How do you interpret a plot of influence?
An influence plot shows the outlyingness, leverage, and influence of each case. The plot shows the residual on the vertical axis, leverage on the horizontal axis, and the point size is the square root of Cook’s D statistic, a measure of the influence of the point.
What does Cook’s distance tell us?
Cook’s distance is the scaled change in fitted values, which is useful for identifying outliers in the X values (observations for predictor variables). Cook’s distance shows the influence of each observation on the fitted response values.
What is a high Cook’s D value?
The measurement is a combination of each observation’s leverage and residual values; the higher the leverage and residuals, the higher the Cook’s distance. Cook’s distance showing item #26 as a potential outlier.
What is a good cook’s distance?
A general rule of thumb is that any point with a Cook’s Distance over 4/n (where n is the total number of data points) is considered to be an outlier. What is this? It’s important to note that Cook’s Distance is often used as a way to identify influential data points.
What is a high DFFITS value?
The DFFITS statistic is a scaled measure of the change in the predicted value for the ith observation and is calculated by deleting the ith observation. A large value indicates that the observation is very influential in its neighborhood of the X space. Large values of DFFITS indicate influential observations.
How do you assess influential observations?
The most common way to measure the influence of observations is to use Cook’s distance, which quantifies how much all of the fitted values in a regression model change when the ith observation is deleted.
What is the difference between Cook’s distance and DFFITS?
DFFIT is the difference in fit of removal of an individual observation whereas Cook’s D is the average change of a fit of an individual observation.
How does R calculate DFFITS?
How to Calculate DFFITS in R
- Step 1: Build a Regression Model.
- Step 2: Calculate DFFITS for each Observation.
- Step 3: Visualize the DFFITS for each Observation.
- Additional Resources.
What is an influential observation in stats?
In statistics, an influential observation is an observation for a statistical calculation whose deletion from the dataset would noticeably change the result of the calculation. In particular, in regression analysis an influential observation is one whose deletion has a large effect on the parameter estimates.
What are Studentized deleted residuals?
Studentized deleted residuals (or externally studentized residuals) is the deleted residual divided by its estimated standard deviation. Studentized residuals are going to be more effective for detecting outlying Y observations than standardized residuals.
What does DFFITS mean in statistics?
The DFFITS statistic is a scaled measure of the change in the predicted value for the i th observation and is calculated by deleting the i th observation. A large value indicates that the observation is very influential in its neighborhood of the X space. Large values of DFFITS indicate influential observations.
Which observations have a large DFFITS value?
The DFFITS graph shows that three observations have a large positive DFFITS value. The observations are the Ford Excursion, the Ford Ranger, and the Madza BB230. For these observations, the predicted value (at the observation) is higher with the observation included in the model than if it were excluded.
What is the difference between DFFITS and dfbetas?
The DFFITS statistic is very similar to Cook’s D, defined in the section “Predicted and Residual Values”. The DFBETAS statistics are the scaled measures of the change in each parameter \restimate and are calculated by deleting the ith observation:
What is the threshold value of a DFFITS value?
In this example, the threshold would be 0.5: We can sort the observations based on their DFFITS values to see if any of them exceed the threshold: We can see that the first five observations have a DFFITS value greater than 0.5, which means we may want to investigate these observations closer to determine if they’re highly influential in the model.