# Questions tagged [partial-least-squares]

A class of linear methods for modeling the relationship between two groups of variables, X and Y. Includes PLS regression.

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### Theory behind partial least squares regression

Can anyone recommend a good exposition of the theory behind partial least squares regression (available online) for someone who understands SVD and PCA? I have looked at many sources online and have ...
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### Regression in $p>n$ setting: how to choose regularization method (Lasso, PLS, PCR, ridge)?

I am trying see whether to go for ridge regression, LASSO, principal component regression (PCR), or Partial Least Squares (PLS) in a situation where there are large number of variables / features ($p$)...
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### What is the connection between partial least squares, reduced rank regression, and principal component regression?

Are reduced rank regression and principal component regression just special cases of partial least squares? This tutorial (Page 6, "Comparison of Objectives") states that when we do partial least ...
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### PCA, LDA, CCA, and PLS

How are PCA, LDA, CCA, and PLS related? They all seem "spectral" and linear algebraic and very well understood (say 50+ years of theory built around them). They are used for very different things (PCA ...
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### Model assumptions of partial least squares (PLS) regression

I am trying to find information regarding the assumptions of PLS regression (single $y$). I am especially interested in a comparison of the assumptions of PLS with regards to those of OLS regression. ...
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### What is the difference between “loadings” and “correlation loadings” in PCA and PLS?

One common thing to do when doing Principal Component Analysis (PCA) is to plot two loadings against each other to investigate the relationships between the variables. In the paper accompanying the ...
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### The limit of “unit-variance” ridge regression estimator when $\lambda\to\infty$

Consider ridge regression with an additional constraint requiring that $\hat{\mathbf y}$ has unit sum of squares (equivalently, unit variance); if needed, one can assume that $\mathbf y$ has unit sum ...
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### Why do all the PLS components together explain only a part of the variance of the original data?

I have a dataset consisting of 10 variables. I ran partial least squares (PLS) to predict a single response variable by these 10 variables, extracted 10 PLS components, and then computed the variance ...
358 views

### Probabilistic models for partial least squares, reduced rank regression, and canonical correlation analysis?

This question results from the discussion following a previous question: What is the connection between partial least squares, reduced rank regression, and principal component regression? For ...
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### What is the relationship between PLS Regression / Discriminant Analysis (PLSR/PLS-DA) and Linear Regression

I'm interested in the problem of feature selection, and I came across PLS-DA, which seems to be a "hack" on PLSR (one more reference). PLSR relates a matrix X to a matrix Y, and PLS-DA relates a ...
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### Difference between PLS regression and PLS path modeling. Criticism of PLS

This question was asked here but no one gave a good answer. So I think it's a good idea to bring it up again and also I would like to add some more comments/questions. The first question is what is ...
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### Variable selection using cross-validated PLS model when permutation test shows lack of significance

I understand that the permutation test on PLS can help to detect overfitting of the PLS model. Usually if the p-value is greater than a criterion, say 0.05, it means that the model is overfitting and ...
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### Are PLS-DA and PLS-LDA the same?

Seems like a trivial question but one for which I can't seem to find an answer. Are PLS-DA (partial least squares discriminant analysis) and PLS-LDA (partial least squares followed by linear ...
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### PCA and PLS: testing variables for significance

I'm trying to understand the process for statistical testing for principal component analysis or partial least squares. Step 1. PCA: I feel that I have a not-terrible understanding of PCA: You find ...
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### Partial Least Squares regression - coefficients vs loadings

In partial least squares regression, what is the difference between the regression coefficients and the loadings for each independent variable in each component? Specifically, I understand in evety ...
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### Is each of the PCA or PLS components just one of the original variables?

I am confused about what a component is in PCA and PLS. Are the components just the original variables but not necessarily in the same order? For example, in PCA, if I had 8 variables in my data, ...
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### Is the PLS-DA approach for categorical variables the same as that used for PLS regression?

I understand the approach used for partial least squares for regression (PLS regression) where the PLS components are chosen such that the correlation between the scores of the PLS components of the ...
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### Choosing the number of PLSR components

I am trying to choose how many components to retain in my PLSR. My total variance explained for the response variable is only about 30%, and the first 2 components explain 99% of this. Intuitively I ...
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### What's the difference between logistic regression and PLS-DA?

I heard just recently about PLS-DA and I was wondering how it differs from multinomial logistic regression, since logistic regression can be also used for categorical dependent variables.