Covariates vs factors

[indexo]

Hi,
What are the differences between covariates and factors?

Chapter 16 got me confused at page 47 of course notes. In the example, the linear predictor is made up of 3 covariates after aliasing but isn't it just 1 single factor here in the example, and aren't Xi's factors?

 

[padasala]

Factors are categorical variables (variables that are bucketed - Gender/make/model/etc) while covariates are ordinal variables aka continuous variables (such as age/sum insured/etc)... i've however, often noticed that the term covariates and factors are used interchangeably

I am assuming you're asking about the intrinsic aliasing question with age bands?

Often times, any software will represent factors as multiple variables rather than just one variable. It is easier for the software to use 4 indicator variables rather than 1 factor (with 4 different values). Thus, a factor (where there are 4 bands) will be split into 4 variables (ageband0-3, ageband4-7, ageband8-9 and ageband10+) for instance

Intrinsic aliasing will kick in here because the 4th variable used (ageband10+) could be linearly represented by 3 variables. Thus, it is enough for the model to have just 3 variables instead of 4 (since if you have 0 for the other three variables, it automatically means that the 4th variable is a 1).

 

[indexo]

Thanks!
In the above example, hence are covariates the Xi's in the linear predictor?

 

[Katherine Young]

All factors (whether they're continuous or categorical) are included in the linear predictor.

See page 14 of Chapter 16, which says:

"X is the design matrix of factors" and also says that the linear predictor is:\[\eta =X\beta +\xi \]Notice that the Core Reading uses the word 'factor' as a generic term to cover both categorical and continuous variables (at the top of page 14 again). This illustrates Padasala's answer to your original question. (Thanks Padasala for your excellent response.)