6. Regression - Categorical variables and BEYOND!!!

Question 1

For a variable with g levels, how many dummy variables do we need to capture all the levels?

Answer 1

g-1

Question 2

With dummy coded variables, what does the constant represent (assuming nothing else in model)?

Answer 2

The mean of the reference group - the score for someone who gets 0 on all variables.

Question 3

Do you have to control for type I error when using dummy coded variables in regression?

Answer 3

Nope.

Question 4

How must dummy variables be interpreted in conclusions?

Answer 4

As a mean difference.

Question 5

Is an interaction effect moderation or mediation?

Answer 5

Moderation. Relationship between X1 and Y depends on the level of –or is moderated by – X2

Question 6

What are the three steps in testing interactions?

Answer 6

1. Calculate an interaction variable
2. Run sequential MR with three predictors –original variables and interaction
3. Interpret either delta R square or b for the interaction

Question 7

What is the regression formula for an interaction?

Answer 7

Y=a+b1X1 +b2X2 +b3X1X2 +e

Question 8

What is mean-centring when it comes to continuous variables?

Answer 8

Subtracting the mean from each score.

Question 9

What are the two steps in calculating an interaction variable?

Answer 9

1. Mean-centre continuous variables

2. Multiply the two variables

Question 10

Why do you mean-centre?

Answer 10

It reduces multicollinearity.

Question 11

How do you interpret the constant with mean-centred variables?

Answer 11

Easier to interpret constant when variables are not mean-centred – otherwise the value is based on a mean of zero. Mean-centredness is only important for calculating interaction, so best use it just for that.

Question 12

Do you need to mean-centre z-scores to calculate an interaction?

Answer 12

Nope, they’re already mean-centred.

Question 13

How do you interpret an interaction between two continuous variables?

Answer 13

Well, you can say there is an interaction and it’s significant.

One other option is to break on of the variables into groups - e.g., high, medium and low ability.

Question 14

Which model should be interpreted, with or sans interaction?

Answer 14

Depends. If the interaction is significant, interpret that model (Model 2). If it’s not, interpret Model 1 and say you tested an interaction, but it was insignificant.

Question 15

What is polynomial regression?

Answer 15

Interaction between the continuous IV and itself. Effect of variable X on DV depends on level of variable X.

Question 16

How do you transform a variable to test polynomials? Three steps.

Answer 16

1. Mean centre the variable
2. Square it
3. Enter it as the last block in equation

Question 17

What’s the quadratic regression equation?

Answer 17

Y= a+b1X1 + b2X1 square + e

Question 18

If the quadratic regression coefficient is positive what shape does that indicate in the data?

Answer 18

Curve is u-shaped function

Question 19

If the quadratic regression coefficient is negative what shape does that indicate in the data?

Answer 19

Curve is inverted u-shaped function

Question 20

If quadratic regression coefficient is very small, what shape does that indicate?

Answer 20

Almost flat line.

Question 21

What does -3.8E-02 mean?

Answer 21

-3.8 x 10 to the power of -2

Question 22

What’s the difference between moderation and mediation?

Answer 22

Moderation = interaction
Mediation = indirect effect - mediating variable

Question 23

What’s the difference between partial and total mediation?

Answer 23

Partial mediation is when an introduced mediating variable partitions part of the direct effect of the IV on the DV.

Total mediation is when an introduced mediating variable accounts for all of the effect of the IV on the DV. The effect of the IV is completely explained by the new variable.

Question 24

What are the four assumptions underlying linear regression?

Answer 24

1. Dependent variable is a linear function of the predictors
2. Each observation is drawn independently
3. Homogeneity of variance
4. Errors are normally distributed with a mean of 0

Question 25

How do you test assumption of independence?

Answer 25

Look at the variability in box-plots, broken down by clusters.

Question 26

What is the risk of violating the assumption of independence?

Answer 26

You may underestimate the standard error, which increases risk of type I error.

Question 27

How do you test the assumption of linearity?

Answer 27

Plot residuals against predictor. Ask for Loess line. Should be straight.

Question 28

What is the assumption of homoscedasticity?

Answer 28

That variance of errors is not a function of the predictors, i.e. the variance of errors is constant at all values of X.

Question 29

How do you test the assumption of normality of errors?

Answer 29

Use a Q-Q plot:

X-axis - observed values of the residual
Y-axis - expected values of the residual if the residuals are normally distributed

If the scatter is close to the ideal line, residuals are normally distributed.

Question 30

How do you test for multicollinearity?

Answer 30

Test tolerance – from 0 to 1 –want score closer to 1.
Test VIF –1 or more, want closer to 1 –Keith says 10 is large. (If lots of predictors, can look for one VIF that stands out from others.)

Question 31

What are the two sources of error in classical test theory?

Answer 31

Method error (e.g. warm/cold testing room)
Trait error (due to characteristics of individual)

Question 32

What is the conceptual formula for reliability?

Answer 32

True score / True score + error

Proportion of observed score that is accounted for
by variance in true score

Question 33

What is the result in regression of assuming that error-laden predictors are free of error?

Answer 33

Underestimate the true effects of the predictors on the dependent variable. Lower R2 because more scatter of scores around regression line.

Question 34

Regression coefficients in simultaneous regression tell us about __________ effects.

Answer 34

Regression coefficients in simultaneous regression tell us about direct effects.

Question 35

Regression coefficient entered last into a sequential model tells us about the __________ effect of that variable.

Answer 35

Regression coefficient entered last into a sequential model tells us about the total effect of that variable.

Question 36

What effects does the variable entered last in the last model of sequential regression tell us?

Answer 36

About the total AND direct effect of that variable. It assumes the variable has no indirect effect (all shared variance already taken by other variables)

Question 37

What are rectangles and ellipses used to signify in structural equation modelling?

Answer 37

Rectangles - observed (manifest) variables

Ellipses - unobserved (latent) variables

Question 38

What are exogenous/endogenous variables?

Answer 38

Exogenous – have arrow coming out – causal
Endogenous – have arrow coming in –effect

If arrow coming out and another arrow coming in, then still Endogenous

Question 39

What is the name for residual in structural equation modelling?

Answer 39

Disturbance

Question 40

What is the formula for disturbance?

Answer 40

Square root of (1 - R square)

Question 41

What kind of regression do you run in SEM?

Answer 41

Simultaneous

Question 42

How do you calculate the indirect effect of a variable on a DV?

Answer 42

Multiply the variable’s effect on mediating variable BY the mediating variable’s effect on the DV.

Question 43

How do you calculate the total effect of a variable?

Answer 43

Add its direct effect and indirect effect.

Question 44

How do you know which model to report in sequential regression?

Answer 44

Report the final statistically significant model (based on the Model Summary Table). So if the last model is not stat. sig., report the penultimate one, assuming it is stat. sig.

Question 45

What is a recursive model?

Answer 45

A recursive model is one in which causal flow travels in only one direction - i.e. no feedback loops or reciprocal causes.