# Do I have to worry about structured/correlated data with dummy coding?

I am trying to decide between multi-state and binary encoding of a categorical variable, and am wondering what pitfalls I should be aware of.

This is the one that I am most concerned about. If I use multi-state coding, then the categorical variable would have eight possible values: "1", "2", "3", "4", "5", "6", "7", "8". If I turn each value into its own variable, then it can be dummy coded with "1" or "0".

My worry in doing this is that the values of the binary-coded variables will no longer be independent. That is, if the value for, say, variable 2 is "1", that will entail that the value for all the other variables is "0".

How do I work around this problem? Is it better to use multi-state coding?

• You cannot use multicode numeric encoding because it is categorical data and 1,2,3... are just labels. When you feed such categotival predictor to a program it internally encodes it into the dummy or other contrast variables. It is all right that dummies are not independent and that they correlate. – ttnphns Nov 16 '17 at 21:24
• Researchers do use multi-state encoding, though. The number of course are not actual integers but just symbols to distinguish the different categorical outcomes. – Namenlos Nov 16 '17 at 22:10
• You did not understand me. Everybody uses to keep the variable as you said, as multi-state (multinomial) categorical variable. The thing, however, is that this form cannot be used in algorithms such as, for example, ANOVA, with that variable as a predictor. When you input such a predictor in to a function doing ANOVA for you it, without saing it to you, internally recodes it into the set of dummy variables, in order to process and do estimation of the model. – ttnphns Nov 17 '17 at 5:14
• Outside of ANOVA, are there any differences between binary-coded variables and multinomial coding? – Namenlos Nov 17 '17 at 5:46