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What are some common pitfalls and best practices for regression modeling?

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Regression modeling is a powerful tool for data analysis, but it also comes with some challenges and pitfalls. In this article, we will explore some common issues that can affect the quality and validity of your regression results, and how to avoid or address them. We will also discuss how ANOVA can help you compare different regression models and test your hypotheses.

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1 Assumptions and diagnostics

Before you run a regression analysis, you need to check if your data meets some basic assumptions, such as linearity, independence, normality, and homoscedasticity. These assumptions ensure that your model is appropriate for your data and that your estimates are unbiased and reliable. To check these assumptions, you can use various diagnostic tools, such as scatterplots, residual plots, Q-Q plots, and tests of significance. If you find any violations of the assumptions, you may need to transform your data, remove outliers, or use a different type of regression.

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Stanley C.

Software Engineer at Google
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Outliers have a large impact on the fit of the regression. You can mitigate this impact by detecting points with large leverage and removing them from the data set. Likewise, transforming data can be used for both removing nonlinear effects and outliers.

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Fanda Yang

Sr. Quantitative Analyst
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It goes without saying that knowing what assumptions for what kind of model in what situation is important. For example, OLS for linear regression models does not require normality assumption to hold. Normality might not be relevant if the model is developed for prediction instead of inference.

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2 Multicollinearity and confounding

Another issue that can affect your regression model is multicollinearity, which occurs when two or more predictors are highly correlated with each other. This can make it difficult to interpret the effects of each predictor and inflate the standard errors of the coefficients. To detect multicollinearity, you can use the variance inflation factor (VIF) or the correlation matrix. To reduce multicollinearity, you can drop some predictors, combine them into a composite variable, or use regularization techniques. You also need to be aware of confounding variables, which are variables that influence both the predictor and the outcome, and can bias your estimates. To control for confounding, you can include the confounding variables as additional predictors, or use stratification or matching methods.

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Fanda Yang

Sr. Quantitative Analyst
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If you have a group of variables that measure relatively the same thing (i.e. GDP and unemployment rate are included in the model to control for the general economic conditions), use PCA to condense them into an index or two might also help with multicollinearity and maintain interpretability to some degree.

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3 Model selection and validation

Once you have a regression model that meets the assumptions and avoids multicollinearity and confounding, you need to evaluate how well it fits your data and generalizes to new data. There are many criteria and methods for model selection and validation, such as R-squared, adjusted R-squared, AIC, BIC, cross-validation, and bootstrap. These metrics and techniques can help you compare different models and choose the one that has the best balance between complexity and accuracy. You also need to test the significance and confidence intervals of your coefficients, and interpret them in the context of your research question and domain knowledge.

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Eric Qian

Data Science & Statistics | Sustainable Energy | Technology Development
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The key to this point is that the model must both fit to the training data and generalize to testing/validation sets. In practice, it is important to be prudent to both overfitting (i.e. fitting to the noise of the training set) and error (i.e. RMSE score, R^2, etc). To properly assess models, consider the bias-variance tradeoff such that we minimize total error, which incorporates bias (the error of the model) and variance (consistency of results to different data). This may be achieved with proper cross validation and hyperparameter tuning.

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4 ANOVA and regression

ANOVA and regression are closely related, as they both use the same underlying framework of the general linear model. ANOVA can be seen as a special case of regression, where the predictors are categorical variables and the outcome is continuous. ANOVA can help you test the overall effect of a categorical predictor, or the interaction effect between two or more categorical predictors, on the outcome. You can also use ANOVA to compare different regression models and test if adding or removing predictors significantly improves the fit of the model. To perform ANOVA, you can use the F-test, the ANOVA table, or the ANOVA function in your software of choice.

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Stanley Lazic

Co-founder & CSO @ Prioris.ai Inc. | Building Bayesian ML models
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When testing for an interaction it's important to consider the scale of the outcome: an interaction may be present when using the raw outcome values but not when using log-transformed values or calculating the percent change from baseline. Interpreting interactions is even harder when using generalised linear models. Some good references here: https://pubmed.ncbi.nlm.nih.gov/22069144/ https://pubmed.ncbi.nlm.nih.gov/36859791/

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5 Best practices and tips

To summarize, here are some best practices and tips for regression modeling: It is important to check the assumptions and diagnostics of your model and data, and address any violations or issues. Additionally, you should avoid multicollinearity and confounding, and use appropriate methods to detect and reduce them. Furthermore, you should evaluate and compare your model using various criteria and methods, and test and interpret your coefficients. ANOVA can be used to test the effects of categorical predictors and compare different models. Lastly, it is essential to report your methods, results, and limitations clearly and honestly, and acknowledge any sources of uncertainty or error.

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6 Here’s what else to consider

This is a space to share examples, stories, or insights that don’t fit into any of the previous sections. What else would you like to add?

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What are some common pitfalls and best practices for regression modeling?

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2

3

4

5

6

1 Assumptions and diagnostics

2 Multicollinearity and confounding

3 Model selection and validation

4 ANOVA and regression

5 Best practices and tips

6 Here’s what else to consider

Data Analysis

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What are some common pitfalls and best practices for regression modeling?

1

2

3

4

5

6

1 Assumptions and diagnostics

2 Multicollinearity and confounding

3 Model selection and validation

4 ANOVA and regression

5 Best practices and tips

6 Here’s what else to consider

Data Analysis

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