# 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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### Multicollinearity and categorical predictor with three levels

If I have a continuous Dependent Variable and two Independent Variables, where one is categorical with three levels and the other is continuous, what assumptions do I need to check for multiple ...
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### Does a decrease in standard error from one model to another suggest collinearity?

Say I have model 1 and model 2. y1 = b0 + b1x1 + u y2 = b0 + b1x1 + b2x2 + u If there is an increase in the standard error of x1 from model 1 to model 2, does this suggest collinearity between the ...
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### Multicollinearity? Non-significant multiple-linear regression, highly correlated regressors but low variance inflation factor

I have a small sample (30 obs) and 4 independent variables, 3 of which are significantly correlated to each other. I have tried to run the simple linear regression on each of them separately and it ...
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### Multicollinearity and interaction terms

My dataset has 2734 observations (but in some speficitations, that number reduces to 1280). I also have interaction terms (in some specifications, even fourth-order terms). As far as I know, ...
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### How multicolinearity affect the prediction

In a linear regression model, if some of the predictors are correlated, then in the output of most software, you will see very large p-value in those coefficients and very high standard error. My ...
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### Elastic net is being used in genome wide analysis. Similar approach would work for survey analysis?

I'm approaching the elastic net procedure for genome wide analysis (GWAS) because it allows for feature selection, groups detection and improved validity. It's a powerful technique when you have many ...
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### How seriously should I consider the effects of multicollinearity in my regression model?

I have a model y ~ x + z and the correlation between x and z is 0.2. This is only weakly positive. So, how seriously should I consider the effects of ...
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### Change in order of predictors breaks logistic model estimation (glm, R)

I am fitting a binomial logistic regression in R using glm. By chance, I have found out that if I change the order of my predictor variables, glm fails to estimate the model. The message I get is ...
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### VIF for generalized linear model

Is the variance inflation factor useful for GLM models. Below example shows OLS is showing VIF>5, but GLM lower. GLM shows instability in the coefficients between train and test set. ...
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### Multicollnearity in backward selection approach

When I build my most parsimonious model using a backward selection approach, do I have to worry about multicollinearity. I mean, do I first check for multicollnearity and drop the variables which has ...
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### Multiple regression - how to deal with mixed linear and non-linear variables

Say I have a bunch of explanatory variables to predict a continuous independent variable. Below, a simple toy example: I think it would be easiest to do a log-log transform and proceed with linear ...
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### Linear regression model mistakenly gives $R^2$ equal to 1

I'm using R to create a linear regression model from survey data about public sentiment for a new technology. I am encountering a problem where the addition of a new explanatory variable raises the ...
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### transform variables then check for collinearity or other way round?

I was planning to construct a model with around 19 explanatory variables and one response variable. I have some confusion on following thing: If transformation is required in case of explanatory ...
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### Multiple regression with correlated variables

I am trying to do multiple regression analysis of a continuous health variable (yval) keeping age, gender, height (cm), weight (kg) and waist (cm) as predictor variables for a database of about 7000 ...
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### What to make of countervailing spatial regression coefficients?

I am running regressions across a country's counties (N about 300). I divide the country in two regions A and B to control for potential unobservables. My explanatory variable varies at the county ...
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### Principal Component Regression with an additional factor

I am looking to tease out the significance and contribution of a particular variable to 2 different continuous responses. I have 7 continuous variables I know to be influential on the two responses (...
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### Three percentage indicators into one (or two measures) in regression moder

I am working with a data set resembling the extract below: ...
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### Invertibility of $X^TX$ with severe multicollinearity in regression

I am studying about multicollinearity in regression and in the book it says, "if there is severe (but not perfect) multicollinearity, two or more predictor variables are highly correlated, so $X^TX$ ...
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### Collinearity and Linear Discriminant Analysis

I trying to conduct linear discriminant analysis using the lda package and I keep getting a warning message saying that the variables are collinear. I want to pinpoint and remove the redundant ...
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### Collinearity in multivariate regression with huge amounts of data

Take the following example: I wish to predict physical performance as a function of height and weight. I already know weight negatively affects performance. Height also negatively affects performance,...
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### Should we test error terms for auto correlation or multicollinearity

I understand the basic difference in definition between multicollinearity and autocorrelation. I.e multicollinearity describes a linear relationship between whereas autocorrelation describes ...
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### Linear Regression - Number of Predictors - Negative Weight [duplicate]

I am trying to prep myself for data science interview & I saw the following question on a forum You have several variables that are positively correlated with your response, and you think ...
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### Variance Inflation Factor less than 1 in ridge regression?

