Transcript of Compile logistic1 Idrees waris IUGC
- 1. LOGISTIC REGRESSION IDREES WARIS 3095
- 2. LOGISTIC REGRESSION
- Logistic regression is statistical technique helpful to predict
the categorical variable from a set of predictor variables.
- 3. WHY WE USE LOGISTIC ?
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- No assumptions about the distributions of the predictor
variables.
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- Predictors do not have to be normally distributed
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- Does not have to be linearly related.
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- 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.
- 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
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- Predictors do not have to be normally distributed.
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- Does not have to be linearly related.
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- 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
- 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
- 21. What are the odds of success?
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 )
- 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
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
Group Failure Success Total Male .33 .67 1 Female .17 .83 1
- 29. HOW CAN WE COMPARE THE ODDS () OF MALES VERSUS FEMALES
- 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
- 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
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- Calculation of logistic value :