Logistic regression is statistical technique helpful to predict
the categorical variable from a set of predictor variables.
3. WHY WE USE LOGISTIC ?
No assumptions about the distributions of the predictor
variables.
Predictors do not have to be normally distributed
Does not have to be linearly related.
When equal variances , covariance doesn't exist across the
groups.
4. TYPES OF LOGISTIC REGRESSION
BINARY LOGISTIC REGRESSION
It is used when the dependent variable is dichotomous.
MULTINOMIAL LOGISTIC REGRESSION
It is used when the dependent or outcomes variable has more
than two categories.
5. BINARY LOGISTIC REGRESSION EXPRESSION Y = Dependent
Variables = Constant 1 = Coefficient of variable X 1 X 1 =
Independent Variables E = Error Term BINARY
6. STAGE 1: OBJECTIVES OF LOGISTIC REGRESSION
Identify the independent variable that impact in the dependent
variable
Establishing classification system based on the logistic model
for determining the group membership
DECISION PROCESS
7. STAGE 2: RESEARCH DESIGN FOR LOGISTIC REGRESSION
8.
1 ) REPRESENTATION OF THE BINARY DEPENDENT VARIABLE
Binary dependent variables (0, 1) have two possible outcomes
(e.g., success & failure), true or false , yes or false.
Like yes =1 and no =0
Goal is to estimate or predict the likelihood of success or
failure, conditional on a set of independent variables.
9. 4. SAMPLE SIZE
Very small samples have so much sampling errors.
Very large sample size decreases the chances of errors.
Logistic requires larger sample size than multiple
regression.
Hosmer and Lamshow recommended sample size greater than
400.
10. 6. SAMPLE SIZE PER CATEGORY OF THE INDEPENDENT VARIABLE
The recommended sample size for each group is at least 10
observations per estimated parameters.
11. STAGE 3 ASSUMPTIONS
Predictors do not have to be normally distributed.
Does not have to be linearly related.
Does not have to have equal variance within each group.
12. STAGE 4: 1 . ESTIMATION OF LOGISTIC REGRESSION MODEL
ASSESSING OVERALL FIT
Logistic relationship describe earlier in both estimating the
logistic model and establishing the relationship between the
dependent and independent variables.
Result is a unique transformation of dependent variables which
impacts not only the estimation process but also the resulting
coefficients of independent variables .
13. 3. TRANSFORMING THE DEPENDENT VARIABLE
S-shaped
Range (0-1)
14. WHAT IS P? p = probability (or proportion)
15. What is the p of success or failure? Failure Success Total
1 - p p (1 - p ) + p = 1
16. What is the p of success or failure? Failure Success Total
250 750 = 1000
17. What is the p of success or failure? Failure Success Total
250/1000 750/1000 = 1000/1000
18. What is the p of success? Failure Success Total .25 .75
1
19. What is the p of success? Failure Success Total .25 = 1 - p
.75 = p 1 = (1 - p ) + p
20. WHAT ARE ODDS?
Odds are related to probabilities
The odds of an event occurring is the ratio of the probability
of that event occurring to the probability of the event not
occurring.
Odds of success = p of success divided by p of failure
omega () = p/(1-p)
21. What are the odds of success?
omega () = p /(1- p )
= .75/ (1 - .75)
= .75/.25 = 3
Failure Success Total .25 = (1 - p ) .75 = p 1 = (1 - p ) + p
22. WHAT IS AN ODDS RATIO?
The odds ratio compares the odds of success for one group to
another group.
Theta () = groupA = p A /(1- p A )
groupB p B /(1- p B )
23. HOW CAN WE COMPARE THE ODDS () OF MALES VERSUS FEMALES
Group Failure Success Total A (Male) 182 368 550 B (Female) 75 375
450 250 750 1000
24. HOW CAN WE COMPARE THE ODDS () OF MALES VERSUS FEMALES
Group Failure Success Total A (Male) 182/550 368/550 550/500 B
(Female) 75/450 375/450 450/450 250 750 1000
25. HOW CAN WE COMPARE THE ODDS () OF MALES VERSUS FEMALES
Group Failure Success Total A (Male) .33 .67 1 B (Female) .17 83 1
250 750 1000
26. HOW CAN WE COMPARE THE ODDS () OF MALES VERSUS FEMALES
Group Failure Success Total A (Male) (1 - p A ) = .33 p A = .67 1 B
(Female) (1 - p B ) = .17 p B = .83 1 250 750 1000
27. HOW CAN WE COMPARE THE ODDS () OF MALES VERSUS FEMALES
groupA = p A /(1-p A )
groupB = p B /(1-p B )
Group Failure Success Total A (Male) (1 - p A ) = .33 p A = .67 1 B
(Female) (1 - p B ) = .17 p B = .83 1
28. HOW CAN WE COMPARE THE ODDS () OF MALES VERSUS FEMALES
male = .67/.33
female = .83/.17
Group Failure Success Total Male .33 .67 1 Female .17 .83 1
29. HOW CAN WE COMPARE THE ODDS () OF MALES VERSUS FEMALES
male = .67/.33 = 2.03
female = .83/.17 = 4.88
Theta () = groupA / groupB
Group Failure Success Total Male .33 .67 1 Female .17 .83 1
30.
Theta () = group A / group B
male / female = 2.03 / 4.88
male / female = .4160
The odds that males succeeds compared to females are only .416
times that of females
How can we compare the odds () of males versus females
31. 4. ESTIMATING THE COEFFICIENTS
It uses the logit transformation.
The logistics transformation can be interpreted as the
logarithm of the odds of success vs. failure.
32. STAGE 5 INTERPRETATION OF THE RESULTS
33. LETS GO THROUGH AN EXAMPLE
34. It is calculating by taking by logarithm of the odd. Odd is
less then 1.0 will have negative logit value ,odd ratios have a
greater the 1.0 will have positive