The Stages in Structural Equation Model Stage 1) Assessing individual constructs Stage 2) Developing...
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The Stages in Structural Equation Model Stage 1) Assessing individual constructs Stage 2) Developing and assessing the measurement model validity Stage
The Stages in Structural Equation Model Stage 1) Assessing
individual constructs Stage 2) Developing and assessing the
measurement model validity Stage 3) Specifying the structural model
Stage 4) Assessing structural model validity
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Stage 1:Assessing Individual constructs One of the most
important steps is operationalization of constructs (Hair, 2006).
In attempting to ensure theoretical accuracy, researchers many
times have a number of established scales to choose from.
Nonetheless, eve with the wide usage of scales, the researcher
often is faced with the lack of an established scale and must
develop a new scale or substantially modify an existing scale to
new context. Therefore, in all of these conditions, the foundation
for the SEM analysis is how selects the items to measure the
constructs (Hair et al., 2006).
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Type of Individual construct Type1: Simple Individual Construct
Type2: Individual Construct with 3 dimension First Order CFA Type3:
Construct with 3 dimension based on Second Order CFA
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Single factor Independent Model Interrelated model
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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.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)
Slide 7
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%.
Slide 8
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.
Slide 9
Detecting outliers The Mahalanobis D 2 statistics is commonly
used to detect case-wise outliers. It computes the overall centroid
and computes the distance of each observation from the centroid.
The Mahalanobis D 2 is known to follow a Chi-square distribution.
The degree of freedom is the number of variables that are being
tested. Usually the inverse chi-square value at a=0.001 is taken as
the trash hold value. For example there are 2 variables, then df =2
Inverse Chi-squared value for a=0.001 at a df of 2 is: 13.186 If
the highest value in the MAH_1 column is 6.784, which is less than
13.186. Thus, there are no major outliers in the file.
Slide 10
different method to handle missing values Listwise deletion:
means a subject with missing values is deleted in all calculations.
Pairwise: means it is deleted subjects with missing data just for
calculations comprising that variable. In using the Listwise
deletion and Pairwise deletion may be losing a large number of
cases, and then could reduce the sample size, therefore these two
methods are not always suggested (Schumacher & Lomax, 2010).
The SEM softwares the option for handling the missing values are
replacing the missing value with means when only a small number of
missing values is present in the data set, or employed regression
imputations for handle missing values when a moderate amount of
missing data present in the data (Schumacher & Lomax, 2010;
Byrne, 2010).
Slide 11
Examples and hands on For Individual construct CFA
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Stage 2) Developing and assessing the measurement model
validity While specified the scale items, it is essential to
specify the measurement model. In this stage, each latent construct
to be included in the model is identified and the measured
indicator variables (items) are assigned to latent constructs (Hair
et al., 2006). The measurement models specify how the latent
variables are measured in terms of the observed variables. In the
other word the measurement models are concerned with the relations
between observed and latent variables (Ho, 2006).
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The Criteria's for Assessment Goodness-Of-Fit (GOF) Indices
Assessing the individual constructs, measurement model validity and
structural model validity depends on a number of Goodness-Of-Fit
(GOF) indices Goodness-of-fit measures the extent to which the
actual or observed covariance input matrix corresponds with (or
departs from) that predicted from the proposed model (Ho, 2006).
GOF measures such as : Chi-Square (non sig), Goodness of Fit
Indicator (GFI), Adjusted Goodness of Fit Indicator (AGFI),
Comparative Fit Index (CFI), Normed Fit Index (NFI), and Tucker
Lewis Index (TLI) indicates a good fit to the model at about.9 or
greater. Root Mean Square Error of Approximation (RMSEA) which a
measure greater than.1 indicates a poor fit, values ranging between
0.08 to 0.1 indicate mediocre fit, and values ranging between 0.03
and 0.08 are indicate better fit model.
