I have been given a database for statistical analysis in which almost all variables are nominal. No expert was involved in the design of the data collection, which is why it causes problems.
The most important variable is therefore a nominal variable with an incredible number of attributes. I would like to include it in regression analysis, but I don't know if there is any theoretical or technical limit to this.
I am also interested whether I can include the variable in point in a factor analysis.
I look forward to your replies, but I welcome any ideas on the possible use of this variable in various statistical analyses. I would be particularly grateful if you could also provide me with a link to some more accessible material.
Thank you in advance,
IStván
Wrt your regression on the nominal variable that yields many dummies one problem could be too many IVs for the model to work. I would just try it and see what happens. I suppose if you are trying to predict with it something like adaptive lasso maybe helpful. I've attached a paper that may be helpful. Best wishes David Booth
David, thank you very much indeed for your detailed answer. Best wishes, István Kósa
Factor analysis only makes sense for binary, ordinal, and continuous (metrical) variables, but not for strictly nominal variables because factor analysis implies that one or more continuous dimensions underlie the variables.
You did not mention the substantive goals / research questions to be addressed in this study. Therefore, it is difficult to make recommendations or suggestions for specific statistical procedures. In general, many of the procedures that are appropriate for nominal variables could potentially be used. If your goal is to summarize or reduce the information in the variables (you mentioned factor analysis), then latent class analysis (which works for nominal variables) may be an option. However, you may also run into problems with LCA when there is an extremely large number of categories and/or variables. Perhaps the number of categories of the variable in question could be reduced down to the most important (or most frequent) ones to avoid some of the complications associated with a large number of low-frequency categories.
You might want to look a this piece as it tackles similar issues Article Using Shrinkage in Multilevel Models to Understand Intersect...
and
Article Intersectionality and English Voting Behaviour: And Was Ther...
This is a suggestion for a technical fix (that is shrinkage) , but I would start by seeking out a theoretically justified classification with fewer categories e.g thousands of occupations classified into much fewer 'industries' or 'classes'
Dear Professor, thank you very much for your detailed answer and for links.
Best wishes,
István
Common maximum likelihood estimates could be prone to failure when a predictor variable or an outcome variable has many categories. To address such an issue, regularization by collapsing categories using the fused lasso is an approach that you might consider. Here is an article that reviews several methods and renders insight into which penalty is appropriate for clustering categories.
Tutz, G., & Gertheiss, J. (2016). Regularized regression for categorical data. Statistical Modelling, 16(3), 161–200. https://doi.org/10.1177/1471082X16642560
Good luck,
- Badges
- Science topic
- Similar topics
- Mathematics
- Statistics
- Sampling Design
- Sample Size