STAGE 3: DESIGNING A STUDY TO PRODUCE EMPIRICAL RESULTSIn this stage the researchers 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.
• 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.)
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.
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.
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)
SOURCES AND REMEDIES OF IDENTIFICATION PROBLEMSDoes 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 )
Problems in Estimationmost 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.
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.
a-Assessing FitThe 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.
b-Path EstimatesOne 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)
C- CFA and Construct Validity One of the biggest advantages of CFA/SEM is its abilityto assess the construct validity of a proposedmeasurement theory. Construct validity Construct validity is made up of four importantcomponents: 1. Convergent validity – three approaches: o Factor loadings. o Variance extracted. o Reliability. 2. Discriminant validity. 3. Nomological validity. 4. Face validity.
Construct ValidityConstruct 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.
• 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 models construct validity are good.
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 andnomological 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.
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 models test of measurement theory.• Some areas that can be used to identify problems with measures as following:
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.
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. HBAT3- SPECIFICATION SEARCHES:(is an empirical trial-and-error approach thatuses model diagnostics to suggest changes in the model)(SEM programs such as AMOS and LISREL can perform specification searches automatically)
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)