Dear Maria Tippler

I would like to ask you first: what is your final goal? what do you want to obtain with PLS? This will help us to answer your question. It is very important to know what is overfitting or not in your data result.

If you know what do you want, why dont you tried first Principal Component Analysis (PCA) to explorer your data and then, based on your goal focus on PLS regression (check here: http://www.statsoft.com/textbook/partial-least-squares )?

All the best, and I hope this help you

@ Edenio Olivares Diaz

Thank you for your message.

I have two goals. First, I want to see if the results from the above mentioned article replicate in my study using an older sample (i.e. 18-21 years old, instead of 12-14 years old). Second, I want to see how drug use influences these findings. The study that inspired me is using PLS correlation models, so I am using the same method. It inspired me because it provides insight on the combined influence between demographic/psychological factors and the brain's activity during a resting state scan.

From my understanding, the more demographic/psychological factors I add (i.e. different types of drug use), the more likely overfitting is possible in my model.

So, as previously (Sharkey et al. article posted above), the PLS correlation was performed using option 3 in the Baycrest software, with 10,000 permutations and 2000 bootstrapping samples. Permutation testing was achieved by randomly permuting some data in the rsfMRI connectivity matrix, and recalculating singular value decomposition results. The significance of the PLS analysis was determined by proportion of random singular values that exceed the original result.

My rather small sample size of 53 participants is a factor of consideration, so, as an extra step, I conducted stability analysis of the permutation testing. For this, 75% of the sample chosen at random, testing was repeated 100 times. In all the 100 cases, all the p's remained

Dear Maria Tippler

As I told you before, I recommend you to do principal component analysis (PCA) first. In this way, you are exploring your data and you will have an idea of your data. PCA, is a very good tools for what you want to do. But remember that it is an exploratory tool, and please standardized or normalized your data (you are using data of many dimensions: i.e. %, grams, Wavelength, etc) while doing PCA. With PCA all the variables will be reduce to principal components (PCA), such components are orthogonal and the first two will explain most of the variance of your data. This means that you can plot then and see how the characteristics of your data are related (exploratory).

There is a very good paper: " Principal component analysis " from Bro, Rasmus and Smilde, Age K (DOI: 10.1039/C3AY41907J). I strongly recommend it to you.

And the good of PCA is that it can be analyzed using free software such as Python or R, and there are lot of codes available online that make it easy to process.

After you have an idea of your data, another good chemometric technique is Multiple Linear Regression (MLR). This technique is good for obtain the regression of Y variable related to multiple X variables. However, those X variable must be few than the number of samples and each of them must be independent variables for obtaining a stable MLR output.

But, please first of all carry out PCA.

I hope that your understand my very summarized explanation,

Wish you all the best,