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This is just a theory question so no code or example is required I think. I want to know if there is a rule of thumb for what constitutes low frequency in MCA? Should the variable be eliminated? Could adjacent categories be amalgamated instead? And what consequences occur if the analysis goes ahead without taking action? Thanks

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  • $\begingroup$ Also, I have seen stats.stackexchange.com/questions/575818/…. I'm hoping for more detail on this. $\endgroup$
    – steve
    Commented Jan 18, 2023 at 13:11
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    $\begingroup$ Not so much expertise on MCA around here it seems... I don't think there's a rule of thumb. Generally the impact of low frequency categories will depend strongly on the behaviour of few observations, and may be much larger than you'd want it to be. I however expect that "how small is too small" depends on the overall dimension of the problem. If there are few other variables and categories, fewer observations will be needed. I'd use amalgamation if the resulting category makes sense in terms of its meaning. "Adjacent" implies you have ordinal variables, which may make it easier. $\endgroup$ Commented Jan 18, 2023 at 14:00
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    $\begingroup$ You could also do sensitivity analysis, i.e., compare solutions with and without the category in question (or with and without variable or amalgamation), and then try to understand from looking at the data whether the impact of the low frequency category is harmful and inappropriate. $\endgroup$ Commented Jan 18, 2023 at 14:02
  • $\begingroup$ Thanks Christian, all good suggestions. Yes MCA doesn't seem to be well-known compared to other techniques. $\endgroup$
    – steve
    Commented Jan 18, 2023 at 14:12
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    $\begingroup$ Just another comment: the webpage at STDHA (sthda.com/english/articles/…) which describes the use OF MCA through R (quite usefully) is the source for the suggestion that low frequency category variables should be dropped. But Costa et al (2013) (hindawi.com/journals/jar/2013/302163) says that MCA does not pre-require the kind of assumptions that Pearson and Fisher tests require. $\endgroup$
    – steve
    Commented Jan 18, 2023 at 17:34

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Le Roux and Rouanet (2005, p.216) suggest a 5% rule of thumb to identify low-frequency categories. What to do once you identified these low-frequency categories depends on the circumstances of your research. Le Roux and Rouanet mention three options: grouping, deletion, and a third method called "specific multiple correspondence analysis".

Low-frequency categories are influential in multiple correspondence analysis, and will often appear remotely from the center of the graph of variables (an exception to that may be when you have a variable with many different categories, hence with many low-frequency categories). In turn, other categories will be pulled toward the center of the graph. This may, or may not, be a desirable property for the purpose of your analysis.

For instance, if you're interested in analyzing these specific categories, it would make little sense to merge or delete them (except, maybe, for the purpose of some sensitivity analysis as suggested in the comment section). However, if these categories are of little interest in themselves compared to others, and can be meaningfully merged with another category, then it may be a good option.

Merging or deleting may have unexpected effects on other categories, so that's something to consider carefully relative to the research question you may have.

Besides merging categories or discarding observations, you can also use a method called "specific multiple correspondence analysis". Contrary to simple deletion, specific MCA won’t remove the observations belonging to these low-frequency categories, but it will take away the influence these categories have on the MCA.

Specific MCA might be appropriate if you have several low-frequency categories, otherwise its effect might be almost indistinguishable from merging categories or removing observations. (NB: this remark comes from simulations I ran. I'm confident in the results of those simulations, but as it's an empirical result and not a theoretical one, it may not apply in all circumstances.)

For a theoretical discussion of "specific MCA", see Le Roux and Rouanet (pp. 203-214). For software implementations, there are at least three R packages offering this method: soc.ca, GDAtools, and FactoMineR. I don't know if other languages or statistical software offer this method, but it may be a question for softwarerecs if you're interested.


Reference

Le Roux, B., & Rouanet, H. (2005). Geometric Data Analysis : From Correspondence Analysis to Structured Data Analysis. Springer Netherlands. https://doi.org/10.1007/1-4020-2236-0

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