)
RAMSEA < .05 indicates close approximate fit, between .05 and .08 reasonable, and
RAMSEA > .10 suggest poor fit (cited from Browne & Cudek, 1993)
-e) Standardised Root Mean-square Residual (SRMR): values less than .10 are
generally considered favorable (Kline, 2005, p141)
Goodness-of-Fit Criteria
(2) Incremental fit measures: These measures compare the proposed
model to some baseline model, most often referred to as the
null or independence model. In the independence model, the
observed variables are assumed to be uncorrelated with each
other. Incremental fit measures have been proposed, such as:
-Tucker-Lewis Index (TLI) -Normed Fit Index (NFI)
-Relative Fit Index (RFI) -Incremental Fit Index (IFI)
-Comparative Fit Index (CFI)
 By convention, researchers have used incremental fit indices > 0.90 as
traditional cutoff values to indicate acceptable levels of model fit. the model
represents more than 90% improvement over the null or independence
model. In other words, the only possible improvement to the model is less
than 10%.
Goodness-of-Fit Criteria
(3) Parsimonious fit measures: In scientific research, theories
should be as simple, or parsimonious, as possible (Ho, 2006).
parsimonious fit measures relate the goodness-of-fit of the proposed
model to the number of estimated coefficients required to achieve
this level of fit. Such as:
 Parsimonious Normed Fit Index (PNFI): When comparing
between models, differences of 0.06 to 0.09 are proposed
to be indicative of substantial model differences (Williams
& Holahan, 1994).
 Akaike Information Criterion (AIC): The AIC is a
comparative measure between models with differing
numbers of constructs. AIC values closer to zero indicate
better fit and greater parsimony. A small AIC generally
occurs when small chi-square values are achieved with
fewer estimated coefficients.
That’s ALL
For the Introduction
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