# 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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### 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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### 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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### What is the “partial” in partial least squares methods?

In partial least squares regression (PLSR) or partial least squares structural equation modelling (PLS-SEM), what does the term "partial" refer to?
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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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### 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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### 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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### Partial least squares regression in R: why is PLS on standardized data not equivalent to maximizing correlation?

I am very new in partial least squares (PLS) and I try to understand the output of the R function plsr() in the pls package. Let ...
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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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### 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 ...
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### Is it appropriate to perform feature selection before running Partial Least Square (PLS) regression?

I'm doing a series of PLS analysis to test the contribution of a set of environmental variables to the invertebrate community of a river. I am introducing into the model 23 environmental variables (2 ...
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### Is it possible to combine bayesian SEM with PLS SEM?

I have already read some books about both two structural equation models. It seems both SEMs are suitable to the situation with small observations and large variables. I assume to use combine both ...
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### When there is only one dependent variable, is partial least squares regression the same as principal component regression?

When there is only one response (dependent) variable, what is the advantage of partial least squares (PLS) regression over principal component regression (PCR)? My understanding is that PLS is only ...
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### How many components to use when doing a PLS regression?

I'm doing a PLS regression with SAS. My man-a asked me to do find the numbers of principal components for the dataset I'm working with through SAS. As I've never done that before, I'm confused on how ...
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### What is the difference between PCA and PLS-DA?

I read a paper Obesity changes the human gut mycobiome (2015) in which the authors used PLS-DA to look at the differences in their groups based on the microbiome of their gut. I am currently working ...
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### What variable importance criterion?

A student of mine developed a heuristic supervised machine learning algorithm for highly multivariate data. It seems to work pretty well, and once the model has been derived from the training data set,...
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### Magnitude and direction of relationship between predictors and dependent in regression

I'm doing partial least squares regression (PLSR), using the df below, to investigate how to predictors (catchment characteristics) influence the dependent (nitrogen in the river). In this data.frame, ...
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### RMSE behaviour during cross-validation of a PLS model - What does it mean?

In PLS regression, one of the approaches in selecting the number of components (Latent Variables, LV) is to perform cross-validation over a range of LV, and select the one with lower Root Mean Squared ...
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