I would say the best approach is to not categorize because you loose information, and any cut off values are arbitrary. So unless you absolutely have to trichotomize your scores I would recommend keeping the scores continuous.

I agree with Christian Geiser . Unless there is some compelling reason to change your variable into categories, it is usually more advantageous to leave the variable as numeric. ... Another approach to categorization is to look at the quantiles of the observations. That is, the top 33% of observations are "high" and the lowest 33% are "low". The advantage with this method is that you will have equal number of observations in each group. This is similar to a "median split".

Hello Shanjida Chowdhury. I also agree with Christian Geiser. If you describe your variables and your research question(s), someone may be able to suggest an approach that does not require categorizing. HTH.

Agree with points above re WHY, but IF you want to here is the code for your method and Sal Mangiafico alternative. You don't say the software you are using so I'll use R which is free and widely used (and readable and easily translated).

cut(x,c(min(x),2/3*min(x)+max(x)/3,min(x)/3 +

2/3*max(x),max(x)),include.lowest=TRUE)

cut(x,quantile(x,probs=seq(0,1,length=4)),include.lowest=TRUE)

the first can be written as

cut(x,3)

because that is what its default does (though I would have expected Salvatore's suggestion to be its default). I started with the other codes since if you are using this in another software those show what is happening more clearly.

I should add, if you believe your factor scores are best measured by groups, you should explore this with taxometric approaches (e.g., Meehl) to see if the data show this, or if you want categories without really worry what the data suggest, latent profile modeling or one of several clustering/classification algos could be used. You should not use a factor analysis to extract continuous factor scores and then categorize.

Daniel Wright I want to create a women's empowerment index. Already I have validated my item CFA followed by EFA. Now I want to categorize factor scores,to know more about the situation that how many women are in the low empowerment phase, moderate empowerment phase, and high empowerment phase. As it is my thesis work, I would not like to use any question-arise method. I have already gone through all of the above suggestions, nobody supports categorizing continuous variables. One other way I have in my mind, After validation through CFA, instead of using a factor score if I go back to my original response, and create a mean score after combining all then using percentile. Can I do this? I am using SPSS and STATA. Thanks.

Bruce Weaver Sal Mangiafico Christian Geiser Thanks a lot for your valuable advice. I want to create a women's empowerment index. Already I have validated my item CFA followed by EFA. Now I want to categorize factor scores, to know more about the situation that how many women are in the low empowerment phase, moderate empowerment phase, and high empowerment phase. As it is my thesis work, I would not like to use any question-arise method. Literally, all of you suggest not to categorize. Now I have to rethink. If you have any alternative grouping procedures for continuous variables please suggest me. Thanks.

Yes, you can categorize the way you have stated. However, you should also check how data falls into those categories. What I mean is, if you see none of the data falls into the category "High", then you should think of categorizing the variable in a different way.

Using the means has the advantage that it is easy for others to use but makes additional assumptions, and if these conditions are not true the measurement becomes worse. It wasn't clear to me what you meant by "validated my item CFA followed by EFA." I haven't used SPSS or STATA for several years, so I will leave it to the other people tagged to supply details wrt those packages.

It was not clear to me either what it mean to validate the items via CFA and then follow with EFA. I thought it was more customary to use EFA to develop a model, then CFA to test it. In any case, Stata has commands for carrying out both EFA and CFA (the -sem- command for the latter). SPSS has a command for EFA, but note that the default settings use PCA followed by Varimax rotation, which is not the approach one should use if there is interest in latent variables (and if the latent variables can be correlated with each other)--see the "Tom Swift" article linked below. SPSS per se has no command for carrying out CFA. SPSS users often buy the additional package AMOS for that.

• http://quantpsy.org/pubs/preacher_maccallum_2003.pdf
• https://www.stata.com/features/structural-equation-modeling/
• https://www.stata.com/capabilities/factor-analysis/
• https://www.ibm.com/docs/en/spss-statistics/28.0.0?topic=reference-factor

Bruce Weaver Thanks a lot

Faruque As Sunny Please provide some references....

Totally agree with Salvatore S. Mangiafico. In my opinion, it is a good option to create categories for your index based on quantiles, instead of creating categories arbitrarily. The categories will facilitate communication with end users, especially policy makers.

Please check the links below:

Converting-continuous-to-categorical-variable:

1. https://datascience.stackexchange.com/questions/45997/converting-continuous-to-categorical-variable

2.https://web.ma.utexas.edu/users/mks/statmistakes/dividingcontinuousintocategories.html

Perform a factor analysis with categorical or categorical and continuous variables:

1. https://stats.oarc.ucla.edu/stata/faq/how-can-i-perform-a-factor-analysis-with-categorical-or-categorical-and-continuous-variables/

2. https://stats.oarc.ucla.edu/stata/output/factor-analysis/

3. http://dwoll.de/rexrepos/posts/multFApoly.html

Also check the post:

https://www.researchgate.net/post/Is_it_possible_to_perform_factor_analysis_on_categorical_data

Shanjida Chowdhury I suppose there is no previously defined such index, or any gold standard. Nevertheless, if there are some indices which measure similar concepts and whose scores are available to you, then you may somehow make use of them comparing their scores with yours.

Faruque As Sunny thanks a lot

Mehmet Sinan Iyisoy thanks

Shanjida Chowdhury you are welcome.