Compile logistic1 Idrees waris IUGC
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- 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 ?
- 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
- 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
- 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 )
- 28. HOW CAN WE COMPARE THE ODDS () OF MALES VERSUS FEMALES
- male = .67/.33
- female = .83/.17
- 29. HOW CAN WE COMPARE THE ODDS () OF MALES VERSUS FEMALES
- male = .67/.33 = 2.03
- female = .83/.17 = 4.88
- Theta () = groupA / groupB
- 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
- 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
- Calculation of logistic value :
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