Summary Logistische Regressie | Statistics for Educational Science | KU Leuven | 2025/26

HS8: LOGISITIC REGRESSION
HC 14: LOGISITIC REGRESSION PART 1

Gewone regressie
- Voorspel je meestel kwaN/ continu uitkomst
- Bijvoorbeeld: Y =b0 +b1 X

Wat is logisitieke regressie?
- Uitkomst ≠ gewone score
- Uitkomst = WEL binair  d.w.z. 0 of 1

Wnr gebruik je logistieke regressie?
- Als DV slechts 2 mogelijke uitkomsten heeft (= dummies)


EXAMPLE
Cross-sectional data originating from the Panel Study on Income Dynamics, 1982.
- See Baltagi, B.H. (2002). Econometrics, 3rd ed. Berlin, Springer.
- Data from 595 participants

Research question:
- Do higher levels of education predict that an individual will be a white-collar worker, rather than a blue-collar worker?
o = P(y=1)  voorpelt dus eigenlijk kans dat regressie gebeurt

- IV/predictor: Years of education. = Numerical variable

- DV/criterion: occupation = Categorical variable with two levels:
 White-collar worker
 Blue-collar worker


DATA STRUCTURE AND NOTATION

Notation:
- i: index for "experimental unit" or observation (i = 1, ..., n)

- Yi : score on criterion (DV) for unit i :
o = is an indicator variable
o Bv. a 2-level categorical variable recoded into a binary dummy variable
o (0 = reference category, 1 = comparison category)

- Xi : score on predictor (IV) for unit i : can be a quantitative or categorical variable

Wanneer gebruik je logistische regressie dus?
- Wanneer je uitkomst binair is: betekenis: waarde 0 of 1.

Doel?
- ≠ voorspellen “hoeveel” y is
- = WEL voorspellen hoe groot de kans is op succes/falen?


DATA VISUALIZATION

,
, WHY NOT LINEAR REGRESSION?

Issue 1: Predicted values can fall outside [0,1]
- Bij gewone linear regression
o The expected value is: E(Y ∨X )=β 0 + β 1 X
o Can produce fitted values less than 0 or greater than 1
Y^ i= β^ 0 + β^ 1 X i
  This makes the model’s predictions invalid for binary outcomes.
  Bij LOGISTISCHE REGRESSIE heeft Y enkel waarde v 0 of 1

 Wat we eigenlijk willen voorspellen is:
o P(Y =1)
 Dus de kans dat iets zich voordoet
 Kansen moeten altijd tss 0 en 1 liggen

Issue 2: Violation of the normality assumption
- Linear regression assumes that the error terms are normally distributed
- With a binary outcome, residuals are calculated as follows:

o e^ i=
{
0−Y^ i
1−Y^ i

- ^ near 0 or 1:
When the model predicts Y  residuals are small
i
- ^ different from 0 or 1:
When the model predicts Y  residuals vary much more
i


o →Residuals vary as a function of the predicted values Y^ i

- ^ i follow the distribution of the predictor variables
The predicted values Y X i , which are not necessarily normal
distributed

Issue 3: Violation of homoscedasticity (constant variance)
- Linear regression assumes that the variance of the errors is constant across levels of the predictors.
o THIS MEANS:
 For a given value of X i  residuals should have same spread for all values of predictors (or fitted
values): ^ iand Y^ i
no pattern between e

- With a binary outcome, residuals are calculated as follows:

e^ i=
{
0−Y^ i
1−Y^ i

- ^ near 0 or 1:
When the model predicts Y  residuals are small
i
- ^ iis different from 0 or 1:
When the model predicts Y  residuals vary much more

o → the residual spread changes as fitted values change