case diagnostics

Question 1

what do regression/model outliers have?

Answer 1

a large residual E^i

Question 2

E^i

Answer 2

discrepancy between predicted y value (y^i) and observed value (yi)

Question 3

how to calculate standardised residuals

Answer 3

divide E^i by the estimate of the standard deviation of residuals, and convert the residuals to z-score units (this calculation includes the potential outlier)
computed by rstandard() function in r

Question 4

how to calculate studentised residuals

Answer 4

divide E^i by the estimate of the standard deviation of the residuals excluding the case i
provides a version of standardised residuals excluding the outlier case
computed by rstudent() function in r

Question 5

high leverage cases

Answer 5

cases with an unusual value of predictor (xi) or a combination of predictor values
have the potential to influence the B^0 (intercept) or B^1 (slope) of the regression model
can increase x variance

Question 6

what values are used to assess leverage

Answer 6

hat values

Question 7

high influence cases

Answer 7

when a case has high leverage and is an outlier - this has a large influence on the estimation of regression models
can have a strong effect on B coefficients - so if we deleted it they would change
-> The degree of change is a way to judge the magnitude of influence

Question 8

what does cooks distance use for considering influence

Answer 8

combines leverage (hat values) with the outlying-ness to capture the influence
Di = outlying-ness * leverage)

Question 9

cook’s distance refers to…

Answer 9

the average distance the y^ values will move if a given case is removed
- if removing the case changes the predicted values a lot (moves the regression line), then that case is influencing our results
a single value which summarises the total influence of a case

Question 10

DFFit

Answer 10

difference between the predicted outcome value for a case with and without a case included

Question 11

DFbeta

Answer 11

difference between the value for a coefficient with and without a case included

Question 12

DFbetas

Answer 12

a standardised version of DFbeta
obtained by dividing by an estimate of the standard error of the regression coefficients with the case removed

Question 13

which diagnostics are used to look at linear models with 2+ predictors in more detail

Answer 13

DFFit, DFbeta, DFBetas

Question 14

what measures the influence of standard errors

Answer 14

COVRATIO

Question 15

COVRATIO

Answer 15

measure the effect of an observation on the covariance matrix of the parameter estimates
- an observation’s influence on standard error

Question 16

COVRATIO values and meanings

Answer 16

more than 1 = precision decreased, standard error increased by a case
less than 1 = precision increased, standard error decreased by a case

Question 17

what to do if identify an unusual case

Answer 17

try to find out why it is unsual as it is not a good idea to delete if it is not showing large influnce

Question 18

what to do if you find an error in data entry

Answer 18

an error could be a value outwith the plausible range
delete if it cannot be corrected

Question 19

what to do if the data is extreme but still legit

Answer 19

consider ways to reduce influence before deleting like windsorising
this could be due to model specification problems

Question 20

sensitivity analyses

Answer 20

used to check if results are similar irrespective of methodological decisions made and check if result patterns are similar

Question 21

what does it mean if results in sensitivity analyses are similar

Answer 21

results are not dependent on the methodological decisions
if they differ a lot, the results are a limitation of your research :(