22. STAGE 3: DESIGNING A STUDY TO
PRODUCE EMPIRICAL RESULTS
In this stage the researcher's measurement
theory will be tested.
We should note that initial data analysis
procedures should first be performed to
identify any problems in the data, including
issues such as data input errors.
In this stage the researcher must make some
key decisions on designing the CFA model.
23. • 1-Measurement Scales in CFA
• CFA models typically contain reflective
indicators measured with an ordinal or better
measurement scale. Meaning Indicators with
ordinal responses of at least four response
categories can be treated as interval, or at least
as if the variables are continuous.
• 2-SEM and Sampling.(Many times CFA requires
the use of multiple samples. Meaning
sample(s) should be drawn to perform the CFA.
Even after CFA results are obtained.)
24. 3-Specifying the Model
• distinction between CFA and EFA
• the researcher does not specify cross
loadings, which fixes the loadings at
zero.
• One unique feature in specifying the
indicators for each construct is the
process of "setting the scale" of a
latent factor.
25. 4-Issues in Identification
• overidentification is the desired state
for CFA and SEM models in general.
• During the estimation process, the most
likely cause of the computer program
"blowing up" or producing meaningless
results is a problem with statistical
identification. As SEM models become
more complex.
26. AVOIDING IDENTIFICATION PROBLEMS
(Several guidelines can help determine the
identification status of a SEM model and assist the
researcher in avoiding identification problems)
• Meeting the Order and Rank
Conditions.(required mathematical properties)
• THREE-INDICATOR RULE.(It is satisfied when all
factors in a congeneric model have at least three
significant indicators)
• RECOGNIZING IDENTIFICATION PROBLEMS(Many
times the software programs will provide some
form of solution)
27. SOURCES AND REMEDIES OF
IDENTIFICATION PROBLEMS
Does the presence of identification problems mean
your model is invalid? Although many times
identification issues arise from common mistakes
in specifying the model and the input data.
• Incorrect Indicator Specification. (4 mistakes e.g.)
• "Setting the Scale" of a Construct.(each construct
must have one value specified)
• Too Few Degrees of Freedom.(Small sample size
(fewer than 200) increases the likelihood of
problems )
28. Problems in Estimation
most SEM programs will complete the estimation
process in spite of these issues.
It then becomes the responsibility of the researcher
to identify the illogical results and correct the
model to obtain acceptable results.
• ILLOGICAL STANDARDIZED PARAMETERS. (when
correlation estimates between constructs exceed
|1.0| or even standardized path coefficients exceed
|1.0|. Meaning there is problem with SEM results.
• HEYWOOD CASES A SEM. (solution that produces
an error variance estimate of less than zero (a
negative error variance) is termed a Heywood case.
29. STAGE 4: ASSESSING MEASUREMENT
MODEL VALIDITY
Once the measurement model is correctly
specified, a SEM model is estimated to provide
an empirical measure of the relationships
among variables and constructs represented by
the measurement theory.
The results enable us to compare the theory
against reality as represented by the sample
data.
we see how well the theory fits the data.
30. a-Assessing Fit
The sample data are represented by a
covanance matrix of measured items, and
the theory is represented by the
proposed measurement model. These
equations enable us to estimate reality
by computing an estimated covariance
matrix based on our theory. Fit compares
the two covariance matrices.
31. b-Path Estimates
One of the most fundamental assessments of construct
validity involves the measurement relationships
between items and constructs
• SIZE OF PATH ESTIMATES AND STATISTICAL
SIGNIFICANCE.
loadings should be at least .5 and ideally .7 or higher
meaning Loadings of this size or larger confirm that the
indicators are strongly related to their associated
constructs and are one indication of construct validity.
• IDENTIFYING PROBLEMS.
means(Loadings also should be examined for offending
estimates as indications of overall problems)
32. C- CFA and Construct Validity
One of the biggest advantages of CFA/SEM is its ability
to assess the construct validity of a proposed
measurement theory. Construct validity
Construct validity is made up of four important
components:
1. Convergent validity – three approaches:
o Factor loadings.
o Variance extracted.
o Reliability.
2. Discriminant validity.
3. Nomological validity.
4. Face validity.
33. Construct Validity
Construct validity is the extent to which a set of measured items
actually reflects the theoretical latent construct those items are
designed to measure.
1- CONVERGENT VALIDITY.
The items that are indicators of a specific construct should converge
• Factor Loadings.
• At a minimum, all factor loadings should be statistically
significant.(standardized loading estimates should be .5 or
higher, and ideally .7 or higher)
• Average Variance Extracted.
• The Li represents the standardized factor
loading, and i is the number of items.
• AVE estimates for two factors also should be greater than the
square of the correlation between the two factors to provide
evidence of discriminant validity.
34. • Reliability.
• Reliability estimate is that .7 or higher
suggests good reliability. Reliability between
.6 and .7 may be acceptable, provided that
other indicators of a model's construct validity
are good.
35. 2- DISCRIMINANT VALIDITY.
the extant to which a construct is truly distinct from
other construct. (The high discriminant validity provides
evidence that a construct is Unique)
3- NOMOLOGICAL VALIDITY AND FACE VALIDITY
(Constructs also should have face validity and
nomological validity)
• face validity: must be established prior to any
theoretical testing when using FA.
• nomological validity: is then tested by examining
whether the corrections among the constructs in a
measurement theory make sense.
36. D- Model Diagnostics
• the process of testing using CFA provides
additional diagnostic information that may
suggest modifications for either addressing
unresolved problems or improving the
model's test of measurement theory.
• Some areas that can be used to identify
problems with measures as following:
37. 1- STANDARDIZED RESIDUALS:
• Residuals: are the individual differences
between observed covariance terms and the
fitted (estimated) covariance terms.
• The standardized residuals: are simply the raw
residuals divided by the standard error of the
residual.
• Residuals: can be either positive or negative,
depending on whether the estimated
covariance is under or over the corresponding
observed covariance.
38. 2- MODIFICATION INDICES:
(is calculated for every possible relationship that
is not estimated in a model)
(of approximately 4.0 or greater suggest that the
fit could be improved significantly) e.g. HBAT
3- SPECIFICATION SEARCHES:
(is an empirical trial-and-error approach that
uses model diagnostics to suggest changes in
the model)
(SEM programs such as AMOS and LISREL can
perform specification searches automatically)
39. 4- CAVEATS IN MODEL RESPECIFICATION:
• CFA results suggesting more than minor
modification should be reevaluated with
a new data set.
• (e.g., if more than 20% of the measured
variables are deleted, then the
modifications cannot be considered
minor)