Why multicollinearity matters

Or vice versa? Or ? Since both forces are working at the exact same time, you can't separate the strength of either one separately. All that you can say is that their combined force is 1 foot per minute.

Now imagine that the first guy pushes for a minute himself, then nine minutes with the second guy, and a final minute is just the second guy pushing. Now you can use estimates of forces in the first and last minutes to figure out each person's force separately. Even though they are still largely working at the same time, the fact that there is a bit of difference lets you get estimates of the force for each.

If you saw each man pushing independently for a full ten minutes, that would give you more precise estimates of the forces than if there is a large overlap in the forces. I leave as an exercise for the reader to extend this case to one man pushing uphill and the other pushing downhill it still works.

Perfect multicolinearity prevents you from estimating the forces separately; near multicolinearity gives you larger standard errors. The way I think about this really is in terms of information. My very layman intuition for this is that the OLS model needs a certain level of "signal" in the X variable in order to detect it gives a "good" predicting for Y.

If the same "signal" is spread over many X's because they are correlated , then none of the correlated X's can give enough of a "proof" statistical significance that it is a real predictor.

Assume that two people collaborated and accomplished scientific discovery. It is easy to tell their unique contributions who did what when two are totally different persons one is theory guy and the other is good at experiment , while it is difficult to distinguish their unique influences coefficients in regression when they are twins acting similarly.

If two regressors are perfectly correlated, their coefficients will be impossible to calculate; it's helpful to consider why they would be difficult to interpret if we could calculate them. In fact, this explains why it's difficult to interpret variables that are not perfectly correlated but that are also not truly independent.

Suppose that our dependent variable is the daily supply of fish in New York, and our independent variables include one for whether it rains on that day and one for the amount of bait purchased on that day. What we don't realize when we collect our data is that every time it rains, fishermen purchase no bait, and every time it doesn't, they purchase a constant amount of bait. So Bait and Rain are perfectly correlated, and when we run our regression, we can't calculate their coefficients.

In reality, Bait and Rain are probably not perfectly correlated, but we wouldn't want to include them both as regressors without somehow cleaning them of their endogeneity. I think the dummy variable trap provides another useful possibility to illustrate why multicollinearity is a problem. Recall that it arises when we have a constant and a full set of dummies in the model. Then, the sum of the dummies adds up to one, the constant, so multicollinearity. Sign up to join this community.

The best answers are voted up and rise to the top. Stack Overflow for Teams — Collaborate and share knowledge with a private group. Create a free Team What is Teams? Learn more. My concern is whether you need a model of this complexity to adequately represent the nonlinear effect of the variable. I am a PhD student working on a sociolinguistic variation research. I used to have binary dependent variable for analysis and worked fine. Now, I have a multinominal dependent variable 5 categorical variables.

Initially, I thought glm can only use for binary data, so I created dummy variables to make 5 binary dep var. The results report different VIF values and some showed big multicollinearity problem, but not all. Later, I learnt that glm can deal with multinominal dependent variable. So, I calculated the VIF again and the problem was not as big as some of those in the earlier calculation. Would this be something I need to consider when choosing which VIF to report?

I usually just do it within a linear regression framework. Is it a cause of concern? If so, how can one handle it? But it may mean that you have low power to test the three-way interaction. Hi everyone. I am finalizing my results for my paper. To prove it use: the matrix norm e.

Thanks for the great article and discussion! Could you state that your coefficient is inflated and thus a conservative estimate of the effect of x on y? So, in that sense, the result is conservative. However, the thing to be cautious about is that collinearity makes your results more sensitive to specification errors, such as non-linearities or interactions that are not properly specified.

So you still need to be more tentative about interpreting results when your predictors of interest have high VIFs. It would be desirable to explore alternative specifications.

Hi Paul, Thank you for looking at my query. I am running the following regression. When I run the above regression I get all the estimates to be significant. The interaction variable and X1 are still significant but x2 is not. The centered interaction term is significant.

After running all the steps mentioned above, I feel the regression in step1 might be appropriate one. Can you please guide me whether regression in step is completely wrong or it is valid but should be used with some caution. I would go with the regression in Step 1. The two effects cancel out in the bivariate models.

