In genetics one often uses data coming from SNP (Single Nucleotide Polymorphismes) which are genetic markers of which several (usually 2) versions (a.ka. alleles) exists in a given population. If you consider a span of such SNP there are often (pretty much always) redundancies and often only a handful of SNP are enough to explain the whole.
Let's say that in my sample I am considering a span 4 SNP of alleles A/T, T/C, A/G and A/G. Let's say that for such a span I only observed the following sequences : ATATA, TTGG & ACAA. Then I can only use two of those SNP to describe the exact same sequences : for exemple the first and second are enough.
To extract such SNP I am thinking of using LASSO logistic regression but I am now wondering if the "form" of the response variable(s) is important.
The variables I'm working with are all categorical with 2 categories and the response variable is the aggregate of all values taken by those variables. So if an individual takes the values A, T, C, G for the variables then the corresponding response value is ATCG.
I am trying to extract the smallest possible set of variable to predict the response variable using LASSO logistic regression.
The question is :
Is is equivalent to use a multivariate model where the response variables are duplicates of the independent variable and a multinomial model where the response variable is a categorical variable corresponding to the aggregate of the independant variable.
Hope I was clear enough, thanks !