Can the goodness of fit indicators be improved in the confirmatory factor analysis of the measurement model by eliminating weak observations? How can these observations be diagnosed?
Bassam A. Alyouzbaky I'm not sure what you mean by "weak" observations, but outliers (cases with extreme values) can certainly have an influence on goodness of fit and parameter values in SEM (in much the same way as they may distort the results of other statistical analyses as well). It is thus important to check for outliers and/or extreme cases before running the analysis
Also, population heterogeneity can lead to misfit. That is, if you examine a causally inhomogeneous population with different observed or unobserved subgroups ("latent classes") for which different parameter values hold in the population, specifying a single model for all individuals can lead to misfit and/or parameter bias. Multigroup analysis (for known/observed groups) and factor mixture modeling (for unknown groups/latent classes) can be helpful in this case. These methods allow you to examine the groups separately and estimate unique parameter values for each group.
Dear Bassam A. Alyouzbaky
Each row should include the results of a distinct model, with lower-factor models appearing first and higher-factor models appearing last. The first row should include the name of each model; the rows to the left should include the chi-square value, degrees of freedom, goodness-of-fit index, and any other relevant information. Each column in your header row should be labeled.
There are a few things you can do as long as you recognize that your model making is now exploratory: 1) Go over the model again and see if you missed any theoretically significant paths/relationships. 2) Examine the standardized residual covariance matrix for indicators of poorly defined connections.
For more deep into the concept, this tutorial might be an asset, have a look: https://www.youtube.com/watch?v=bbmOMh1hDpA
Best Regards
Dr. Fatemeh Khozaei
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