# Can we estimate independent parameters when $p > n$?

I am using a ridge regression method to estimate the effect of SNPs (p = 10000) as random effect for a population of n=2000 individuals.

I know that when we estimate fixed effects, the number of independent variables is going to be determined by the n, it means that if we have an n = 2000, the maximum number of independent vectors to estimate will be 2000. But what happen when p variables are treated as random effect?

I come from the biology, so please let me know if any further explanation of my question is needed.

• I would guess it depends on the particulars of your software. but the number of variables will stay at p=10000. If say you had 10,000 variables that were exactly the same, then the ridge regression solution would be to use the same coefficient for each (ie 1/10,000 of coefficient using single variable) Jun 3, 2021 at 13:47
• Hi, thanks for the comment. Can you explain a bit in what way do you think it would depend on the software? Jun 3, 2021 at 14:25
• you could get errors - lack of convergence? etc depending on what variance-covariance structure you impose/is default.. see eg stats.stackexchange.com/questions/86958/… Jun 3, 2021 at 14:45