# Questions tagged [multicollinearity]

Situation when there is strong linear relationship among predictor variables, so that their correlation matrix becomes (almost) singular. This "ill condition" makes it hard to determine the unique role each of the predictors is playing: estimation problems arise and standard errors are increased. Bivariately very high correlated predictors are one example of multicollinearity.

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11 views

### What does concurvity really tell you for generalized additive models?

Though it is based on R programming but I also want to know the concept thus posting here. I simulated a data and run a binomial gam using mgcv. I generated 2 ...
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### Coefficient of highly correlated variables under LASSO and ridge

I have been presented with some interesting questions but unfortunately, I am struggling to provide satisfactory answers. The questions are as follows: How will the regression coefficients of two ...
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### Machine learning approach for inherent multicollinearity?

I have to perform the classification of a categorical variable using R. My model has 121 predictors (already filtered for possible importance) all of which are numeric. Many of these predictors are ...
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### Is it possible to add residuals as an explanatory variable to take away effects of correlated variables?

See I have a response variable $y$ and two explanatory variables $x$ and $z$, but there's a strong correlation between $x$ and $z$. Now I'm interested in how $x$ and $z$ influence the value of $y$ ...
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### How to deal with collinearity or concurvity between fixed effect variables and random effect variables?

My current work involves asking subjects from different groups to pronounce multiple words, and I am interested in understanding the relationship between word duration and groups. In R syntax, this ...
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### R - mlogit - "system is exactly singular" error

I'm trying to conduct a multinomial logistic regression that tests the likelihood that survey respondents will select one of three options, depending on characteristics of the option and of the ...
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### Regression with proportion values in the independent variables

I want to perform a regression where my independent variables all sum to 1. The independent variables are proportions of money invested in different categories. What I have done: When checking the ...
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### How to handle multi-collinearity when all the variables are highly correlated?

In my dataset, all the variables are highly correlated (correlation coefficient > 0.95). However, the correlation with the dependent variables is very low (<0.35). I checked the variation ...
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1 vote
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### Multicollinearity and Interaction Effects

I know similar questions were asked before. However, none of the existing answers help me with my problem: I have a gls model with y=B0+B1X1+B2X2+B3X1X2+e. The VIF value for X1 and the interaction ...
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### How does multicollinearity between some variables affect non-collinear ones?

In a multiple regression model, i.e. $y \sim x_1 + x_2 + x_3$, where $x_1$ and $x_2$ are collinear (e.g. present high correlation around 0.8), it is well known that many problems arise regarding ...
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### Efficient way to reduce VIF?

I'm working with an essentially linear unsupervised modeling approach which (predictably) has problems when there is (multi)-collinearity. To avoid this, I've written some code which removes variables ...
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### Using VIF (variance inflation factor) to reduce the data set and account for multicollinearity decreases the r2 and the performance of my model

Currently I am working on three models to predict the personality factors of subjects according to three data sets. All three data sets are exported features from video interviews, i.e. audio features,...
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### Should individual $R^2$ of a predictor always be greater than $\Delta R^2$ when removing that predictor from an expanded model?

I'm running some regressions with a set of somewhat correlated predictors. Let's call these predictors $x$, $y$ and $z$, and my dependent variable $d$. I'm focused on the effect of $x$ on $d$. I first ...
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### Geometric intuition for how ridge ($L_2$) regularization helps under multicollinearity

We have some nice posts (1, 2 and likely more) illustrating multicollinearity geometrically. Now, ridge regression ($L_2$ regularization) is known to be a remedy of multicollinearity. What is the ...
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### Multi-collinearity

I have a binary response variable (presence/absence) and four independent variables (min.temp, max.temp, precipitation and elevation. My scatter matrix is showing collinearity between 3 of the ...
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### What is the influence of multicolinearity on the likelihood ratio test?

I learned the two concepts separately and I try to find out how these concepts relate to each other. To illustrate the question introduce three models. The models establish a relation between age (AGE)...
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1 vote
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### How to account for multicollinearity in a partial F-Test?