Slide 15
Construct validity Construct validity is the extent to which a
set of measured items actually reflected the theoretical latent
construct those item are designed to measure. Thus, it deals with
the accuracy of measurement. Construct validity is made up of four
important components which they are: 1) Convergent validity: the
items that are indicators of a specific construct should converge
or share a high proportion of variance in common, known as
convergent validity. The ways to estimate the relative amount of
convergent validity among item measures: Factor Loading: at a
minimum, all factor loading should be statistically significant. A
good rule of thumb is that standardized loading estimates should
be.5 or higher, and ideally.7 or higher. Variance Extracted (VE):
is the average squared factor loading. A VE of.5 or higher is a
good rule of thumb suggesting adequate convergence. A VE less
than.5 indicates that on average, more error remains in the items
than variance explained by the latent factor structure impose on
the measure (Haire et al., 2006, p 777). Construct Reliability:
construct reliability should be.7 or higher to indicate adequate
convergence or internal consistency. The Criteria's for
Assessment
Slide 16
Construct validity 2) Discriminant Validity: the extent to
which a construct is truly distinct frame other construct. To test
the discriminant validity the VE for two factors should be grater
than the square of the correlation between the two factors to
provide evidence of discriminant validity. 3) Nomological Validity:
is tested by examining wheather the correlation among the
constructs in a measurement theory make sense. Constructs of
interest should be related to other constructs according to
hypothesised ways derived from the theory in which the construct is
embeded, forming the nomological net for that set of constructs
(The matrix of correlations can be useful in this assessment. 4)
Face Validity: must be established prior to any theoretical testing
when using CFA. Without an understanding of every items content or
meaning. It is impossible to express an correctly specify a
measurement theory. The Criteria's for Assessment
Slide 17
Examples and hands on For Measurement Model
Slide 18
Stage 3)Specifying the structural model Once the measurement
model is specified and validated with CFA, then the structural
model represented by specifying the set of relationships between
constructs. The structural equation model is a comprehensive model
that specifies the pattern of relationships among independent and
dependent variables, either observed or latent (Hair, et al., 2010;
Ho, 2006; Landis et al., 2001).
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Slide 20
Stage 4) Assessing structural model validity The assessing
structural model validity focused on two issues comprising; a) the
overall and relative model fit, and b) the size, direction, and
significance of the structural parameter estimates, depicted with
one-headed arrows on a path diagram (Hair et al., 2006).
Slide 21
Accounting for Error Thus, SEM provides estimates for two types
of error variance error terms and residual terms: Error term:
represents measurement error associated with observed variables,
i.e. the degree to which the observed variables do not perfectly
describe the latent construct of interest (Hair, Black et al.
2006). Such measurement error terms represent causes of variance
due to unmeasured variables as well as random measurement error
(Garson 2006). Residual term: represents the error in the
prediction of endogenous factors from exogenous factors, that is to
say, how much variance in the associated endogenous variable was
not accounted for by influences in the model (Texas 2002).
Slide 22
Examples and hands on For Structural Model
Slide 23
Approaches to aggregation Total disaggregation: In a totally
disaggregated model, each item serves as an indicator for a
construct. Partial disaggregation: In a partially disaggregated
model, several items are summed or averaged resulting in parcels.
These parcels are then used as indicators for constructs. Total
aggregation: In a totally aggregated model, all of the items for a
scale are summed or averaged. The result is that if only one scale
is used to measure each construct, then there is only one indicator
per construct and the model is a path analysis rather than a latent
variable model. If more than one scale was used to measure a
construct, then it is still possible to specify a latent variable,
and each indicator is a total scale score (Coffman and Maccall.um,
2005).
Slide 24
Parceling Parcels are aggregations (sums or averages) of
several individual items. Advantages of parcels (Coffman and
Maccall.um, 2005) : 1) parcels generally have higher reliability
than single items(Kishton & W idaman, 1994). 2) A second
advantage of using parcels rather than items as indicators of
latent variables involves the reduction in the number of measured
variables in a model. From this perspective, models with parcels as
indicators are likely to fit better than models with items as
indicators because the order of the parcel correlation matrix is
much smaller than the order of the item correlation matrix. 3) They
can be used as an alternative to data transformations or
alternative estimation techniques when working with nonnormally
distributed variables. The most often used estimation method in
structural equation modeling, maximum likelihood, assumes
multivariate normality of the measured variables in the population.
If the measured variables are not multivariate normal, then
estimates of fit measures and estimates of standard errors of
parameters may not be accurate (Hu & Bentler, 1998).