I have just read a paper in which the authors performed a meta-analysis to extract correlation coefficients (specifically between five personality variables and emotional intelligence). They then used confirmatory factor analysis to test if all the variables involved formed a higher-order factor (specifically a general factor of personality correlated with EI). The total number of samples was 128; these were also broken down into subsamples, as there are various measures of EI (k ranged from 18 to 45). I was wondering if it is valid to use CFA in this way, particularly with such small subsamples? Specifically, one of the analyses they reported in detail was k = 22 and there were six variables with fifteen inter-correlations in the analysis. Would their results be meaningful, or are they over-interpreting the data?
In a meta-analysis, $k$ typically refers to the number of correlation coefficients that were meta-analyzed. An aggregated coefficient could therefore be based on thousands of individual observations. So, no, without knowing more about this particular paper, there is nothing here to indicate problems with this.
By the way, what the authors are doing falls under the general label of "meta-analytic structural equation modeling" (MASEM).