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Questions and Answers
What are some possible reasons to eliminate a case from a dataset?
Malfunctioning equipment, subjects wiggling in an fMRI scanner, new assistants running the experiment incorrectly, scoring or data entry errors, and severe interruptions in the experimental or survey process.
What is the justification for eliminating data without obvious reasons for doing so?
There is little justification for eliminating data without obvious reasons.
What is the approach of trimming data to balance the elimination of outliers?
Trimming the same number of data points from each side of the outcome variable distribution.
What is the purpose of Iteratively Reweighted Least Squares (IRLS) method?
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What is the effect of outliers on the precision of parameter estimates in a regression model?
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What is the role of regression diagnostics in outlier detection?
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What is the concept of trimmed means in statistics?
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What is the purpose of Yuen's method in statistics?
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How can outliers affect the performance of a regression model?
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What is the importance of checking for outliers in a dataset before fitting a model?
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Study Notes
Regression Model Analysis
- The "leave one case out" approach examines the influence of a single case on a regression model by analyzing how the model changes when that case is removed.
- The HAT diagonal (ℎ) can be used to calculate the results of removing each case without running multiple regressions.
Residual Analysis
- PRESS residuals are used to examine the influence of individual cases on a regression model.
- Internally Studentized Residuals standardize ordinary residuals by dividing them by their standard error, taking into account the leverage of associated predictors.
- The standard deviation of the ith residual is a function of leverage and variance of residuals in the population: 𝜎 𝜎 1 ℎ 𝑠 1 ℎ.
- Internally Studentized Residuals fall between 0 and 𝑁 𝐾 1, allowing for a sense of what is considered a small or large residual.
Outlier Analysis
- Outliers can be mitigated using a modified OLS estimation method that iteratively reweights and re-estimates the model until parameter estimates converge.
- This method can be applied to any Generalized Linear Model (GLM) like multiple regression, ANOVA, and ANCOVA.
Multicollinearity
- Multicollinearity occurs when there is a linear relationship between one predictor and the remaining predictors in a multiple regression model.
- The squared multiple correlations (R2) from each equation indicate the proportion of variance in a given predictor that is a perfect linear function of the other predictors.
Handling Outliers
- Outliers may be eliminated due to obvious errors or interruptions in the experimental or survey process.
- Alternatively, outliers can be handled using methods like Iteratively Reweighted Least Squares, which sets residuals exceeding a bound equal to that bound, or trimmed means, which balance data elimination from each side of the outcome variable distribution.
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Description
Learn how to examine influence in linear regression using the 'leave one case out' approach and PRESS residuals. This method helps to understand how the regression model changes when one case is removed, without having to run multiple regressions. Test your knowledge of linear regression analysis and its applications.
