1. Logistic regression
Who survived Titanic?

2. The sinking of Titanic
Titanic sank April 14th 1912 with 2228 souls 705 survived.
A dataset of 1309 passengers survived.
Who survived?

3. The data Sibsp is the number of siblings and/or spouses accompanying
pclass
survived
name
sex
age
sibsp
parch 1
Allen, Miss. Elisabeth Walton
female 29
Allison, Master. Hudson Trevor
male
0.9167 2
Allison, Miss. Helen Loraine
Allison, Mr. Hudson Joshua Creighton 30
Allison, Mrs. Hudson J C (Bessie Waldo Daniels) 25
Anderson, Mr. Harry 48
Andrews, Miss. Kornelia Theodosia 63
Andrews, Mr. Thomas Jr 39
Appleton, Mrs. Edward Dale (Charlotte Lamson) 53
Sibsp is the number of siblings and/or spouses accompanying
Parsc is the number of parents and/or children accompanying
Some values are missing
Can we predict who will survive titanic II?

4. Analyzing the data in a (too) simple manner
Associations between factors without considering interactions

5. Analyzing the data in a (too) simple manner
Associations between factors without considering interactions

6. Analyzing the data in a (too) simple manner
Associations between factors without considering interactions

7. Analyzing the data in a (too) simple manner
Associations between factors without considering interactions

8. Analyzing the data in a (too) simple manner
Associations between factors without considering interactions

9. Could we use multiple linear regression to predict survival?
Logistic regression
Response variable is defined between –inf and +inf
Response variable is defined between 0 and 1
Normal distributed
Bernoulli distributed

10. Logit transformation is modeled linearly
The logistic function

11. The sigmodal curve

12. The sigmodal curve
The intercept basically just ‘scale’ the input variable

13. The sigmodal curve
The intercept basically just ‘scale’ the input variable
Large regression coefficient → risk factor strongly influences the probability

14. The sigmodal curve
The intercept basically just ‘scale’ the input variable
Large regression coefficient → risk factor strongly influences the probability
Positive regression coefficient → risk factor increases the probability

15. Logistic regression of the Titanic data

16. Logistic regression of the Titanic data
Summary of data
Coding of the dependent variable
Coding of the categorical explanatory variable:
First class: 1
Second class: 2
Third class: reference

17. Logistic regression of the Titanic data
A fit of the null-model, basically just the intercept. Usually not interesting
The total probability of survival is 500/1309 = Cutoff is 0.5 so all are classified as non-survivers.
Basically tests if the null-model is sufficient. It almost certainly is not.
Shows that survival is related to pclass (which is not in the null-model)

18. Logistic regression of the Titanic data
Omnibus test: Uses LR to describe if the adding the pclass variable to the model makes it better. It did! But better than the null-model, so no surprise.
Model Summary. Other measures of the goodness of fit.
Classification table: By including pclass 67.7 passengers were correctly categorized.
Variables in the equation: first line repeats that pclass has a significant effect on survival. B is the logistic fittet parameter. Exp(B) is the odds rations, so the odds of survival is 4.7 ( ) times higher than passengers on third class (reference class)

19. Logistic regression of the Titanic data now adding family relations
‘3 or more’ is set as reference groups by SPSS

20. Logistic regression of the Titanic data now adding family relations
The model correctly classify 79.1% of the passengers

21. Logistic regression of the Titanic data now adding family relations
Basically all factors seems to affect the probability of survival.

22. How was it with age?
Linear associations are easy to model, because the factor enters the predictive value directly.
But it is not really look linear, maybe a third order polynomial?
Three new factors for age is calculated: first, second, and third order of the age divided by the standard diviation.

23. How was it with age?
The third-order age factor did not add significantly to the model.
By adding third order polynomial the model can correctly categorize 79.4 vs 79.1 before.
ParChild is no longer a significant factor and can be omitted from the model

24. Using the model to predict survival
Omitting the second and third order age and ParChild factors
What is the probability that a 25 year old woman accompanied only by her husband holding a second class ticket would survive Titanic?
z =
-0.589*(-5)/14.41
+1.718
+2.552 =

25. Analysing interaction of selected factors
pclass * sex, age * sex, pclass * Siblings/Parents
But the model does not converge…

26. Analysing interaction of selected factors
Collapsing the sibling/spouse number eradicated their mutual interaction

27. Is it realistic that Leonardo survives and the chick dies?