# Tagged Questions

Partial Least Squares (PLS) is a class of linear methods for modeling the relationship between two groups of variables, X and Y. Includes PLS regression.

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### Spatial and temporal variation in Partial Least Squares analysis

I want to explore and model temporal variation in responses from several fixed areas ("sites") based on climate variation and also how the characteristics of the sites influence the responses. I have ...
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### Contradictory p-value and confidence interval in permutation test

I am using the MICOM procedure to test for measurement invariance among groups in PLS SEM modelling [1]. This procedure consists of 3 steps, where in step 3 one tests for equality of composite means ...
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### Cross-validation scheme used in the Introduction to Statistical Learning, Chapter 6, Lab 3

I've been really enjoying the Introduction to Statistical Learning textbook so far, and I'm currently working my way through chapter 6. I realize that I am very confused by the process used in lab 3 ...
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### How to compute percent of variance explained in X and Y for each component of a PLSR?

I am not a mathematician and my question is probably trivial but I did not manage to find an answer on the web. I need to compute the percent of variance explained (eigenvalues?) in X and Y for each ...
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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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### plots of covariance with jackknifed confidence intervals in OPLS

The SIMCA-P software is able to produce plots of covariances with jackknifed confidence intervals for OPLSDA models. Is there any R package implementing the same feature? Or is there other means of ...
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### How would Y-aware PCA for binaries look?

I recently stumbled upon Y-aware PCA in the blog of win-vector. They describe how PCA can be adjusted not to explain variation in $X$ but covariation of $X$ and $Y$. This is explained for the case ...
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### Prediction of independent data with PLS

In Matlab's plsregress function and in many other statistic toolboxes, there is a BETA vector returned that simplyfies the regression problem to(excluding the ...
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### Better Predictive Model?

I'm running a bunch of different models trying to find one that is best at predicting using a Validation set and Root Average Squared Error(RASE) calculated from residuals as my main criteria. My data ...
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### can I perform plsreg2 with inverse probability weighting?

I am trying to perform partial least square (pls) with more than one response, so I use plsreg2 in the plsdepot package in r. But plsreg2 does not include a "weights" argument, so I wonder is it ...
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### orthogonal latent trend

Assume I have 2 explanatory variables (or factors) X which explain y. I want to extract a trend (and maybe seasonality) from y which is/are orthogonal to X. Is there are a way to do this? Can PLS do ...
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### If there is only one variable in Y, does the first PLS component go in the exact same direction?

In partial least squares (PLS), I have multiple variables in X and only one variable in Y. If I only choose one PLS component to use for the PLS model, can I assume that this PLS component is in the ...
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### 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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### Diagnostics for PLSR?

I am trying to apply sPLS2 type pf regression my matrix y has a set of clinical variables and matrix X has some gene data. I am using mixOmics package in R. My question is how to decide that my ...
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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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### My predictors have strong collinearities, yet linear regression performs as good as partial least squares. Why?

I am trying to predict a single response from twelve explanatory variables. There exist strong correlations between my variables. The correlation matrix looks as follows, and the data have a ...
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### High classification errors in PLS-DA

I'm doing PLS-DA on mass spectrometry data, trying to predict whether the sample was subject to some intervention or not. I'm using simple cross validation where I take 20% of my samples at random, ...
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### Do I have multicollinearity? [duplicate]

I am examining the impact of 7 IVs on one DV using regression anaysis. Some of the IVs are significantly correlated with each other, which is consistent with theory. While the single OLS regression ...
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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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### How exactly is dependent variable expressed in terms of independent variables using Partial Least Square Regression? [duplicate]

I understand the working of NIPALS algorithm but while doing the regression using PLS how exactly the relation between known and unknown is established using Principle Component Analysis. The idea is ...
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### interpreting predictions of linear regression in multi-group classification problem

I am attempting multi-group classification with linear regression model. As I have five groups the response is five-dimensional and so is the prediction for any particular observation. I understand ...
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### Can I use ANOVA to compare two partial least square model?

When comparing two linear regression, we could use ANOVA as below. anova(model1,model2,test="Chisq") But when comparing two partial least square model, I could ...
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### How to determine statistical significance of individual terms in PLS regression?

I am currently using partial least square (PLS) in my analysis, with interaction term in the regression. My question is how could I determine the significance of the interaction term, given that the ...
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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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### How to use PCA in regression?

