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There was an extended discussion on this list about fit indices and model testing.
From this discussion I memorized that chi-square test is the first and most important test, and everybody seem to agree with that (although there are some disagreement regarding usefulness of other fit indices).
Please help me interpret the following sentence:
"The chi-square test again did not indicate an especially good fit in any of the countries [chi-square p-value=0 for all the models]. However, the other indices that were used indicated a good fit between model and data. CFI was ranging from 0.977 to 0.997 and RMSEA from 0.024 to 0.062. As the indices of model fit did not differ much between the measurement model and the structural model, the latter can be considered to offer a good representation of relationships between variables." ( Myrberg & Rosén (2008): A path model with mediating factors of parents' education on students' reading achievement in seven countries, Educational Research and Evaluation, 14:6, 507-520 http://dx.doi.org/10.1080/13803610802576742
Someone outside this list explained to me that In large samples p-values are often significant, expecially when sample sizes reach the thousands -- then everything becomes significant. In the paper I mention sample sized are definitely very large , from 3500 to 6000.
I wonder why nobody in the discussion on the chi-square and other fit indices never mentioned the relationship between p-values and sample size?
And does it mean that SEM is not applicable to very large samples?
Indeed, most of the sample sizes people mention when asking practical questions on this list are in the range of 100-400.
Could anyone give a reference where SEM was used on a very large sample (several thousands)?