I have a dichotomic 55 items (0,1) in acheivement test in mathematics , can I do confirmatory F.A for validity ??? if yes , Do I do it according to Bloom taxonomy or the cognitive fields of mathematics??? I need reference. thanks.
Whether or not you will 'need' Bloom's taxonomy depends on what the nature of the purported structure is for the 55-item measure that you are trying to confirm. It is that structure that is the key (for a CFA).
I prepared an achievement test in mathematics at the end of primary school students, following the necessary scientific steps: content analysis, specification table ... The number of items was 65 , and with the stages of achieving psychometric characteristics according to the two theories (CTT& IRT), the number of items became 5 5 according to the exploratory FA steps. I came up with 5 factors by following the parallel analysis, so I wanted to check another way to provide evidence of VALIDITY by CFA.. Here is the problem: Is the theoretical structure is the areas of the curriculum that I used to construct the test, or levels of knowledge according to Bloom taxonomy (knowing that I chose only three levels).Following confirmatory analysis, I found that some items go beyond the correct one.- Either the achievement test that involves two responses zero and one or yes or no, is not likely to analyze the factor exploratory and confirmatory ???????- Either there are conditions I do not know I have encountered the problem of the right one in the loading of items I mean standard scores ....Note that good psychometric properties are found in the Rash model. So do I avoid the CFA or the problem IS in the dichotomic items.??
By using the EFA to identify 5 factors, you've let the observed relationships in the data govern the structure. If that structure happens to map well onto some theoretical or rational organization (e.g., levels of the cognitive domain in the Bloom et al. taxonomy; or content/operation strata of the table of specifications), good. If not, then you may have to think carefully about what the structure might truly represent.
If your research goal was to create a measure that maps onto an a priori structure, then the CFA would, of course, be based on that structure. If your research goal was to build a single measure that dependably sorts the items/tasks and examinees on a common scale, then IRT would be the preferred approach (though I would certainly look carefully at the Rasch assumption of equal item discriminations as well as unidimensionality--given that your EFA apparently identifies multiple factors).
It isn't an issue of dichotomous items (though tetrachoric/polychoric correlations are a better choice here than the usual Pearson correlations).