# 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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### PLS Regression on data with high number of zeros in dependent variable

I want to perform a PLS regression on a data set coming from spectral images (NIRS). My goal is to relate the different spectra to the total amount of a compound. To do this, I have a dataset ...
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### Meaning/interpretation of intercept_ in partial least squares

After using sklearn library for Partial Least Squares, I have doubts about the interpretation of the "intercept" of the model. As you can see in the code that follows, and its corresponding ...
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### How to determine the ideal number of components for PLSR using RMSE?

I would like to determine a non-visual, numeric based approach to determine the ideal number of components for my PLSR model. There are 10 components in the model for 1 target variable. If I simply ...
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### How to calculate cumulative Q2 in OPLS-DA

In SIMCA User Guide, $p.450$, cumulative $Q^2$ is calculated by: $$Q^2(\text{cum})=1−∏_{a=1}^{N_\text{comp}} \left( \frac{PRESS}{SS} \right)_a \tag{1}$$ where $∏_{a=1}^{N_\text{comp}}(PRESS/SS)_a$ ...
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### Is this image a good summary of the geometric representation of PLS?

I was wodnering if I could get feedback/criticism on an image I made that seeks to visually explain (in part) what PLS is. Orally I would say that we have three predictor variables ($x_1, x_2, x_3$) ...
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### Can I restrict the predicted values in Partial Least Squares model?

I'm using the R package pls, and I want to use the Partial Least Squares method to create a prediction of my data. The input I'm ...
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### Should I expect statistical analytical problems in this PLS-SEM structure?

Dear all great statisticians ... I am a doctoral student and my conceptual framework contains five variables. Among these variables are a mediator and a moderator. I am not sure of the validity of ...
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### How does one apply loadings of a PLSR model to a data point?

Problem: I am having difficulty understanding how I would apply the loadings of my latent variables to each individual observation in a dataset. Current understanding: I have a model that has used the ...
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### Is it advisable to use PLSR components in another linear equation?

I currently possess biological data from two groups (healthy vs disease) in the form of protein concentrations and I was interested in determining what the relationship was between these protein ...
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### Can the first latent variable of a PLSR model explain less variation in either X or Y compared to the second latent variable?

I currently have a n x m dataset as the X block and a n x 1 dataset as the Y block. I am using the ROPLS package in R, and I've noticed that there are times when R2Y is greater in the second latent ...
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### What can I do about model tuning parameter instability?

I am trying to determine the importance of watershed characteristics on the slope of the concentration-discharge relationship for several rivers. I am using partial least squares regression (plsr) ...
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### Why can't fit I fit a multivariate regression (OPLS) model when my variables are univariately (Pearson/Spearman) correlated?

I have a dataset of 950 lipids (X) and want to see if any are correlated with cognitive function (Y). When I try to fit an opls regression model, it errors and says that "No model was built ...
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### Help deciding the number of components for PLSDA using mixomics

I have a lipidomics dataset with more than 1800 features and 30 samples and I want to apply PLSDA. So, I used MixOmics to do this and here is my code: ...
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### Linear independency of Loading matrix of Partial Least Squares

I'm now studying for a partial least squares regression (PLS-R). Unlike PCA, it says that score vectors are orthogonal, while loadings are not. Does this mean that loading vectors (which are actually ...
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### What does the apostrophe mean with the explanation of how PLS works?

https://learnche.org/pid/latent-variable-modelling/projection-to-latent-structures/conceptual-mathematical-and-geometric-interpretation-of-pls What does the ' mean with t'? I wasn't 100% sure.
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### Variable selection based on PLS

What is the logical way to select the variables from PLS? Does choosing the feature from loadings and loading weights make sense? Loadings... Loading weights... Regression coefficients... Variable ...
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### Measuring features effect and importance in Partial Least Square (PLS) regression

Context: it is possible to assess features importance and effect for a model using model-independent scoring techniques such as Partial Dependence (PD) profile, Acculumated Local Effect (ALE) profile, ...
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### Using PLS to determine relative contributions of different drivers to the variability of a source?

I have a several drivers that are influencing the variability of a source. The drivers are not independent of one another, so I cannot use linear regression. Instead, I used Partial Least Squares (PLS)...
39 views

### Incorporating group charasteristics in multi-output regression setting

I'm working on a multi-output regression problem involving the prediction of over 80 numerical targets using an equivalent number of numerical features. I have achieved encouraging results with ...
453 views

### What test is most appropriate if you're interested in an interaction, but have more variables than samples

I would love to get some advice regarding the following please! I have a dataset (n = 99) that comprises of: Composite scores for 7 different cognitive domains Measures of 934 lipid species, which ...
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1 vote
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### Multiple linear regression with possibly non-independent explanatory variables

For a given household for which I have many years of historical data, I want to predict the home gas consumption (heating) with a few variables among: ...
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### Dependent and independent variable in PLS regression for sensor array data

I have been using PCA for the pattern recognition of my gas sensor array data. But recently decided to use PLS using OriginPro software. My sensor array data consists of responses coming from 8-10 ...
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### Obtaining Residual Sum of Squares from a large OLS problem using a naive sequential approach - why doesn't it work?

Suppose we have an OLS problem with a large number of predictors: $Y = X_1 + X_2 + \cdots + X_p$. I want to obtain its RSS. I don't need to know the regression coefficients or individual residuals, ...
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### Can I use clustering to compare diseases, after partial least squares correlation?

