Lecture 6 - Binary Logistic Regression

Question 1

Logistic Regression is…?

Answer 1

….a modified form of the linear regression framework we have learned about so far. Logistic regression modifies the output from the linear regression model to transform it from a linear line to a sigmoidal curve, which has bounds of 0-1. Normal linear regression does not have bounds and in theory can run to infinity in either direction.

Question 2

The point of logistic regression is…?

Answer 2

…to model a criterion variable which is binary i.e. one that can only take on one of two values. Just like in linear regression, the predictor variables can be continuous or categorical, and multiple predictors are fine.

Question 3

The output from a logistic regression is usually interpreted as…?

Answer 3

…providing a probabilistic ‘guess’, based on the predictor variable scores, as to whether the criterion variable will be a 0 or a 1. So, if for a given person the output of the model is 0.9, this can be considered a 90% guess that that individual has a ‘1’ on the criterion variable.

Question 4

In the SPSS output, where is the difference in -2LL between the model and model without predictors?

Answer 4

In the Omnibus table, under chi-square.

Question 5

In the SPSS output, where is the equivalent of SSE-left, but for -2LL, between the model and model without predictors?

Answer 5

In the Model Summary table, under -2 log-likelihood.

Question 6

What is the Likelihood ratio?

Answer 6

The difference in -2LL between the model and model without predictors.

Question 7

What is the name of the equivalent for Likelihood ratio in linear regression?

Answer 7

SSE-reduced.

Question 8

Using the SPSS output from Logistic regression. How can you calculate the -2LL of the model with no predictors (the equivalent of SSE-total)?

Answer 8

Add the likelihood ratio from the Omnibus table with the -2LL (SEE-left equivalent) from the Model Summary table.

Question 9

What is the -2LL?

Answer 9

-2 Log Likelihood. It is -2 multiplied with the Log likelihood.

Question 10

Why do we use -2LL and not only the Log Likelihood?

Answer 10

Because the -2LL has a known distribution, the chi-square distribution, making it possible to compare two values of -2LL and calculate a p-value for the difference between these two values.

Question 11

How do you calculate Hosmer & Lemeshow’s r^2?

Answer 11

(Likelihood ratio) / (-2LL of the model with no predictors )

Question 12

What does the Likelihood ratio divided by -2LL of the model with no predictors calculate?

Answer 12

Hosmer & Lemeshow’s r^2

Question 13

What does Hosmer and Lemmeshows r^2 mean?

Answer 13

What proportion of -2LL we reduced by including predictors in the model

Question 14

In the “Variables in the Equations” table, what does the “B” column denote?

Answer 14

The b0(bottom) and b1(top) of the model.

Question 15

What is the “Wald” number/value and how is calculated in logistic regression?

Answer 15

Wald is a measure that can be thought of as the equivalent to the t-value in linear regression. It compares a predictor’s b1 to the predictor’s SE (being the “b1” of the no-predictor model. This generates a p-value. Wald is calculated by:

(b1 for the predictor / SE for the predictor) ^2 = Wald

Question 16

Formula for odds?

Answer 16

Odds=P/(1-P) P = probability

Question 17

Formula for probability from odds?

Answer 17

Probability=Odds/(1+Odds)

Question 18

what is Exp(B)

Answer 18

Exp(B) tells us how much the odds of Y go up/down for every 1 increase in X.

Question 19

How do you get from the probability of Y when X = 9.0 to the probability of Y when X = 10.0, using calculations involving odds?

Answer 19

1. Convert the probability of Y when X = 9.0 into Odds.
2. Apply Exp(B)(10-9) to the Odds:
   ((10-9)Exp(B)*Odds) = New Odds
3. Convert New Odds back to probability

Question 20

When would a “Chi-square test” be used in traditional psychology?

Answer 20

When you have BOTH a binary criterion variable AND a Binary predictor.

Question 21

When can Chi-square tests NOT be used?

Answer 21

Chi square can’t handle a continuous predictor variable, or multiple predictors, so in that situation students would then be taught to use logistic regression

Question 22

What is the general linear model called after it has been transformed?

Answer 22

the generalized linear model

Question 23

Name two advantages of using -2LL instead of SSE as a measure of goodness of fit.

Answer 23

1. -2LL can be compared directly to another -2LL. When using SSE, we first have to calculate F.
2. Using -2LL allow us to compare models with the same number of predictors, which is much harder to do using SSE or F-values.

Question 24

What is the validity of that measurement tool?

Answer 24

to what extent the tool is measuring what we really want to measure, rather than something else

Question 25

what are Nuisance Variables?

Answer 25

things that we do not want to measure but also affect how people respond to our measurement tools.

Question 26

Describe Nominal Data

Answer 26

Options have:
No order
No specific interval
No true zero

e.g. colours, gender, ethnicity

Question 27

Describe Ordinal Data

Answer 27

Options have:
- Order

(No specific interval)
(No true zero)

e.g. 1st 2nd 3rd (race positions)

Question 28

Describe interval Data

Answer 28

Options have:

• Order
• Specific interval

(No true zero)

eg. likart scale: bad—neutral—good

Question 29

Describe Ratio Data

Answer 29

Options have:

• Order
• Specific interval
• True zero

e.g. 0-100%, reaction time.

Question 30

How does the public often interpret interval scales like a “5-star system”?

Answer 30

Public interpret these points as ordinal rather than interval data. 5 means good, not perfect, and 4 means something is wrong, not almost perfect. Cultures of what each point on the scale ‘means’ can develop.

Question 31

What type of test needs to be used to interpret ordinal data?

Answer 31

non-parametric tests