Constrained multiple linear regression with multiple dependent variables

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Daniel van den Berg 2022년 11월 22일
댓글: Daniel van den Berg 2022년 11월 23일
I am doing a calibration of my mass spectrometer in order to quantify the amount of product that is being produced in my electrochemical cell from the mass peaks. I have 9 mass peaks (X) and 8 chemical products (Y) that I want to fit together through multiple linear regression.
I have about 860 separate data points with 86 different concentration profiles that are linearly independent. I already successfully calibrated the reverse (linked the products to each of the mass peaks), but then when I take the inverse of this matrix I suffer from huge error propagation and I am not able to quantify my products anymore. However, when I want to do calibration to link my product concentrations (Y) to my mass peaks (X) using mvregress from MATLAB, I get a coefficient matrix (beta) that is optimized to the data, but contains values that are statistically not correct. I get T-stat values that are negative or <2.
Instead I would like to do a Multiple Linear Regression where I can put constraints on the values of beta (put them to 0 as I know there is no linear dependence of that mass peak on that product concentration). Is there a function I could use for this? I tried mvregress and LSQLIN but LSQLIN only takes a single dependent variable.
Furthermore, I have no background in data science or chemometrics, so if there is anything that I do wrong or if any you have any other suggestions, please let me know. It is much appreciated :)
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Daniel van den Berg 2022년 11월 23일
Thank you so much for your quick answer! However, in the documentation it says that the input d needs to be a vector, while my dependent variables are a matrix of multiple dependent variables. Also, when I try to implement it, I do get an error that "Matrix dimensions must agree."
Therefore, there must be something that I am doing wrong. If so, could you please be so kind to tell me where my error or wrongful assumption is?

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Matt J 2022년 11월 23일
편집: Matt J 2022년 11월 23일
lsqlin is applicable with,
N=size(beta,1);
C=kron(X.',eye(N));
d=Y(:);
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Daniel van den Berg 2022년 11월 23일

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the cyclist 2022년 11월 23일
I think mvregress does what you want. It has been ages since I've used it, but I wrote a pretty detailed answer that gave three examples of design matrices for regressions with multiple response variables. The syntax is tricky, but I think if you carefully understand my three examples, you will get the gist, and be able to figure out if it will work for your case.
I'm pretty sure you can enforce "structural" zeros for coefficients, although that answer does not have an example of it.

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