Now I also want to include the research question: How did the trade change in a certain year due to a great economic sanction which hindered trade to important trading partners: I expect that there is a redistribution towards countries that did not pose the sanction and that this redistribution depends on the political affinity index variable.

However, as you said, this generally poses no problem. The problem is that both variable estimated separately support my hypothesis sig. If I include both however, there is a very high correlation between these two variable and both loose their significance. Can I exclude the variable? Thank you very much Best regards Christina Mack. I would not exclude the 2-way interaction. If you exclude it, then the estimate for the 3-way interaction may be picking up what should have been attributed to the 2-way interaction.

Shoul I be concerned for collinearity eventhough the coefficients are significant?? Thanks in advance for your answer. Well, the fact that both are significant is encouraging. What you should be concerned about, however, is the degree to which this result is sensitive to alternative specifications. What if you used height instead of LN height? What about other plausible transformations? When the VIF is that high, the picture can change dramatically under different specifications.

I am carrying out regression which involves interactions of the variables and also the quadratic and cubic terms of multiple variables. I am getting values of VIF of the order of Can I ignore these as square and cubic terms are highly correlated with the original variable. Well, you may be OK but do you really need a model this complex?

My concern is that your power to test the interaction may be low with the inclusion of the quadratic and cubic terms. Is it valid to assess collinearity in a mixed model with partially cross-classified random factors by examining the VIF values?

It has been suggested to me that VIF is not an appropriate measure to use in a multi-level model as it assumes the errors are independent identically distributed. I use VIF simply a rough guide to how much collinearity there is among the predictor variables.

So it could still be useful in a multi-level situation. However, in that case, it would not have exactly the interpretation as the multiplier of the sampling variance of a coefficient when predictors are uncorrelated. If the VIF is below 2. Can tolerance be ignored so long as the VIF is fine? Tolerance is just the reciprocal of VIF, so they cannot give inconsistent results. Thus a VIF of 2. You want the tolerance to be high, not low.

Let me rephrase the question. Run the model with just x and z and possibly other variables. The VIF is based on the R-squared for predicting each predictor variable from all the other predictor variables. But since the intercept is a constant, the R-squared would be 0 and the VIF would be exactly 1 in all cases.

My VIF result is as follow; which my td is my variable of interest and other variables are my control.. Kindly advice what should I do as my td is also high more than 10?

Should I ignore the multicollinearity problem? And if I need to drop the variables, which one should I drop;- either based on the highest VIF result or looking at the lowest t-stat in the regression? Hard to say what to do about it. Are they measuring the same thing, or are they conceptually distinct?

If the former, then you might be OK with dropping one or both. But experiment and see what happens to the TD coefficient. We have calculated the five factor scores to predict other outcome. Howerver there is collinearity among the five factor scores resulting in high value like 0.

What is the solution for this? I have a probit model where I want to estimate the probability of cesarean section of women who delivered in public and private hospitals. I have a high correlation, 0. Probit and OLS give me similar results, but I am a bit concerned about this correlation.

When using the regression:. But, the uncentered VIF are 8 for hospital, 7 for the interaction, and 43 for age. Notes: hospital: dummy 0 public, 1 private conv: dummy convenient day or not cespref: dummy preference for CS or not. Hard to say without more investigation. I have a regression model with panel data fixed effect model.

But x has high correlation with v, over 0. But w, v, and z have low one, less than Can I ignore the multicollinearity? Or no need to do? And high over-time correlations for the dependent variable can lead to problems, but not quite the same as for a simple regression model.

I am working with a time and individual fixed-effects model of agricultural area at county level vs. It seems almost inevitable that there would be some multicollinearity when including such variables. I have a regression model with 3 IVs; strength of identity continuous , corptype binary and Sense of Connectedness binary. There is also an interaction term of strength of identity and corptype. When I ran this model the VIFs were:. Strength of Identity: 2. I note earlier you mentioned that when the IVs are binary, if their interactions have a higher VIF score, it is not that significant.

