# Context (optional)

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.

# Question

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 !

• I don't understand how your response variable works. So is it 1 if it is ACTG and 0 otherwise? What about in your multivariate case? What are other possible outputs? – rep_ho Oct 1 '16 at 16:12
• It's unclear what you are asking, but if you are asking how to find a minimal spanning set of a vector space, you want a QR or SVD decomposition. See ncbi.nlm.nih.gov/pmc/articles/PMC1182114 for the application to haplotype tagging with SNPs. – Andrew M Oct 3 '16 at 22:58
• @rep_ho No the response variable is a categorical variable with as much categories as there are unique sequences (so ACTG is 1 but there is also CCGT, AGTT, and so on). The multinomial case describes the same sequences but each 'letter' is a variable so I got n categorical variables (with only 2 categories) where n is the number of genetic markers – Riff Oct 4 '16 at 7:52
• @AndrewM I know of that method but I not only want to know the tagSNP set, I also want to know the allelic sequence specific to each haplotype. – Riff Oct 4 '16 at 7:54
• It sounds more like multilabe problem then – rep_ho Oct 4 '16 at 9:30