But do note that the reported coefficients that you get will depend upon which group you exclude (but, again, when you add pieces correctly, you get the exact same results). You could try LASSO to see whether either or both of the predictors is maintained in a final model that minimizes cross-validation error, but the particular predictor maintained is also likely to vary among bootstrap sample. I’ve tried using the stepAIC() function in R for variable selection, but that method, oddly, seems sensitive to the order in which the variables are listed in the equation… If you artificially construct such data, e.g. by doing $(x,y)\mapsto(x,y,x+y)$ then you do distort space, and emphasize the influence of $x$ and $y$. If you do this to all variables it does not matter; but you can easily change weights this way. This empasizes the known fact that normalizing and weighting variables is essential.

Due to this nonlinear transformation, I believe there’s no guarantee that the SHAP values will be preserved in magnitude or rank. I’m unsure how to use SHAP here without affecting the production model by reducing multicollinearity. About comparing the two predictors, an accepted approach seems to involve the usage of bootstrap to generate a distribution of correlations for each predictor. Then you can measure the difference between the two distributions with an effect size metric (like Cohens’ d). The effect of this phenomenon is somewhat reduced thanks to random selection of features at each node creation, but in general the effect is not removed completely. On that note though, I tried quickly throwing a few sets of 100 dimensional synthetic data into a k-means algorithm to see what they came up with.

And I would worry about whether any differences you find would necessarily hold in other data samples. As a consequence, they will have a lower reported importance. Because it is so hard to determine which variables to drop, it is often better not to drop variables.

How to deal with multicollinearity when performing variable selection?

• First correlation and multicollinearity are two different phenomenon.
• I’ve tried using the stepAIC() function in R for variable selection, but that method, oddly, seems sensitive to the order in which the variables are listed in the equation…
• In such cases, you would probably be advised to drop one or more variables instead.
• Then reverse the order, starting with your novel predictor and seeing whether adding the standard predictor adds anything.
• The worst case scenario is that there is only one cointegrating vector which you will not find by doing analysis on subsets.
• So my gut feeling earlier was quite possibly wrong – k-means migth work just fine on the raw data.

LASSO will reduce the absolute size of your regression parameters, but that is not the same thing as the standard errors of those parameters. Determining which of 2 “measures of the same thing” is better, however, is difficult. When you have 2 predictors essentially measuring the same thing, the particular predictor that seems to work the best may depend heavily on the particular sample of data that you have on hand. If you’re analysing proportion data you are better off using a logistic regression model btw – the l0ara package allows you to do that in combination with an L0 penalty; for the L0Learn package this will be supported shortly. In short the variables strength to influence the cluster formation increases if it has a high correlation with any other variable. It just about the interpretation meaning, so remove the highly correlation variable is suggested.

Interpreting Multicollinear Models with SHAP: Challenges with XGBoost and Isotonic Regression

I’m trying to select amongst these variables to fit a model to a single percentage (dependent) variable, Score. Unfortunately, I know there will be serious collinearity between several of the variables. For variable selection for interpretation purposes, they construct many (e.g., 50) RF models, they introduce important variables one by one, and the model with lowest OOB error multicollinearity meaning rate is selected for interpretation and variable selection. Irrespective of the clustering algorithm or linkage method, one thing that you generally follow is to find the distance between points. Keeping variables which are highly correlated is all but giving them more, double the weight in computing the distance between two points(As all the variables are normalised the effect will usually be double).

Should one be concerned about multi-collinearity when using non-linear models?

But if the 2 predictors are highly correlated, it’s unlikely that either will add to what’s already provided by the other. There is no rule against including correlated predictors in a Cox or a standard multiple regression. In practice it is almost inevitable, particularly in clinical work where there can be multiple standard measures of the severity of disease.

SEM: Collinearity between two latent variables that are used to predict a third latent variable

• What to do if you detect problematic multicollinearity will vary on a case by case basis.
• A unique set of coefficients can’t be identified in this case, so R excludes one of the dummy variables from your regression.
• You could also compare the 2 models differing only in which of the 2 predictors is included with the Akaike Information Criterion (AIC).
• The L0 penalty then favours sparsity (ie small models) whilst the L2 penalty regularizes collinearity.