Therefor should I be concerned about multicollinearity and therefor centering my variables? I would not be concerned about this multicollinearity.

It is not essential to center the variables. However, in the interaction model, when I add the interaction between a and b, and a and c, the vif of the interaction terms increase to over Paul, thank you for this insight. However I have some few concerns. I predicted an inverse mills ratio after estimating a multinomial logistic regression model which I plugged it in my regression model using the BFG approach.

Unfortunately the four mills ratio had high VIFs over hundred. I cannot simply remove them because it will further tell me whether to use ESR or PSM to estimate the impact of adoption on income based on its significance level. What can I do to address this problem? The Mills ratios are only included to adjust for bias. I would only be concerned if the variables of primary interest had high VIFs.

Dear Prof. Allison, I have count panel data and I am going t use xtpoisson or xtnbreg in Stata. Do I still need to check for multicollinearity according to your analysis? If I am not wrong, Poisson and negative binomial models belong to generalised linear models family. Allison, May I ask you a question? I know that collinearity does not affect the significance of the interaction, but the coefficient of the lower order term is also my concern.

So I am in a dilemma, no centering, and the coefficient of the lower order term encounters a co-linear. If centering, coefficient of low-term is without practical meaning. The one consequence of the high VIF is that the standard error for the main effect will be large, which means a wider confidence interval and a lower p-value. Is it ok to ignore multiple collinearity problems if the lower term and the interaction are all significant?

Dear Paul, Is multicollinearity a concern while developing a new scale? Should one be cautious that there is no multicollinearity during the EFA stage? Your insights will be deeply valued. Regards, Vikas. For scale development, you typically want high correlations among the potential items for the scale.

I have four main explanatory variables all ratios which I derive from a categorical variable with four levels. When I found the high VIFs I somehow related to your point on categorical variables with more than three levels and thought that the way I did it was alright. Practically then the three variables included do most of the explanatory work and in most of the cases the cover every category in the observed data.

However Stata does not seem to have problem with that. I am not sure whether I should have a problem with it. This is related to the categorical variable situation that I described in my post. Any one have any input? Thanks so much Allison for this information. I wish to ask if two variables have a strong negative correlation say Thank you for your helpful posts and suggestions on this blog!

OR is it just among the independent variables without considering year dummies? OR can I remove the year dummy parts? Allison, Thanks so much for posting this resource!

If a set of interval-level variables represents the count of events within each category of a mutually exhaustive set of categories within aggregated units each variable reflects count of each dummy , can this be simultaneously included into a regression model or do they need to be entered individually in separate equations? Similarly, would the same principles apply for variables representing the spatial density of these same variables with spatial autocorrelation handled in the equations?

Autocorrelation issues aside, can you safely include all 3 count variables as predictors into an equation to determine what the independent effects of each school type are controlling for the effects of the other types? Or, is this multicollinear. Try it and see. How does a smaller fraction of people in the reference category cause the correlation of the other two indicators to become more negative?

And why does selecting a variable with a larger fraction of people as the reference category fix that? Consider a three-category variable, with dummies for categories D1, D2, and D3.

If category 3 has just 1 case, the correlation between D1 and D2 will be very high. Allison, Firstly thanks a lot for your posting on the multicollinearity issues. My study deals with a panel dataset, and VIF value for firm size, which is one of the control variables, increases a lot from 1 to 10 if I add firm dummies in the regression model.

In this case, can I ignore the high VIF value of the variable? Other VIF values look fine with the firm dummies. I really wonder the reason behind the increase in VIF after including firm dummies. Is there anything I can do? Thank you again! This is simply a consequence of the fact that most of the variation in size is between firms rather than within firms. Nothing you can do about that. Allison, Thanks a lot for this informative post. Would you please explain a bit more on this statement?

Are there any statistical simulation examples on this issue? Thank you in advance. My suggestion was to run a linear regression with any dependent variable and check the multicollinearity diagnostics in that setting. I am writing this to ask a question about high correlations between an IV1 continuous and a IV2 binary:developed country1 and developing country0.

