mlr with outliers

Types of outliers and where to detect them

A. in y-space: Standardized residuals

B. in x-space: Mahalanobis distance

C. in xy-space: Cook’s distance

Outliers in y-space diagnosis and reason

Standardized residuals ▪ Poorly predicted cases (what is right and what is wrong)

Standardized residuals are normally distributed, rule of thumb

cases with |z| > 3.3 are outliers in y-space, only frequentist on JASP

Outliers in x-space diagnosis and why

Mahalanobis distance

▪ Extreme combination of scores on predictors ▪ Large value indicates outlier

x-space outliers rule of thumb and critical value

▪ Critical value depends on # predictor.

MDcritical ≈ 10 + 2×(# predictors)

Outliers in xy-space

seriously affect your conclusions!

Outliers in xy-space • Diagnosis and why

Cook’s distance ▪ Outlier on both predictors and dependent variable

Outliers in xy-space Rule of thumb

Cases with CD > 1 are outliers in xy-space

Y space

Standardized residuals

True problem if |z| > 3.3

X space

Mahalanobis distance

True problem if Mahalanobis distance is > 10.82 (or approximately 10 + 2 × 1 = 12)

XY space

Cook’s distance

True problem if CD > 1

Both: • X space • Y space

Mahalanobis distance for X and standardized residual for Y

Reasons for outliers

Typo or miscoded missing value

Member or no member of the intended population

If no observable errors, keep the observation in your dataset

Typo or miscoded missing value

Exclude impossible values • Fix unambiguous typos made by the researcher/coder • Investigate suspected typos made by respondent

Member or no member of the intended population

Student of 60 years old • If not member, remove from the analysis (and explain why)

If no observable errors, keep the observation in your dataset

Report on this potential outlier • May investigate if the outlier influences the conclusions