Multicollinearity means predictor variables are correlated with each other, making it harder to determine the role each of the correlated variables is playing. Mathematically, it means the standard errors are increased. Multicollinearity can have counter-intuitive effects.

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Why do t statistics decrease (standard error for cofficient increases) when multicollinearity exists?

Can anybody show how the t statistic decreases when multicollinearity exists? It is easy to prove using the F test, but I don't know how to prove it using the t test.
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32 views

Different coefficient values from multiple versus bivariate regression

I wonder how to generate such data, so that in single variable regression feature coefficient would be positive, and in multiple regression would be negative. So I read several related questions on ...
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833 views

Why does this regression NOT fail due to perfect multicollinearity, although one variable is a linear combination of others?

Today, I was playing around with a small dataset and performed a simple OLS regression which I expected to fail due to perfect multicollinearity. However, it didn't. This implies that my ...
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21 views

Vif and stepwise regression

I used the VIF to detect multicollinearity, I want to use forward selection and backward elimination procedures. My question is: Do I have to use all the variables in my dataset in the procedures or ...
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7 views

reconciling Linearity and Multicollinearity assumptions in ANCOVA

For ANCOVA, many textbooks and other resources require, among other assumptions, that covariates be linearly related to the dependent variable, which makes sense. However, many of the same sources ...
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28 views

Issue with linear mixed effects model and interaction : any alternate method?

I have a variable (Y) which I'd like to know if it can be explained by linear regression with two other variables (A and B) or the interaction of A and B. Let's say, to simplify, than I have two ...
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26 views

Is it appropriate to test for collinearity in a mixed model using VIF?

My study is examining predictors of skin lesions in pigs. I am looking at the effect of predictor variables (including weight at 4 weeks, 9 weeks and 20 weeks) and I have carried out a mixed model ...
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28 views

Is the intercept estimation affected by multicollinearity?

Suppose I am running a regression $$x_t = \alpha + b_1y_{1t} + \dots + b_m y_{mt} + \varepsilon_t$$ where the $y_{i}$ are potentially linearly correlated (Some have an IVF bigger than 4; generally ...
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36 views

Train & predict probabilities using LDA having multiple collinearities

I am trying to fit an LDA model and predict conditional probabilities of class membership with it. I believe I understand the basic method to do this using the covariance matrix and class means, but ...
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37 views

Adding new variables makes regression coefficients individually insignificant [duplicate]

I have a multiple regression where all my coefficients are significant. When I add new variables my initial variables become insignificant. Furthermore, my new variables (that in a simple regression ...
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1answer
26 views

Regression — multicolinearity and VIFs

I understand that variance inflation factors can be used to detect multicollinearity. What is the intuition behind the VIF formulation? What aspect of this formula shows it detects multicollinearity ...
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10 views

Nonlinear least squares for multicollinear data - regularization etc?

Is there an existing technique that can be used to fit NLLS on multicollinear data? Such as ridge regression for NLLS, or any other technique used to solve the same problem? My model takes the form ...
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33 views

Does multicollinearity affect performance of a classifier?

I know that wikipedia references are sometimes frowned upon here, but this one has me puzzled: Wikipedia - Multicollinearity I know what multicollinearity is, and ...
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52 views

Alternatives to Box-Tidwell transformation for ridge regression?

I would like to fit the following model by ridge regression (the xs correlate strongly with one another) $y = \beta_1 {x_1}^{\lambda_1} + \beta_2 {x_2}^{\lambda_2} + \beta_3 {x_3}^{\lambda_3} + ...
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1answer
66 views

how does multicollinearity affect feature importances in random forest classifier?

I have a random forest binary classifier, but the results from the feature importances are somewhat erratic. Here's what I want to know: Does multicollinearity ...
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32 views

Correlation between two explanatory variables

I have a multiple regression. Two of my independent variables are "Repeated Partnerships" and "Company size". When adding the explanatory variable "Company size" to the regression it is statistically ...
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100 views

Lasso Regression for predicting Continuous Variable + Variable Selection?

I'm attempting to predict vegetation productivity based on climatic and land use variables (the latter are categorical). I found that there is a multicollinearity problem between the predictors ...
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1answer
116 views

Multicollinearity in simple linear regression (not multiple)?

I am doing a simple linear regression analysis with 1 independent variable. I am checking data against assumptions. As I am checking against Tolerance and VIF level, I get the their values equal to 1 ...
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52 views

Multicollinearity problem and differencing time series

I have to estimate the regression equation by OLS and do in-sample forecasting of the time series. It has a trend and seasonal variations. So I try to estimate the model which looks like $$\text{ln} ...
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56 views

model estimation with feedback loop in variables

I have the following problem regarding fitting of a model where some variables can be biased so that their values are based on knowledge or at good guestimate of $Y$ in the past. In other words: some ...
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Choosing predictors in regression analysis and multicollinearity

I would like to run a linear regression analysis and I'm uncertain about including predictors. I have three predictor variables available. One is based on a lot of previous research. Therefore I am ...
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1answer
36 views

How to solve multicollinearity in OLS regression with correlated dummy variables and collinear continuous variables?

I have predicted an ecological variable using OLS regression which showed the model accounts for more than 72% of the variance in the dependent variable (DV). However, I am also interested in which ...
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53 views

How to combine two variables in linear multiple regression

I have LRM with two variables related to education level: one is responsible of higher school graduation (binary, 1 or 0), another one represents the number of years spent on education (discrete, not ...
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1answer
50 views

Is multicollinearity an issue when doing stepwise logistic regression using AIC and BIC?