I wanted to see if the effect of IV1 on DV has different slopes depending on whether the country is a developed or developing country. Or should I separate the sample into two groups and run two different regression models one for the developed and the other for the developing? Dear Dr Allison Very interesting post. Could one use VIF factor for logistic regression? I do not see such a command on SAS. Thank you so much for this information.

I am doing a study with the state level data in the US with the time span of 4 years. I am adding a dummy variable for each state and each year to account for state-level and year-level fixed effects. The dummy variables cause very high VIF values larger than 10 for my continuous independent variables. Without the dummy variables the VIF values are lower between 5 and This means that my independent variables are highly correlated. What can I do at this point?

I tried Ridge Regression but the problem with Ridge Regression is that it does not give me any p-vale to test for the significance of my variables. I am looking for a suggestion which helps me to overcome the multicollinearity issue and gives me a way for testing the significance of each variable.

I have heard that some scientists claim that multicollinearity between IVs can explain variance in the DV, which implies that the R2 of the model can increase. Adding a variable that is highly collinear with a variable that is already in the model can, indeed, increase the R2 substantially. This can happen when the two variables have a positive correlation but coefficients that are opposite in sign. Or when the two variables have a negative correlation but coefficients of the same sign.

I am currently doing a hierarchical regression model, where control variables are entered in the first block, key independent predictors and moderator variables in the second block, and one interaction term in the last block. I found out that one of the moderator variables which is inputted in the second step of the model has VIF of 2.

Is it something I need to be concerned about? If so, what do I need to do? I presume you mean mediator variables because moderators are necessarily in interactions. I have positive correlations, low VIF and tolerance stats but still get negative beta values on one of the instructional variables at step 2. The beta values are insignifcant and in fact adding the variables to the model makes no change in terms of the variance explained.

Can I ignore this or is it still valid to report the results, given that the lack of variance is in itself a useful finding? We are creating an index of neighborhood change in a metro area. We use 7 variables, 3 of which are likely to covary: education, occupation, income. The index is calculated for all the census geographies of the metro area.

But what if the co-variance is very different in different tracts? What if in some tracts people are educated but blue collar, and in others uneducated but rich? In other words, I have a variable included at level 1 and a composite of that variable at level 2. The point of the analysis is to see how the estimated influence of that variable at each level simultaneously. Is there a way to check for multicollinearity here? Is multicollinearity an issue that I need to address via PCA for example if I am only interested in building a good predictive model?

I was told recently that unstable parameter estimates in the presence of multicollinearity would result in unstable predictions as well but I have also read elsewhere blog posts etc that multicollinearity is not an issue if I am only interested in making predictions.

But simulations that I have done persuade me that high multicollinearity can produce some increase the standard errors of predictions. However, the effect is not dramatic. This is a great little summary. I have a question regarding point 3 that I am hoping you can clarify. Specifically, since the VIF for each level of a factor variable depends on which level is set to the reference, what is the point of looking at by-level VIFs for factor variables?

And as I note in the post, if the reference category has a small number of cases, that can produce a high VIF. I did VIF tests both in construct and item level. The VIFs of every construct are below 3. Is it serious? How can I deal with this problem? Hello, I am running a generalized linear mixed effects model with the negative binomial as the family. When I run a vif on the model, I get a very very high VIF value for predictor variable of interest The predictor is a factor variable with 4 levels.

Hard to say without more information. Is the high VIF for just one out of the 3 coefficients? How many cases in the reference category? Are there any other variables with high VIFs? The multiple regression model used to examine this is only based on categorical time variables such as weekday, month, year, holiday, etc the data used is daily revenue. The result shows a highly significant impact of GDPR on revenue. However, it can be seen that when examining the covariance matrix GDPR and the indicator variable for , which was the year GDPR was introduced, has a simple correlation of Sounds to me like what you have, in effect, is a regression discontinuity design.

BTW, Statistical Horizons will be offering a course on this topic in the fall, taught by one of the leading authorities on the topic. Thank you very much for your interesting and clear posts.