I am trying to setup a model in R. I want to test if strategies picked by different agents have a joint significant effect on the outcome. My idea was to create a partial F-Test: ...
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48 views

### What test do I run to check multi-collinearity for not normal data?

I have 7 study subjects which I have grouped in 3 combinations ID1, ID2 and ID3. I have 15 behaviours which I have grouped into 5 combinations (Bgroup1, Bgroup2 etc..) Within each level, there are ...
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### Find Variance Inflation Coefficient in linear regression model with country fixed effects - R

I have the following model in R: ...
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### How can Variance Inflation Factor be used to measure multicollinearity in panel data / fixed effects model

I would like to check my data for multicollinearity. The dataset I have consists of panel data and I'm not sure how to go about it. If I were to calculate the variance inflation factor for the data as ...
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### Can I ignore high multicollinearity in a proportional binomial GLM from a fully factorial experimental design dataset?

I am running proportional binomial GLMs with 2 factors (Test Salinity and Region) but I am running into an issue with high multicollinearity. The reason for this is because this is a lab experiment ...
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### Lag variables on OLS after PCA (Principal Components Analysis)

I have about 60 macroeconomic and financial indicators; all of them stationary (logs and differencing), with monthly data for the last 25 years. I am trying to predict changes in a financial variable (...
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### Should Collinearity be resolved even when all coefficients of independent variables are significant in regression?

I've derived a regression model with continuous independent variables and got conefficients which are all significant in t-Test, but the multi collinearity exists. Do I have to resolve collinearity ...
1 vote
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### Are the assumptions of collinearity and no influential observations relevant when all predictor (independent) variables are categorical?

In order to run a simple linear model (e.g. using lm() function in R) I am under the impression that the following assumptions must be met: Normality of residuals Homoscedasticity No collinearity (...
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### Addressing multicollinearity when removing or imputing is not an option

I'm working on a project where the goal is to predict sales of certain generic products. There are many features, but social media metrics are causing me currently some headache. Social media metrics ...
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### Do AIC improvements make multicollinearity 'worth it'? (and an analagous question about GAM concurvity and fREML)

To what extent is it the case that I can ignore multicollinearity if adding in those terms improves my AIC? Frankly I'm a little rusty on my theory, but I've seen some people suggesting that AIC is a ... 24 views

### Rigorous book for multivariable concepts

I am looking for a rigorous book that clearly defines and explains terms such as ‘endogenous variable’, ‘exogenous variable’, ‘multicollinearity’, ‘heteroscedasticity’ and other such terms whose names ...
85 views

### High Adj. $R^2$ (by economic data standards) but insignificant p-values

I'd like to start by saying I'm not a statistician - I have stats education at the Masters level, but no specialization or advanced work experience. I'm currently trying to regress financial return ...
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1 vote
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### Regression model has very high const VIF value where as the other features have value between less than 4. Should I drop const?

I am a beginner in modelling. I have created a linear regression model using statsmodel and I see the const has VIF value around 124 where as the other features have value around 4. I already referred ...
1 vote
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### Boxplots: valid method for visualizing collinearity?

I recently heard one can detect collinearity between a factor (Species) and a continuous covariate (TL) simply by making a boxplot. If the plots don't overlap, there is evidence of collinearity. I'm ...
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### Interpretation of p-values in linear mixed model with collinearity

Imagine I am looking for the association between test score and whether eating candy (candy Yes or No) before taking the tests. I randomly select students from 8 random schools (A,B,C...H). Here is ...
161 views

### Adding a variable with no relationship with $Y$ increases $R^2$

I'm confused by something I've found by adding a variable with no relationship with a DV, using multiple regression with four predictors and one DV (Y). If I regress $Y$ onto $X_1,~ X_2,$ and $X_3$, ...
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### Interpreting causal effects in multiple linear regression models with multicollinearity: Which methods to use?

