Logistic Regression and Multilevel

Question 1

Binary logistic regression

Answer 1

Used when the dependent variable is binary. “Transforms” an S-curve into a linear output – the maximum (average) likelihood

Question 2

Z-test

Answer 2

Alternative to T-test. Means-based test, which is robust for most distributions (including binary).

Question 3

Coefficients (β)

Answer 3

Log-odds associated with a one-unit increase in the predictor variable.

Question 4

Pseudo R2

Answer 4

Indicates the proportion of variance explained by the model in logistic regression.

Interpretation: Similar to R² in OLS, but values are typically lower due to the nature of logistic models. The higher, the more variance explained

Cut-off values:
strong: pseudoR2 > 0.2
moderate: 0.1 < pseudoR2 < 0.2
weak: pseudo R2 < 0.1

Question 5

Odds -ratio exp(B)

Answer 5

Represents the change in odds of the dependent event occurring (e.g., success vs. failure) for a one-unit change in the independent variable.

If OR=2, this means the odds of the outcome occurring are twice as likely with a one-unit increase in the predictor.

Interpretation:
OR > 1: Increased odds of the event occuring
OR <1: Decreased odds of the event occuring
OR = 1: No effect

Cut-off values:
Strong effect: OR > 2 (indicates more than double the odds)
Moderate effect: 1 < OR < 2 (indicates increased odds)
Weak effect: OR < 1 (indicates decreased odds, with OR = 1 indicating no effect)

Question 6

Moderation

Answer 6

Moderation and mediation models are used when one is interested in a direct relationship

Moderation or interaction occurs when the effect of an independent variable
on a dependent variable varies according to the level of a third variable, termed as moderator variable, which interacts with the independent variable. However, the moderator must be unrelated to the independent variable.

In other words, the size of the effect of IV on DV depends on an additional variable.

In regression analysis, a moderator is typically assessed through an interaction term, which is created by multiplying the independent variable (IV) by the moderator variable (MV).

Example: Social support moderating stress and health.

Interpretation: if Β3=0.5, it suggests that for every one-unit increase in the moderator, the effect of the independent variable on the dependent variable increases by 0.5 units.

Question 7

Mediation

Answer 7

Moderation and mediation models are used when one is interested in a direct relationship

Mediation refers to an indirect effect of an independent variable on a dependent variable that passes through a mediator variable. The mediator must be related to the independent variable.

The indirect effect is either complete or partial.
Example: Job skills mediating education and income.

Question 8

Interaction models

Answer 8

Interaction models are statistical models that include interaction terms to assess whether the effect of one independent variable on the dependent variable changes at different levels of another independent variable. This is closely related to moderation.

Example: Training program’s effect on performance varies by experience level.

Question 9

Moderation chart

Answer 9

Parallel: moderator has no effect

Different slopes: moderator strengthen or weakens the effect

Lines cross: moderation changes both the strength and the direction of the relationship after the point of crossing