As far as I understood, it should not be a problem as long as I don't have perfect multicollinearity since I don't mind if the standard errors get inflated. However, what about using the ...
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56 views

Fixed and time effects - R plm() vs. Stata xtreg

I have to do some panel regressions and because I received the data as an .dta stata file, I first ran all regressions in Stata and all went fine. Later I wanted to reproduce these regressions in R ...
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Regression using membership percentages as independent variables

I'm trying to do a linear regression in which some of my independent variables are percentages that total to 1. In a simplified manner, I have ~500 HIV infected patients in which I've measured ...
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62 views

How can we calculate the variance inflation factor for a categorical predictor variable when examining multicollinearity in a linear regression model?

For example, if we have the linear regression model: $E(y) = \beta_0 + \beta_1 x_1 + \beta_2 x_2 + \beta_3 x_3 $, where $ x_1 =\begin{cases} 1 & \mbox{if level 2} \\ 0 & \mbox{otherwise} ...
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Calculate VIF using standard deviation in binary logistic regression

I want to test my binary logistic regression model for multicollenearity. Hence, i want to calculate Variance Inflation Factor (VIF). But i'm confused with R-squared value which is needed to ...
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Multicollinearity in Zero Inflated Negative Binomial Regression

I am trying to model counts govt, based on the counts lp,const,...
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(How to Mean Centering for interaction effect?) Social Research case

I want to ask on how to mean centering in case data in SPSS are all on likert scale. I have googled some information that steps in mean centering are: calculate mean of variable Substract variable ...
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7 views

Poisson and Multicollinearity [duplicate]

Does Multicollinearity important in Poisson model?, as it is influential in OLS. I had a correlation matrix and find out that some of my Covariates have a bit of multicolliniarity (0.3).
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54 views

Interpretation of elastic net coefficients under multicollinearity

I am studying the elastic net regression and in some material I read, it was mentioned that the method will choose a group of regressors that are correlated while LASSO can pick one among the ...
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1answer
33 views

Should I convert a categorical variable with k levels to (k-1) or k binary variables?

I'm building a predictive model with a combination of numeric, binary, and categorical variables. The outcome is binary. For methods like SVM, I have read on stack exchange that the categorical ...
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VIF to find multicollinearity

I tried VIF on the Longley dataset to look for multicollinearity. (I have used a custom function returned in ...
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Interpreting proportions that sum to one as independent variables in linear regression

I'm familiar with the concept of categorical variables and the respective dummy variable coding that allows us to fit one level as baseline so as to avoid collinearity. I'm also familiar with how to ...
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Centering variables in regression leads to the same model of original variables, why still doing that?

The regression model y= b0+ b1 x + b2 x^2 + b3 x^3 and the second regression model y = b0 +b1 (x-u) + b2 (x-u)^2 + b3 (x-u)^3 where u is the mean of x These two models lead to the same curves, or ...
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What are some of the potential consequences of adding junk controls in your regression?

Let's say I am running a regression in which my dependent variable is homicide and my variable of interest is access to violent videogames. Let's say that I also throw in the kitchen sink with ...
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Cause of omitting independent variable in regression

As you can see in the output below DNTN is omitted but it's still in data What's the cause of omitting independent variable in the regression when the number of ...
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21 views

How to show the equality of two Variance Inflation Factor(VIF) definitions

How to show the diagonal elements of the ${C = (X'X)^{-1}}$ are $C_{jj} = \frac{1}{1 - R_{j}^2}$ where $R_{j}^2$ is the coefficient of multiple determinations from the regression of $x_j$ on the ...
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Where is the explanatory effect of common variance among covariates accounted for in regression procedures?

As a follow up to the excellent answers provided for: Does the order of explanatory variables matter when calculating their regression coefficients? (Which I've found incredibly useful from a ...
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32 views

Should potentially multicollinear variables be dropped

I did correlation analysis for a set of variables and calculated the VIFs. For a couple of independent variables, the VIF is less than 4, however the correlation coefficient with other input variables ...
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70 views

When 2 variables are highly correlated can one be significant and the other not in a regression?

In regression, when 2 parameters are correlated and added to a model separately, how likely is it that one parameter will be a significant predictor of the response variable while the other is not? ...
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Should I use mean-centering on predictors for collinearity involving the intercept?

In one of my linear regression models, a predictor showed collinearity with the intercept based on condition indexes and variance decomposition proportions diagnosis. Then I found that this predictor ...
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Motivation to center continuous predictor in multiple regression for sake of multicollinearity?

I'd like to discuss the centering of continuous predictor variables in multiple linear regression with an interaction term for the sake of "relieving" multicollinearity. I've read about ...
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Why is multicollinearity a sample phenomenon?

We say that multicollinearity is a sample phenomenon. That means we postulate the PRF such that each independent variable is bound to have an independent effect on the dependent variable but due to ...
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36 views

Multicollinearity in WLS regression

I run a weighted-least squares regression to account for the heteroscedasticity in my data. When I examine the Pearson correlations between all predictor variables, I can't detect high collinearity. ...
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1answer
59 views

gam smoother vs parametric term (concurvity difference)

I have a gam model that is: gam=gam(sv~s(day,bs="tp")+s(range,bs="tp")+s(time,bs="cc"),data=train.all,gamma=1.4,method="REML") the ...
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Multicollinearity in Auto Regressive models

I have just started learning about time series analysis. I had a doubt regarding AR models. I understand that in Auto Regression, we regress one variable on values of the same variable at different ...
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Interpreting OLS Regression Coefficients with High Multicolinearity

I am having trouble understanding the interpretation of OLS coefficients when predictors are highly correlated. My understanding of OLS coefficients is that they estimate a change in the expected ...