I'm currently reading in the Applied Predictive Modeling book about PCA for dimensionality reduction. I've read the following: If the predictive relationship between the predictors and response is ...
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### Use observation-weighted optimisation metric in PLS machine learning

I would like to build a model that trains a PLS algorithm to minimise a weighted sum of square errors (where the weights are proportional to the magnitude of the true y observation). The reason for ...
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### Rotation in (Univariate) Partial Least Squares Regression

according to a not so recent paper (http://www.sciencedirect.com/science/article/pii/S0167947303003049), it is a good idea to Varimax-rotate the factors that have emerged by Partial Least Squares. ...
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### PLS using a kernel matrix

I would like to use a kernel matrix generated with a custom kernel function to fit a PLS-DA model (I am thinking of caret's PLS-DA at the moment), with only one binary response variable in the Y block....
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### Examining PLS Results in R

I would like to know how I can go about examining the results of a partial least squares regression. Specifically, I am interested to know what the coefficient is for each component, and what the ...
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### Problems with implementing cross-validation for OLS, PLSR and PCR

I am new to regression methods. I am creating Multiple Linear Regression, Partial Least Squares Regression and Principal Component Regression models for my dataset, and I am a bit confused with the ...
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### How to pre-process data for partial least square PLS regression in R?

I have a data frame that is consisted of 20 observations and 35 variables. I want to prepare the data for partial least square regression PLS in R. Many authors suggest: 1)Check whether the ...
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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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### How to pick the best model with cross validation?

Based on my understanding the leave one out cross validation is to hold a sample out as the test set and fit a model with remaining data and then calculate the error of prediction of the test sample ...
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### Dichotomous Variables Problem

I'm currently in the process of making research about Investments. And I bumped with a problem of using variables in PLS. So would very much appreciate your advises, because I am in a dead-end for now....
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### Can we apply PLSR with only a few variables?

I have 110 samples for predicting a dependent variable based on 16 independent variables: Analysed corrlation martrix and removed all the variables that were not correlated with the dependet ...
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### Combining PCR/PLSR components with some other predictors in one regression model

I am investigating the value of adding regressors to a base model ('restricted model') by applying different transformation methods to the additional regressors. My restricted model can be denoted as ...
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### Heteroscedasticity in machine learning predictions

I am using a machine learning method (PLS) to predict a continuous variable, which currently does a pretty good job, with reasonable RMSE etc. However, the residuals exhibit heteroscedasticity, where ...
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### What is partial least squares (PLS) regression and how is it different from OLS? [duplicate]

Assume we have a simple linear regression model expressed as $$y= X \beta + \epsilon,$$ where $y$ is a vector of size $n \times 1$, $X$ is a matrix of size $n \times p$, $\beta$ is the regression ...
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### PLS with more variables than data points

Does it make sense to run partial least squares (PLS) on a data set that has many more columns (variables) than it has rows (data points)? I am using plsr in R. I ...
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### Using predict with PCR in R [closed]

I'm trying to follow the documentation on the pcr method in R So I do the following ...
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### When do all PLS components together explain only part of the variance of the original data?

According to this question and answer, the sum of variances of all partial least squares (PLS) components is normally less than 100%: Why do all the PLS components together explain only a part of the ...
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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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### What does 'iteration limit reached without convergence' mean in SAS Proc PLS

I receive the warning 'iteration limit reached without convergence' when using PROC PLS in SAS. What does this warning mean? I have 1,540 observations, 900 dependent variables and 600 independent ...
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### Measurement model of my data is perfect but Structure model very poor? why?

First order reflective Measurement model is perfect on all psychomterics (AVE, CR,), but when it comes to structural paths majority of them are insignificant,AND EVEN r^2 is below .50 why so?
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### PLS identify only peaks not troughs, and ignore certain region

I recorded a few Raman spectra for varying concentration of a substance. I processed the data in R and these are my steps: Remove baseline using baseline.corr with lambda=1e3 and p=0.01 Run PLSR on (...
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### How to analyze generated components from partial least squares in SAS

I am using PROC PLS in SAS with multiple independent variables and multiple dependent variables. I would like to know how my independent variables are contributing to the scores for the first couple ...
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### How to choose between different options in partial least square regression?

There seem to be several methods of performing partial least square regression. For example in pls pacakge in R, following are available: ...