Lecture 4: Linear and logistic regression

Question 1

What is the difference between logistic and linear regression?

Answer 1

Linear regression: DV needs to be continuous, IV can be nominal or continuous
Logistic regression: DV needs to be nominal while IV can be nominal or continuous

Question 2

What is b0?

Answer 2

the expected DV at the average IV

Question 3

What is b1?

Answer 3

the difference in the expected DV if IV increases by 1

Question 4

When is centring used?

Answer 4

If there are a lot of values around the 0 point on the x axis. Centring is subtracting the mean from every score of a variable, so the new variable will have an average of 0-> in interpretation say average instead of 0

Question 5

What is the baseline model?

Answer 5

It is the model without the predictor, so it is the mean model
y(i)= b0 + error(i)

Question 6

What does linear regression compare?

Answer 6

The model with the predictor compared to the mean model

Question 7

What are the linear regression steps?

Answer 7

1. Check whether the whole model is better than the mean model using ANOVA
2. If more predictors, is the extended model better than the previous model using model summary
3. Interpret the individual predictors by looking at the coefficients

Question 8

What are the different methods to enter multiple predictors?

Answer 8

Enter (confirmatory) which is always used in this course
- predictors entered all in once or in blocks (hierarchical)
- researcher determines order
Or can use stepwise (exploratory)
- predictors entered based on correlations
- SPSS determines the order

Question 8

What is b2?

Answer 8

the difference in expected DV between the two conditions for the other predictor while the predictor remains constant

Question 9

How is each model being compared?

Answer 9

1. Model 1 and 2 compared to mean model
2. Model 1 with mean model, model 2 with model 1

Question 10

How to look at SPSS output?

Answer 10

1. Check ANOVA for any significant output
2. Check model summary for any significant output

Question 11

How can you determine how good the model is?

Answer 11

By measuring the fit of the model in linear regression. R^2 is the amount of explained variance in the dependent variable by the predictors. Can interpret by % of extra variation on top of the previous model.

Question 12

What are the rules of thumb for R^2?

Answer 12

• R2 simple regression: .01 = small, .09 = medium, .25 = large
• R2 multiple regression:.02 = small, .13 = medium, .26 = large

Question 13

What is the standardized coefficient beta?

Answer 13

effect of predictor on dep.
variable when both predictor ánd dep. variable are standardized, and allows u to compare the different predictors in the model

Question 14

How to report all aspects of the model?

Answer 14

Model with only one predictor was….
The model with 2 predictors and significant and better/worse
How much variation did the predictors explain
Did the predictors predict the DV while the other remains constant?

Question 15

What is logistic regression?

Answer 15

The logistic function of b0 + b1*x(i)

Question 16

What is p in this case?

Answer 16

probability (P) that the outcome (y=1) occurs at a certain
value of the predictor (x) for subject i. P can vary between 0 (= very unlikely the outcome (y=1)
occurs) and 1 (= very likely the outcome (y=1) occurs)

Question 17

What are the different models that SPSS fits?

Answer 17

1. fit of the most simple model
2. fit of model with the predictor with predictor
3. comparison model fit with predictor with baseline model fit
   -> if model with predictor is less inaccurate than the baseline model then it should be included in the model

Question 18

What are the steps of logistic regression?

Answer 18

Step 1: is the extended model less accurate than the previous model?
Step 2: interpreting the individual predictors by providing direction of the effect of the individual predictors

Question 19

What is the log likelihood (LL)?

Answer 19

The amount of unexplained info after model fit. The larger the LL, the worse the model fits.

Question 20

What is -2LL?

Answer 20

Log likelihood multiplied by -2, which compares the model with the predictor with the baseline model. The distribution is similar to chi-squared test distribution. X2= -2LL (baseline)- (-2LL model)

Question 21

How to interpret the classification table?

Answer 21

That either the baseline or the predictor model predict x% correct

Question 22

How to interpret the iteration history?

Answer 22

Look at the final iteration and interpret the log likelihood, the fit model is less/more inaccurate than the baseline model

Question 23

What is the interpretation of exp(b)?

Answer 23

change in odds of the outcome (probability of outcome
(y=1)/probability of no outcome (y=0)) if predictor increases by 1
Exp(b)= 1 which means no effect of the predictor. Exp(b)>1 means that the odds outcome increases with the increase predictor. Exp(b)<1 means that the odds outcome decreases with the increase predictor

Question 24

What is the equation for multiple logistic regression?

Answer 24

P(y) = f{b0 + b1x1(i) + b2x2(i)} + error(i)
This is when 2 blocks are used to test how much extra variation one predictor explains compared to another

Question 25

What do the omnibus tests represent?

Answer 25

Step= difference with the baseline model
Model= the difference with the previous model which can be the baseline model or the model looking at only one predictor

Question 26

How can the predictors be interpreted?

Answer 26

Chance of recovery vs. no recovery increases by a factor of 1.71 if
working memory increases by 1

Question 27

How can you report all the linear regression output?

Answer 27

The model with benzodiazepines significantly predicted change in panic symptoms, F(1, 50) = 4.72, p = .035, R2 = .09. When therapeutic relationship was added to the
model, the model remained significant, F(2, 49) = 12.69 , p
< .001, R2 = .34, and significantly better than the model with benzodiazepines only, F(1, 49) = 18.96, p < .001, DR2 = .26.
The use of benzodiazepines and therapeutic relationship together explained 34% of the variation in change in panic symptoms. This is a large effect.
Benzodiazepines at pretest significantly predicted treatment success, b = -3.33, t(49) = -3.26, p = .002. For subjects who use benzodiazepines, the expected change in
panic symptoms was lower (and thus less treatment success) than for people who do not use benzodiazepines, if the therapeutic relationship remains constant.
Therapeutic relationship significantly predicted treatment success, b = 0.78, t(49) = 4.35, p < .001. The better the therapeutic relationship, the larger the expected change in panic symptoms (and thus more treatment success), if the use of benzodiazepines remains constant.

Question 28

How can you report logistic regression output?

Answer 28

Catastrophic cognitions: b = 0.49 and Exp(B) = 1.62. The chance of a diagnosis versus no diagnosis at posttest increases with a factor of 1.62 when catastrophic cognitions
increase by 1. In other words, the chance of a diagnosis versus no diagnosis at posttest increases if catastrophic cognitions at pretest are higher.
Social functioning: b = -1.42 and Exp(B) = 0.24. The chance of a diagnosis versus no diagnosis at posttest increases by a factor of 0.24 for people with high versus low social functioning at pretest. In other words, the chance of a diagnosis versus no diagnosis at posttest decreases for people with high versus low social functioning.