Week 1 - GLM

Question 1

3 things modelling consist of

Answer 1

X variables
Relationship among X variables (correlation)
Relationship among X and Y variables

Question 2

Regression Model

Answer 2

X variables are jointly and simultaneously related to Y

Are a linear weighted composite (Sum of X’s, weighted by what b is)

Assumption linearity (Straight relationship NOT Curvilinear - learn this later)

Predicted score and residual uncorrelated (Systematic and error are not correlated)

Relationship between X and Y not additive

Question 3

Basis of GLM

Answer 3

Model + error = data

Question 4

Error (Residual)

Answer 4

Part score leftover after systematic variation in X variable accounted for

Baseline to test the strength of X and Y variables in significance testing

Want error as small as possible (Should be if model is correctly specified)
- Should then only contain random/measurement error (Only happen if all systematic variation in Y is accounted for)

Not linearly related to the X’s
- uncorrelated to X’s and not accounted for by the model

Question 5

Additivity GLM

Answer 5

Utilised in hierarchical modelling

Question 6

GLM in Regression

Answer 6

Model = Systematic relation among X’s

Error = random, uncorrelated individual difference

Question 7

Important to consider in GLM regression

Answer 7

Specification of model

Mis-specification lead to less reliability and questioning whether the model is truly systematic

Importance of theory to highlight important factors

Question 8

What are the 4 stages of Box and Jenkins Linear Modelling

Answer 8

1) Model specification
2) Parameter estimation
3) Modelling Checking and fit assessment
4) Prediction

Question 9

1) Model Specification

Answer 9

Choose and specify constructs to be included in the model

Specification error the most serious you can make

• Leav out important variables or include varaibles that are irrelevant
• Every other error can be fixed but this one

Question 10

2) Parameter estimation

Answer 10

Deriving the F, R, b-weights

Question 11

3) Model Checking/ fit assessment

Answer 11

Rarely performed in social science

Look at the r2 (How much variacne accounted for by the model)

Question 12

4) Prediction

Answer 12

Never done in social science

Seek to predict new data with existing parameters

Does observed Y fit in with model of predictors and predicted relationship

Use data to test our prediction

Question 13

Incorrectly specified model

Answer 13

May contain systematic effect of a variable that has been left out of the model

Question 14

Consequences of incorrectly specified model

Answer 14

Inflate error

Inflate b-weights (Make there look like there is a bigger effect when in reality there is not)

Question 15

How to increase statistical control

Answer 15

Adding control predictors into the model to take their systematic variance out of the error term
- Variance that the control variable share with Y is partialed out (Other variables can exert a unique effect on the variance on Y whilst controlling for these nuisance variables)

Question 16

What are the three types of Multiple regression?

Answer 16

1) Simultaneous (Entry of all factors at once) (Forced entry)
2) Hierarchical (Uses additive properties of GLM to assess predicted X’s over several regressions)
3) Stepwise Regression (Used for data mining and marketing to come up with best predictors for a given sample)
- Use statistical rules and not theory
- Consecutively remove items from the model to lower the r2 to a predetermined amount

Question 17

What is b-weight?

Answer 17

Partial slope

Effect of That particular X on the outcome adjusting for every other X in the model

Question 18

What happens when predictors highly correlated?

Answer 18

Can partial each other out

Question 19

Model Comparison in Hierarchical

Answer 19

Compare models to explain Y

New predictor must account for part of Y not explained for by previous predictors in the nested model

Each new regression start with residualised Y outcome from the previous block

R2 become change in R2 across models (blocks)