# Lasso Regression to get most important factors?

I'd just read about Lasso-regression and would like to ask if the following approach would correct from a statistical point of view.

So given I've a list of genes and would like to observe their change over time. Can I use Lasso-regression to "filter" for the genes, which have the most impact during the observed time-period? Data would look similar than in the Table below.

+--------+-----+-----+----+-----+
| Years: | 1   | 2   | .. | 10  |
+--------+-----+-----+----+-----+
| Gene 1 | 0.2 | 0.3 |    | 0.7 |
+--------+-----+-----+----+-----+
| Gene 2 | 0.4 | 0.9 |    | 0.9 |
+--------+-----+-----+----+-----+
| ..     |     |     |    |     |
+--------+-----+-----+----+-----+


How do you define "impact" in this context? If you want to use regression you should have a dependent variable. Otherwise, if you just want to tell which genes change the most over time you can just compute the variance.

• Hi, thank you for your answer! You're correct that I want to filter for the genes, which change the most over time! I thought I should use regression, bc my idea was to approach the problem like gene-expression values are dependent on time. May 14, 2021 at 14:49
• If I understand correctly, you'd like to be confident about which genes are increasing expression over time. I'd conduct a simple linear regression for each gene, with time as an independent variable and its expression as a dependent variable, and sort genes by either 1) the coefficient size, i.e. a large positive coefficient means the gene expression has increased a lot over time, or 2) using the Pearson correlation coefficient, where values closest to +1 mean that time explains most of the variation in gene expression and therefore you can be very confident that it increases with time. May 14, 2021 at 15:23
• Nice. Thank you!! I've already done that but didn't know how to set a threshold so I looked for further methods. But, if that's the way to go I prob just continue with the LR approach. May 14, 2021 at 18:49
• If you want a more formal threshold you can do a linear regression and compute a confidence interval around the coefficient. You can discard genes whose confidence interval includes zero or are strictly negative. If you find an answer or comment useful don't forget to leave an upvote :) May 14, 2021 at 22:03
• Schuler: I'll upvote u as soon as I reach 15 credit-score :) May 15, 2021 at 11:38

You mentioned that you would like to identify which genes have the most impact. You need to have a response variable that has a relationship with your explanatory variables, which are genes in this case, to fit a Lasso-regression. Lasso will allow you to do variables selection in your model, and study which genes have the most effects on your response. So, in other words, Lasso can be also used as for dimension reduction in high dimensional data.

• Just keep in mind that the probability that lasso will select the right variables is very near zero. The data very seldom have sufficient information content for making these choices accurately. That is even more true when there are collinearities among features. May 13, 2021 at 21:37
• Thank to the both of you. I just recently slided into the field of data-analysis so please forgive me for my naive knowledge. As @Nick stated my intention was some kind of dimension-reduction as I'd like to get the most impactful sites from ~1M entries of CpG sites. (I wrote genes in my example as it would probably resonate with more ppl). May 14, 2021 at 14:56
• @FrankHarrell Would you mind to please explain me what the pitfalls of my lasso approach would be in more detail? May 14, 2021 at 14:57
• Please see fharrell.com/talk/stratos19 May 15, 2021 at 19:18
• Thanks Frank for the additional details. By the way, I came across your website a few weeks ago. I really appreciate you sharing your insights through your articles and posts.
– Nick
May 16, 2021 at 15:47