The sample consists of participants and for the product term X:M , I obtained a p-value of. VIF values were So, my first thought was that p-values were being inflated due to multi-collinearity issues. Then, I was struggling because I was not being able to find a way to prove the significance of this moderator. After reading your post, I centered the variables and, as expected, I obtained the same p-values and no collinearity issues: VIF values decreased to 1.

I would like to know your wise opinion about borderline p-values. In my opinion, this effect is relevant and deserves to be highlighted. I already read some papers where borderline significance is further assessed with Bayesian tools.

Can you please shed some light in the right way to follow? But personally I like to see p-values that are much lower than that. I would say that the evidence for this interaction moderation is very weak. Just like non-Bayesian models. However, there are Bayesian approaches to dealing with multicollinearity that may be somewhat different. See, e. I am working on a meta-analysis and I would like to account somehow for multicollinearity present in the included studies.

Especially, as there are some studies with small sample size e. Is there any rule of thumb indicating how may potentially correlated factors at a certain level of aggregation e. I usually still exclude a reference group, is this correct?

And is collinearity acceptable is this situation? But in this case, most software does not give you an overall test. Is there a way to get an overall test? Not sure what kind of test you are looking for. You can certainly get the usual collinearity diagnostics. And most software can produce upon request a test that all the coefficients for the percentage variables are zero.

Thank you for your informative post. You seem to explain that the coefficients of other variables are not influenced by this centering. I have two questions. Q2: When I run the following models, the Sex and Age2 estimates across models are identical and the Age estimates are very close. Why is this so? But when you center the variable, you change the zero point. Q2 — Models 5 and 6 should also include the main effects of each of the variables in the interaction. Make that change and ask me again.

I apologize for the lack of clarity. I wrote my models like you input them in R, but they do include main effects. Here is the complete equation. I find that: 1. The Sex estimate in Model 5 differs from the Sex estimate in Model 6. All other estimates between Models are identical. All these results are to be expected. The general principle is this: When you have interactions and polynomials as predictors, the highest order terms are invariant to the 0 point of the variables.

But all lower order terms will depend on the 0 point of each variable in the higher order terms. What about lagged variables? For example, you lag the trading price of an asset to predict whether the market will move up or down. If you have multiple lags, you can easily run into multicollinearity problems, and this is not a problem that can be ignored. Thank you very much for this insightful article. This is by far the most helpful resource I found on the topic of multicollinearity.

My indepdendent variables are three dummy variables presenting the membership in four groups the control condition is the reference category and is not included as a variable. The N is almost identical for all four groups with , , , and The dependent variable is a count variable I am using a negative binomial regression model The aim of my project is to determine the impact of membership in one of the treatment groups on the number of a specific action taken by users in a mobile application.

While I have low VIF values of 1. For example: Treatment 1 does not seem to have an effect on the dependent variable, whereas treaments 2 and 3 have a strong positive effect according to my full model and looking at the despriptive statistics. If I now run a model including only the Treatment 1 variable, it becomes more negative and highly significant.

While my notion would be to simply base my interpretation on the full model, and report the low VIF factors as proof that there is no collinearity issue, I am not sure if this would be statistically sound this project is part of a Master Thesis. This is not a collinearity issue. You should first do an overall test of the three dummies the null hypothesis is that all three coefficients are zero.

This can be done with test command in stata or the test statement in SAS. Dear sir Is it necessary to check multicollinearity for panel data provided the appropriate model is Fixed effects model?

Thank you for this very insightful article! It offers a really helpful and comprehensive overview of multicollinearity issues. However, my question concerns multicollinearity in longitudinal research. I would expect a rather high correlation between t1 and t2 of the same variable. But how should I deal with multicollinearity between variables across measurement points, which are not the repeated measures? Thank you very much! I am using Proc surveylogistic to estimate odds ratios and CI for the association between IV 4 categories and a binary outcome.

I have 6 categorical covariates. You suggested using Proc reg to assess multicollinearity. In this case, what is the dependent variable. In other words how do I build this model? Thank you for this interesting and useful resource. I am reviewing a manuscript and the authors have attempted to perform an analysis which I believe is incorrect, due to the perfect collinearity of the two variables of interest.