I was trying to determine the biasing constant in ridge regression when I came across a phenomenon that seems quite puzzling, to me at least. I let the GCV criterion choose a constant for me and then ...
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### Predictor variables sum up to 1 but not necessarily correlated - is it a problem? [closed]

I am trying to fit hierarchical mixture model (using ML and MCMC, but this shouldn't matter) where the linear predictor part contains 17 independent variables. These are habitat variables: for each ...
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### Principal component regression on polynomial terms

One of the data sets I am working upon had 3 variables which were having almost 100% correlation among themselves. Since I am learning regression modelling I thought I'll do principal component ...
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### Should fixed effect dummies be included in multicollinearity diagnostics (VIF calculations) for regression?

I am currently in the progress of performing multicollinearity diagnostics for a logistic regression model using tolerance and VIF calculations based on recommendations in Allison (2012) (Logistic ...
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### Why do we use the term multicollinearity, when the vectors representing two variables are never truly collinear?

When two vectors $a$ and $b$ are collinear, then $a = xb$, (where $x$ is a scalar) so in linear algebra, collinearity is a narrowly and clearly defined (and binary) concept. Two vectors -- in my ...
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### Variable selection multiple data types

I'm working on a data set containing 45 predictors that cover metric, ordinal and nominal variables. Aiming to finally build a model, which explains the interacting effect of a set of predictor ...
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### what if response variable is 'yes or no' in R?

How to analyze above the data to predict the probability that people have disease with a model? Factors thought to influence infection include city, age, and diet. BUT, I don't know how to do because ...
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### Logistic principal component regression where PCs are correlated with an additional binary predictor

My scenario is this: I collected a bunch of vegetation data (% cover counts in a quadrant at different heights) in patches where birds were seen foraging and also in control patches where no foraging ...
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### Covariate related to independent variable - best solutions

I have 2 groups (tinnitus sufferers and controls) who are significantly different in age - I would normally control for age as a covariate (as it is a cognitive task) but it violates the assumption of ...
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### Looking for and dealing with collinearity in a GLM

I've got this dataset with one continuous dependent variable and two categorical explanatory variables. I'm wanting to run glms on the data but I'm finding problems with what I think is collinearity. ...
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### Mean centering variables NOT in a moderation/interaction term [duplicate]

I am trying to assess the impact of multicollinearity in a regression because I have two separately measured variables which have the reversed signs problem (one predictor is +b regression weight, the ...
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### Multicollinearity among categorical variables - Is it normal?

I'm building a logistic regression model in which almost all of the input variables are categorical. There are multiple sets of categorical variables, for example, day of the week, age range buckets, ...
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### Too many predictors to manually check linearity

Say I have 1000 potential predictors in a logistic regression. I don't have time to check each predictor manually for linearity. I could wait till after variable selection, but in that case I wonder ...
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### Coefficient changes sign when adding a variable in logistic regression

In my logistic regression the sign of coefficients of a variable (location distance of an amenity) changes based on other variables (with time -ve, with travel distance +ve) in the model. When the ...
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### Curse of dimensionality mimics multicollinearity?

Why does the curse of dimensionality mimic multicollinearity, in the following sense.. Consider the random vector $Y = [y_{1}, \dots, y_{4}]$ where each element is ~ Uniform (0,1). Take 10 samples ...
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### Many dependent variables, few samples: is this an example of “large $p$, small $n$” problem?

"Large $p$, small $n$" typically refers to "many independent variables, few samples". In my case, I have $1$ independent variable, $300$ dependent variables, and $n < 20$ samples. Thus, my case ...