Multicollinearity in Bayesian linear regression?

Comments

• eniseg2

  February 2020

  And what about autocorrelation?

  My approach so far has been to run a frequentist model that parallels the Bayesian one to check the assumptions...
• EJ

  February 2020

  Hi eniseg2,

  The problem of multicollinearity is a hard one. From looking at the individual models you can assess whether it is the case that high-probability models either include the one predictor, or the other, but not both. Of course the investigation starts with considering the scatterplot and the strength of the relation. If the predictors are highly collinear, and both are important, then the inclusion probabilities should remain near 0.5 (because in the models that matter, only one of the two collinear predictors is included).

  If you want to walk to royal road to address this issue you could think of using a network approach, or a SEM model. But that is a lot of extra work with models that are a lot more complicated.

  Cheers,

  E.J.
• Albert

  July 2023

  Hi there! When dealing with highly correlated predictors like literacy and years of education, it's important to consider the issue of multicollinearity in your linear regression analysis. Including both predictors in one regression may lead to inflated standard errors and difficulties in interpreting the individual effects of each predictor.

  Based on your Bayesian inclusion probability plot suggesting to only keep years of education, it seems that education years might be a stronger predictor for your outcome variable compared to literacy. In this case, you can remove literacy from the regression model to avoid multicollinearity and focus on the independent effect of years of education.

  Alternatively, if you have a strong theoretical basis or previous research indicating the importance of literacy, you can consider adding it to the null model as a separate analysis to explore its individual contribution to the prediction of cognitive functions.

  Remember to assess the variance inflation factor (VIF) to quantify the degree of multicollinearity between predictors. If the VIF values are high (typically above 5 or 10), it suggests substantial multicollinearity, and you may need to address it by selecting a single predictor or using alternative techniques such as principal component analysis.

  Best of luck with your analysis!

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• wmwgold

  May 19

  Hi there! When dealing with highly correlated predictors like literacy and years of education, it's important to consider the issue of multicollinearity in your linear regression analysis. Including both predictors in one regression may lead to inflated standard errors and difficulties in interpreting the individual effects of each predictor.

  • Based on your Bayesian inclusion probability plot suggesting to only keep years of education, it seems that education years might be a stronger predictor for your outcome variable compared to literacy. In this case, you can remove literacy from the regression model to avoid multicollinearity and focus on the independent effect of years of education.
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• photoroom

  May 19

  And what about autocorrelation?

  My approach so far has been to run a frequentist model that parallels the Bayesian one to check the assumptions...

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• Kerloosingh

  September 10

  In Bayesian linear regression, multicollinearity can be managed through the incorporation of prior distributions. These priors can regularize the coefficients, mitigating the impact of collinearity. This approach helps stabilize the estimates and improves model interpretability.

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• afsana

  September 27

  Multicollinearity in Bayesian linear regression can lead to inflated uncertainty in coefficient estimates, making it difficult to assess individual predictor effects. However, Bayesian priors can help stabilize estimates and mitigate these issues compared to traditional methods.

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