I have two datasets from patients with different diseases, which contain multiple measures of regional brain function and performance on different memory tasks. The memory tasks used in each dataset ...
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### Why am I getting negative components with my custom NIPALS algorithm

I've recently been learning about the Nonlinear Iterative Partial Least Squares (NIPALS) algorithm for computing the principal components of a dataset. I am trying to code a NIPALS class from scratch ...
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### How to interpret PLS-MGA’s results based on the significance of the corresponding group specific path coefficients

As a more general follow-up question to Elisa’s post on “[h]ow to interpret regression coefficients” when carrying out a PLS-structural-equation-modeling multigroup analysis (PLS-MGA), when comparing ...
1 vote
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### References for SIMPLS - Partial Least Squares

I am currently learning partial least squares analysis. I understand the idea, and the method I know to get PLS is NIPALS. Since I am currently writing a paper about this subject, I want to learn ...
1 vote
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### PLSR: trait vs spectroscopic data gives very low R2 on plsr model in R

here is the sample data. I have spectroscopy data as X-variables (from X1 to X80) and corresponding Y variable. I need to run plsr model in R using "pls" package. There are two sheets. In ...
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1 vote
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### Could I remove LOCs of an HOC to have the compositional invariance?

So, I am testing a theory, proposed in the literature, and I want to do a multigroup analysis on it. One of the HOCs(reflective) of the model has three LOCs(all reflective); when I run the tests on ...
1 vote
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### Reflective-formative higher-order construct path issue in PLS-SEM

I have a reflective-formative higher-order construct that combines seven reflective first-order constructs. I validated this higher-order construct in a study using the PLS-SEM method in which all ...
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### Preprocessing of spectroscopy data for PLSR: do I need to normalize the data for every wavelength?

I want to apply a partially least square regression on spectroscopy data to model a chemical content of my probe. So, every wavelength of the spectrum serves as one variable in the model. Doing some ...
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### Choosing Which latent variables to display and analyze

Attached is a plot of the R-squared for each additional latent variable (LV) included in a PLSR. When choosing which LVs to display on a biplot (and ultimately determining which factors best explain ...
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### high feature correlation but good OLS prediction

I have regression results where unconstrained OLS is near optimal - out of sample scores are almost the best when compared to some other constrained regression models. Although the ratio of number of ...
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### Reasoning behind variable importance in projection (VIP score)?

I have been using partial least squares regression to do latent variable modeling of a few data sets. Now I am wanting to look at variable importance but am getting stumped on the reasoning behind the ...
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### Is it sound to use PLS components in a model trained with the same response?

I have some high-dimensional spectral data I want to use in modeling plant productivity using a supervised model like random forest. I want to use the model for inference as well as for prediction in ...
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### Why does X @ coef_ + intercept_ does not equal Y_pred for sklearn PLSRegression?

I performed partial least squares regression using Python's sklearn.cross_decomposition.PLSRegression using the example data in the sklearn docs. I am surprised that X @ coef_ + intercept_ does not ...
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### In using PLS for feature selection, is directionality between X and Y necessarily implied?

In systems epidemiology such as in metabolomics, sometimes we are interested in identifying putative biomarkers of intake e.g., intake of a food item. So we analyse the metabolome to investigate ...
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### Is it possible to predict on new data using PLS SEM?

Using the seminr package in R, I have fitted a model based on PLS SEM with several exogenous (latent) variables and one endogenous latent variable (ELV) measured by ...
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### How to work with Proportion of variance explained in PLS Regression?

I have some very basic questions regarding PLS. I ran PLS using SPSS on small dataset. n=312, Dependent variable=1; Independent Variables=9. Here is the output of Proportion of Variance Explained. As ...
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### Regression in data with one group, having just zeros as outcome

I have a data set, consisting of positive and negative patients (virus infection). If the patient is negative, it has 0 as outcome (y), if it is positive it has a positive value, up to 100. The input (...
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### R-square vs. NFI?

I ran a path model (no latent variables) in smartPLS3. It's not a complicated model. But after the analysis was computed, I checked the model fit measures. R-squares are small (all of them < .3), ...
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### Transformation of data

I have a question regarding transformation of data. I have handled some data with both negative and positive elements by using the transformation: log(Y+1-min(Y)) which is all good. The problem is ...
1 vote
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### How to convert SMART-PLS structural coefficients from standardized (correlation) to unstandardized?

I need use smartPLS but i also have prediction purpose (coefficients should also act like b-coefficients of regression). How to do this in smartPLS, since all coefficients are standardized?
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### Partial covariance matrix after linear transformations

Let $X=(X_1,\ldots,X_n)$ and $Y=(Y_1,\ldots,Y_m)$ be two multivariate random variables. We denote with $\Sigma(X)$ the $n\times n$ covariance matrix $\text{cov}(X_i,X_j)$ and with $\Sigma(X,Y)$ the \$n\...
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### I don't completely understand the concept of PCA analysis [closed]

First of all, PCA analysis is not something I came across in my economics studies. But, recently, I wanted to make a PCA analysis of American GDP. I started to read about the fundamentals of PCA and ...
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### Partial Least Squares NIPALS Algorithm Question: How is w chosen to maximize cov(Xw, Y) [duplicate]

Recently I found a nice slideshow that explains PLS and the idea behind it pretty well. I think I understand the majority of the slides but I'm a bit confused with the first step of the NIPALS ...
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### Highly Correlated Datasets - Why and What Next?

I've got three datasets (of different biological data) that are highly correlated - such that if I use the typical findCorrelation from the ...
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### LDA followed by multiple PLS models OR PLS2 to include both the continuous dependent variable and the categorical variable

I have 1200 spectral Xvariables. I use PLS-LDA to reduce Xvariables and classify them in groups (contaminants). After that I need to quantify the "amount" of contaminant by PLS. First I ...
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