If you run a model including both predictors on multiple bootstrap samples, you might well find that only 1 of the 2 is “significant” in any one bootstrap, but the particular predictor found “significant” is likely to vary from bootstrap to bootstrap. This is an inherent problem with highly correlated predictors, whether in Cox regression or standard multiple regression. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. If the non-linear model is tree-based model, then you shouldn’t consider it serious. But for xgboost, it will choose anyone of them, and use it until the last tree build. Old thread, but I don’t agree with a blanket statement that collinearity is not an issue with random forest models.

Firstly, as pointed out by Anony-mousse, k-means is not badly affected by collinearity/correlations. In addition, regularization is a way to “fix” Multi-collinearity problem. My answer Regularization methods for logistic regression gives details. Say we have a binary classification problem with mostly categorical features.

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In such cases, you would probably be advised to drop one or more variables instead. One thing to note is that although calculating a VIF is easy in a standard regression and many packages/programs will do this automatically, it is not easy in a latent variable model. The calculation of VIF for a variable requires regressing it on all other predictors in the regression, which in a latent variable model means this has to be done in a latent variable model. As a result of this complexity, it is not surprising that this cannot be easily automated (and as far as I am aware has not been done). I want to run a cointegration test in the ARDL and VAR/VECM frameworks.

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Two of the variables that are different measures of the same thing. When included in separate models, both show a strong association with survival. So to answer your question following this logic, the notion that correlation implies multi-collinearity is incorrect, hence does not necessarily will cause multi-collinearity. And you should use proper statistical methods to detect those two individually. Connect and share knowledge within a single location that is structured and easy to search. There is a lot of material in the book about path modeling and variables selection and I think you will find exhaustive answers to your questions there.

Let us first correct the notion and widely belief of “highly correlated variables cause multi-collinearity”. Ive seen countless internet tutorials suggestion to remove correlated variables. First correlation and multicollinearity are two different phenomenon. Therefore, there are instances where there is high correlation but no multi-collinearity, and vice-versa (there is multi-collinearity but almost no correlation). There are even different statistical methods to detect those two.

Your dimensionality is. 100 variables is large enough that even with 10 million datapoints, I worry that k-means may find spurious patterns in the data and fit to that. You’ll artificially bring some samples closer together doing this, yes, but you’ll do so in a way that should preserve most of the variance in the data, and which will preferentially remove correlations. This way you avoid wrong estimates of coefficients due to multicollinear variables, and your p-values and standard errors are no longer biased. Run the Cox regression first with the standard predictor, then see whether adding your novel predictor adds significant information with anova() in R or a similar function in other software. Then reverse the order, starting with your novel predictor and seeing whether adding the standard predictor adds anything.

While the cluster centre position estimates weren’t that accurate, the cluster membership (i.e. whether two samples were assigned to the same cluster or not, which seems to be what the OP is interested in) was much better than I thought it would be. So my gut feeling earlier was quite possibly wrong – k-means migth work just fine on the raw data. If you want to work with subsets, it could make sense to start from checking whether all the variables are cointegrated pairwise. If no, you cannot tell whether the whole system is cointegrated or not.

However, assume that the features are ranked high in the ‘feature importance’ list produced by RF. As such they would be kept in the data set unnecessarily increasing the dimensionality. So, in practice, I’d always, as an exploratory step (out of many related) check the pairwise association of the features, including linear correlation. For example, if we have two identical columns, decision tree / random forest will automatically “drop” one column at each split. If you include all the possible categories as dummy variables plus an intercept, as R does by default, then you have a perfectly multicolinear system.

You may try recursive variable importance pruning, that is in turns to remove, e.g. 20% with lowest variable importance. For some reason, I found that the variables listed at the beginning of the equation end up being selected by the stepAIC() function, and the outcome can be manipulated by listing, e.g., Var9 first (following the tilde). I noticed recently that if I change the order of the players, I get different co-efficient values for each player. Finally, there could be some hybrid strategies based on the ideas above. The worst case scenario is that there is only one cointegrating vector which you will not find by doing analysis on subsets. However once one of them is used, the importance of others is significantly reduced since effectively the impurity they can remove is already removed by the first feature.