I have 10 independent variables (IV) that may predict my dependent variable. There's a lot of multicollinearity in my data (r between IVs is r=0.4 on average but not higher than r=0.8). I suspect that'...
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### polynomial orthogonal contrasts for ordinal independent variable with dummies for each level as well: collinearity problem?

If I have an ordered categorical variable as a predictor (independent) variable in a regression, can I also include the same variable as a nominal categorical variable, to prove that there is no ...
1 vote
119 views

### Multicollinearity for ordered logistic regression

How is multicollinearity calcuated for an ordered logistic regression if R^2 is not determined for this type of regression? Because the formula for vif says: 1/(1-R^2) In R the looking up ...
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446 views

### What is the R squared of a regression where none of the variables are collinear?

If a regression has 100 observations and 100 variables and none of them are collinear, what is the r squared? I know that it means that the full rank assumption is satisfied, so does this mean the r ...
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### Is this regression impossible because of full rank assumption violation? [duplicate]

If there are four variables each with five observations: X1 X2 X3 X4 5 3 0 2 0 9 -9 0 3 1 0 2 7 3 0 4 5 2 0 3 Why can't you regress a dependent ...
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49 views

### Two ways to get rid of multicollinearity

I have a couple of questions concerning multicollinearity in a linear regression model $Y=X \beta + \epsilon$. If the design matrix presents some multicollinearity i.e. $\det(X^TX) \approx 0$, we can ...
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### Singularity Issue in Two-part regression (Using Rstudio)

I am trying to fit a two-part model to my data. The project I am working on in my econometrics class is figuring out the total expenditure for people with asthma. I got my data from the MEPS Survey. ...
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1 vote
88 views

### Regression summary returning coefficients with value and standard error equal to zero

I'm creating a classifier using linear regression to classify images of hand-drawn digits from the MNIST dataset. I realize that linear regression is not the appropriate approach, but this is for a ...
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### Multicollinearity in a polynomial regression

I am trying to understand what kind of problems multicollinearity in a polynomial regression cause. While doing so, I came across this set of lecture notes: http://home.iitk.ac.in/~shalab/regression/...
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1 vote
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### Relative Importance Analysis for Non-negative Linear Regression

I have a set of 32 intercorrelated variables and a target. I hypothesised that these variables would linearly and positively contributed to the target, and hence a non-negative linear regression model ...
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### Variance inflation factors not equal to $C_{jj}$

I am following a book which states that the diagonal elements of $C = (X'X)^{-1}$ are called the variance inflation factors: $$VIF_j = C_{jj} = \frac{1}{1-R^2_j}$$ where $R^2_j$ is the coefficient ...
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### Does MDI (Mean Decrease Impurity) suffer from multicolinearity in Gradient Boosted Trees?

The two most popular Feature Importance measures for tree-based (ensemble) models like Random Forest (RF) and Gradient Boosted Trees (GBT) are the Mean Decrease Impurity (MDI) and Mean Decrease ...
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### ordinal logistic regression with multicollinearity among the independent continuous variables

I have an ordinal dependent variable, named A (small, medium, big) and independent continuous variables (C, C1, C2 and C3) highly correlated between each other. For example the sum of the variables C1,...
1 vote
108 views

### VIF after LASSO?

In have been working on a project along with other colleagues in which the dataset has almost 100 variables. The earlier approach was to use LASSO for subset selection and then use VIF to remove the &...
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### Multicollinearity and leave one out cross validation

I am comparing the relative performance of several models with the RMSE and LOOCV. One of them is based on multiple linear regression. I am interested in the final predictions, however, while ...
1 vote
119 views

### Pearson Correlation and Point-Biserial correlation

I have a question about correlation. My research has 8 independent variables out of which 3 are continuous variables and 5 are dichotomous/binary variables. I have to check multicollinearity before ...
1 vote
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### How to deal with multicollinearity in r [closed]

I am using metafor package for my meta-analysis. As part of the meta-analysis, I did a meta-regression analysis where I found out there is a multicollinearity issue ...
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