The authors attempted to examine the association of nutrient A from say bread with a disease outcome, and claim that they wish to take away the effect of nutrient B from bread in their Cox model by including nutrient B as a covariate. It is akin to putting the same variable in the model twice. Is my interpretation correct? Most regression programs will just boot one of them out.

Thank you for all of you helpful guidance! I have a question for you about multicollinearity among interaction terms. I am conducting a hierarchical linear regression with four steps. Each variable is continuous. In the fourth step of my model, I have entered four interaction terms and there appears to be multicollinearity among two of the interaction terms.

The original correlation matrix may not be positive definite. Pairwise deletion may be inappropriate. And, I have mean centered the variables before calculating the interaction terms. I am wondering if this is a situation in which I should be concerned about multicollinearity. Thank you so much for your feedback and guidance—much appreciated!

Well, multicollinearity might reduce your power. But I would be inclined to believe the results in your fourth step. I have 4 dummies for 5 prime minister terms, and 3 of them have VIFs around 10 I am already using the largest category as reference.

All of them are not significant according to the results of the regression as well as in the results of a Wald test. Are the high VIFs influencing their significance in any way? In other words, are their lack of significance legitimate despite the high vifs?

Are there any other variables that have high VIF? Have you done a joint test that all four have coefficients of 0? They are all stationary, and when I used their residuals in the regression, their VIFs are still high 10ish but the VIFs for the Prime minister dummy variables become lower but still larger than a 5.

What do you mean as a joint test? I ran the Wald test by using the test command in Stata for all 4 dummies after the regression; is that sufficient? The Wald test should be sufficient. Thank you for this post. I have been reading your post and a lot of the answers with great interest. I have a situation in which I use a pooled cross section at the firm level, with about 15 countries and 2 time periods.

I am using Elections as a dummy-IV. In addition, I am using country-year fixed effects. The country-year dummies by themselves, and especially combined with the IV cause some perfect multi-collinearity, leading R to remove about 5 country-years i. US , Canada etc.. No, I would not extend my arguments to perfect multicollinearity. What your data are telling you is there is insufficient variation within county-years to estimate the effects of your IVs.

Stata will throw out whichever collinear variables come last in the model. So I recommend putting your country-year variables first. Nice post, and it is amazing that you have continued to keep up with responses for 8 years to the day since your original post! I am noticing a number of comments seeking additional clarification about the 1st point you make here, which you provide already in some of your responses.

Though you provide several citations in your responses to other comments, I did not catch one for this first point. Is there a favorite reference you have that elaborates on this first point?

I have a dilemma in my research regarding multicollinearity and I wonder whether the 2nd situation you referred in the article can answer it. I went through all the comments and did not find a similar question. My multicollinearity issue is with some of my predictors that are rainfall data of a given year all continuous predictors. But this performance cannot be guaranteed on a new test data unless we are sure that TotalCharges will continue to have a similar correlation with other predictors.

Also, we find the AUC on validation is the same when the model was fitted after removing the TotalCharges variable, and when the model was trained on PCA transformed train data. This makes it evident that, by identifying and removing a feature causing correlation has given us similar results that could have been achieved by using principal component analysis. Though simple, correlation analysis can go a long way in developing a good model. Correlation between predictors and response is good!

Clairvoyant is a data and decision engineering company. We design, implement and operate data management platforms with the aim to deliver transformative business value to our customers. Sign in. MLmuse: Correlation and Collinearity — How they can make or break a model.

Rekha M Follow. Clairvoyant Blog Clairvoyant is a data and decision engineering company. Data Science Correlation Multicollinearity. Clairvoyant Blog Follow. Written by Rekha M Follow. More From Medium. Harshita Chopra in Omdena. Can AI help in fighting against Corona? Rahul Agarwal in Towards Data Science. Are sentiments at a hospital interpreted differently than at a tech store.

Harsh Maheshwari in MLearning. LOTI: Weeknote Eddie Copeland in loti-ldn. Shravan C. Learning Text Analytics using Google Trends!