The BEAST of Bias

Question 1

What are outliers/influential cases?

Answer 1

An atypical case, which influences the beta values

Can pull the model down

Question 2

How do you detect outliers/influential cases?

Answer 2

Looking at residuals/deviation - predicted value will be far away from the observed value so large residual
Graphs - boxplots, histograms
Cooks distance - measures influence of a single case on the model, if bigger than 1 = problem
Standardised residuals

Question 3

Why can’t you detect an influential case using residuals?

Answer 3

Influential case has been so influential, that it has dragged it down so much so the residual is small

Question 4

What are the assumptions of the linear model?

Answer 4

Linearity and additivity
Spherical residuals - independent errors and homescadastic errors
Normality of something - residuals, sampling distribution

Question 5

What does linearity and additivity refer too?

Answer 5

The relationship between the predictor and outcome is linear, otherwise used the wrong model
Predictors should be added in

Question 6

How to check for linearity and additivity?

Answer 6

Graphs

Equation

Question 7

Most important assumption

Answer 7

Linearity and additivity

Question 8

What does spherical errors refer too?

Answer 8

Errors should be independent - not related to each other (autocorrelation)

Errors should be homoscadistic - variances should be consistent at different levels of the predictor variable

Question 9

What does violation of spherical errors mean?

Answer 9

B’s unviolated but not optimal

SE incorrect, so P and CI’s will be incorrect as they use SE

Question 10

How do you check for spherical errors?

Answer 10

Levene’s test - if significant, means HOV
Variances - similar size
Variance ratio - biggest variance divided by smallest
Graph of standardised (zresid) against predicted (spred) residuals
Durbin Watson - between 0-4 if independent

Question 11

What do graphs of zresid against zpred show?

Answer 11

Funnel shape - heteroscadistic

Sausage shape - non linear

Question 12

What does normally distributed refer too?

Answer 12

Normality of residuals - diff between observed and predicted value, b will be unbiased but other methods better

Normality of sampling distribution - 1.96 comes from normal dist so intervals will be wrong. P values associated with B assumes a normal distribution

Question 13

What is the central limit theorm?

Answer 13

As long as the sample is big enough, sampling distribution will be normal
only worry about normality in small samples

Question 14

Exploring normality

Answer 14

Graphs - histograms, box plots, pp-qq plots (if S shape, problem)

Numbers - skew and kurtosis, want them to be 0 (if above 2/2.5 = skewed)

Test: kolmogorov-smirnov K-S test - dont quant to use this

Question 15

Ways of correcting problems

Answer 15

SD based trim (twin values outside of 2SD from mean) - really bad idea

Transform data - creates more problems

Winsorizing - substitute outliers with hight value which isn’t an outlier

Robust estimation - 20% trim, M estimators, the bootstrap or adjust SE

Question 16

What is bootstrapping?

Answer 16

Takes samples loads of times, order them and uses these to determine limits between which 95% of scores fall, creates CI based on data not theory, don’t need to rely on normality

Question 17

Standardised residuals

Answer 17

95% of standardised residuals should lie between + or - 2
99 should lie between + or - 2.5
if 3 or more, outlier

Question 18

How to work out how many standardised residuals lie between 2/2.5?

Answer 18

Work out either 5% of the sample size or 1%, to see how many standardised residuals you can have

Question 19

What is multicollinearity?

Answer 19

Checking if 2 predictors correlate to highly

Question 20

How to check for multicollinearity?

Answer 20

Tolerance should be bigger than 0.2 or VIF smaller than 10

Question 21

When should you worry about normality?

Answer 21

With small samples