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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Problems with calculation of numerical identification w.r.t. ANOVA smooth for large scale matrices

Suppose we have two (centered) Spline-matrices $\boldsymbol{B_1}$, $\boldsymbol{B_1}$. Then $\boldsymbol{X_1} = [\boldsymbol{B_1},\boldsymbol{B_2}]$ contrains lower order smooths and ...
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Mahalanobis distance in a hierarchical cluster analysis in SPSS

I am conducting a hierarchical cluster analysis in SPSS on my database with several neuropsychological and psychiatric variables. In my database, some of my variables (that is: two pairs of variables) ...
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15 views

Time dummies in panel data — absorbing effects?

I am conducting a data analysis. I have a panel with individual firms with firm-specific and macroeconomic variables. I would like to run an OLS regression adjusted for firm clustering effects and ...
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15 views

GBM, it's overfitting/multicollinearity problem and parameter setting up

I recently came across a predicting problem (0-1 outcome, with more than 80 variables), I decided to use GBM (Gradient Boosting Machine by Friedman)to handle this job. I let the GBM use only 70% of ...
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Multicollinearity in a “population model”

I was talking with a colleague who told me that at the time of making logistic regression across a population did not have to worry about assumptions such as multicollinearity, because when analyzing ...
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248 views

Pattern mining on a small data set

I have a small data set 30 features/predictors and 30 observations. My target variable is Oil production and my predictors are well & reservoir properties (depth, trajectory, temperature, pressure ...
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30 views

Logistic Regression - Two Dependent variables not playing well with each other

My name is Abhi and I trying to teach myself logistic regression by solving some of the problems available on the internet. I am using R and RStudio as the development environment Problem Statement ...
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21 views

How is predictor importance in a cluster analysis (in SPSS) affected by dichotomy and multicollinearity?

I want to use a cluster analysis (CA) in SPSS to define different profiles in my dataset. I am using different continuous variables for this, including several neuropsychiatric measures. I am new in ...
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27 views

Low correlation between predictor variables in linear regression

I know that one if one is trying to perform linear regression, multicollinearity can be an issue because it can "lead to unreliable and unstable estimates of regression coefficients." Suppose for a ...
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22 views

Multicollinearity

In a regression model with dummy variables, how does one check for intearction between the dummy variable and the independent variables?Wouldn't there be problem of multicollinearity when such ...
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55 views

VIF in GLM model in R

Before running or building a model, ho can we check on the multicollinearity between different covariates in GLM model in R? I know that SAS Proc MIXED procedure gives a column for VIF which is very ...
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21 views

Correlated explanatory variables where both are significant

I am running a multiple linear regression using SPSS to test the effect of ethnicity and ethnic/racial attitudes or perceptions on political predispositions. One model, as an example, looks like ...
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How to obtain VIF values for independent predictors used in a loglinear poisson generalized linear model?

The correlationmatrix shows that some of my predictors are correlating (Pearson, 0,288 0,492 and 0,360) I think it is useful to have additional information to decide whether this is acceptable or not. ...
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49 views

Why does Ridge Regression work well in the presence of multicollinearity?

I am learning about ridge regression and know that ridge regression tends to work better in the presence of multicollinearity. I am wondering why this is true? Either an intuitive answer or a ...
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42 views

Evidence of collinearity, yet significant coefficients – is this a problem? [duplicate]

I have two main explanatory variables of interest in the model I use. It is only when I include them both that the coefficients are significant. The correlation between them is 0.98 and the vif-value ...
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1answer
65 views

Multicollinearity with Interaction (high VIF)

When I check the VIF of my independent variables with the dependent variable, it looks normal and less than 5 but when I add the interaction variables, the VIF increase to 48 for some variables. I ...
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52 views

Why is least squares performing as well as ridge regression when there is multicollinearity?

I am learning about ridge regression, so I am implementing it in MATLAB as practice. However, I am having trouble finding a structure of data where ridge regression performs better than an ordinary ...
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37 views

perfect collinearity among multiple continuous variables

When there is a perfect collinearity among more than two continuous variables, how do you deal with it and how are the regression results interpreted? I have three independent variables which ...
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51 views

Dealing with linear dependent variables

I have a large dataset with many subject each with responses from a consecutive year going back 10 years (ie 100,000 persons per year (not necessarily 10 data points per person as they may not have ...
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42 views

Non-linear model robustness

I am building a non-linear model aiming to describe the mechanistic process of resource allocation. There several terms, and what makes the model non-linear is competition between lines that are ...
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125 views

When can we speak of collinearity

In linear models we need to check if a relationship exists among the explanatory variables. If they correlate too much then there is collinearity (i.e., the variables partly explain each other). I am ...
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135 views

Is multicollinearity a concern in nonparametric statistics?

Should I be concerned about multicollinearity in nonparametric statistics?
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47 views

Can I use simple regression with variables that are not significant in multiple regression?

As I am testing a number of models, I notice that none of my demographic variables are ever signficant. For example, I am testing a model to predict the dependent variable 'perceived ...
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25 views

multicollinearity in OLS regression [duplicate]

If I have a dependent variable Y and two independent variables X1 and X2 , that are highly correlated. Y ~ beta1*X1 + beta2*X2 What issues can multicollinearity cause in an OLS regression, apart ...
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85 views

Panel Cointegration, Moderating Effects and Multicollinearity

I am running a panel fixed effects regression on 21 countries and 16 years. Its a secondary data taken from OECD website mostly. My model looks like this: $$ \log{(GDP/Labor)}_{i} = \beta_0 +\beta_1 ...
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31 views

Multicollinearity over intervals

You have multicollinearity when you have 2 variables $(X_1, X_2)$ that have a relationship, $X_1=a+X_2$ where $a$ is constant. My question is: is there still a multicollinearity issue if $a$ is not ...
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Is extra sum of squares $SSR(X_p|X_1,…X_{p-1})$ in multiple regression always positive?

An extra sum of squares $SSR(X_p|X_1,...X_{p-1})$, assuming that no pair of predictor variables are perfectly correlated, measures the marginal reduction in the error sum of squares. Eventually one ...
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Is centering a valid solution for multicollinearity?

Let's assume that $y = a + a_1x_1 + a_2x_2 + a_3x_3 + e$ where $x_1$ and $x_2$ both are indexes both range from $0-10$ where $0$ is the minimum and $10$ is the maximum. I found by applying VIF, CI and ...
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42 views

PLS Regression and collinearity

From what i know PLS regression is used when there is more variables than observations and when there exist multicollinearity between the independent variables. I have data for a regression model that ...
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37 views

How to deal with multicollinearity without dropping variables

In establishing a linear model, if two variables are highly correlated, then it turns out to have high VIFs. If we applied data reduction techniques, like PCA, we will lose explainability to some ...
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42 views

Identifiability in linear regression

If we have a generative model: $X_2=X_1a_1+\varepsilon$, where $\varepsilon \sim \mathcal{N}(0,\sigma_2^2)$, do we have $X_1=X_2a_2+\varepsilon '$, where $\varepsilon \sim \mathcal{N}(0,\sigma_1^2)$ ...
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Why do both the VIF and tolerance statistics exist, when the latter is just the reciprocal of the former?

Is taking the reciprocal helpful in some way, or is it just a matter of historical accident that there came to be two terms to describe the same thing? (From the Wikipedia page.)
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487 views

Variance-Covariance matrix interpretation

Assume we have a linear model Model1 and vcov(Model1) gives the following matrix: ...
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Multicollinearity if independent variables sum to one?

I am intending to explain the variation in dependent variable Y through a number of ratios that, combined, sum to 1 in each period t Hence, $$ Y_t = \alpha + ...
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Variance inflation factor for generalized additive models

In the usual VIF calculation for a linear regression, each independent/explanatory variable $X_j$ is treated as the dependent variable in an ordinary least squares regression. i.e. $$ X_j = \beta_0 + ...
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When including a linear interaction between two continuous predictors, should one generally also include quadratic predictors?

Suppose I am fitting a linear model, and I have two continuous predictors x1 and x2. I think that they might interact, so I add ...
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78 views

Dealing with multicollinearity in logistic regresson model

I have 5 quantitative predictor variables in my logit model, and when I use the cor function in R on those 5 variables, I see that $x_{1}$ and $x_{2}$ have ...
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Infer causality with high collinearity

I recently started to ask myself how to measure the impact of education on indexes like GDP: what is the outcome of mathematics or computer science on GDP, at the country level for instance. In this ...
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27 views

handling multicollinearity by backwards regression and omitted variable bias

Suppose I try to estimate a production function as follows: $logY=b_0+b1*logX_1+b_2*logX_2+b_{11}*(logX_1)^2+b_{22}*(logX_2)^2+b_{12}*(logX_1)*(logX_2)+u$, where $Y$ is the output, $X_1$, $X_2$ are ...
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Techniques for scaling data matrix to avoid rank deficiency issues

I have a $n \times p$ matrix $A$ where $n$ is the number of observables and $p$ is the number of observations. $n \gg p$ In my code, I have done $[E,V] \,=\, eig(A)$ and doing a least squares ...
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How to deal with imperfect multicollinearity

I am estimating a model for an assignment, and found out that there is a 0.9 correlation between two of the independent variables. So If I am not wrong I should omit one variable and redo the ...
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I have my data set, now what?

I have a basic understanding of basic statistics, but I believe I've gotten myself out of my depth. I have a data set with a dependent variable (time span) and three quantitative independent ...
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275 views

Collinearity in time dummies, fixed effect regression

I am running a fixed effect panel regression with 81 groups x 20 periods, so approx 1620 (unbalanced) observations. I use the following to create dummies: ...
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Dealing with multicollinearity by smoothing coefficients?

I would like to perform a linear regression. However, the predictor variables are families of variables indexed by time. Let's say the regression problem is: target ~ ...
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295 views

Regression for really small data with high degree of multicollinearity and outliers

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Multicollinearity in GLM

I have run a general linear model which includes 3 scale IVs and 2 categorical IVs and 1 scale DV. I am testing the assumptions of regression and I a not sure how to test multicollinearity since I ...
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1answer
217 views

Confused about multicollinearity, variable selection and interaction terms

I have run a few tests/methods on my data and am getting contradictory results. I have a linear model saying: reg1 = lm(weight = height + age + gender (categorical) + several other variables). If I ...
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Testing for multicollinearity in logistic regression

So far I have checked the tolerance value, VIF and condition indexes. But checking the variance of the regression coefficients I have to wonder: how little variance of the regression coefficient ...
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Utilizing PCA when rotated factor loadings are difficult to relate to real world variables?

In my ongoing attempts to make sense of a highly correlated dataset without just throwing out most of the variables i am at the point of attempting to interpret PCA output. I hope i am right in the ...