compile logistic1

LOGISTIC REGRESSION IDREES WARIS 3095:

LOGISTIC REGRESSION IDREES WARIS 3095

Logistic Regression:

Logistic Regression Logistic regression is statistical technique helpful to predict the categorical variable from a set of predictor variables.

Why we use logistic ?:

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. 3

Types of logistic regression :

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.

Binary logistic regression expression:

Binary logistic regression expression Y = Dependent Variables ß ˚ = Constant ß 1 = Coefficient of variable X 1 X 1 = Independent Variables E = Error Term BINARY

Stage 1: Objectives Of logistic regression:

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

Stage 2: RESEARCH DESIGN FOR LOGISTIC REGRESSION:

Stage 2: RESEARCH DESIGN FOR LOGISTIC REGRESSION

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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.

4. SAMPLE SIZE :

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.

6. SAMPLE SIZE PER CATEGORY OF THE INDEPENDENT VARIABLE :

6. SAMPLE SIZE PER CATEGORY OF THE INDEPENDENT VARIABLE The recommended sample size for each group is at least 10 observations per estimated parameters.

stage 3 ASSUMPTIONS:

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. 11

Stage 4: 1. Estimation of logistic regression model assessing overall fit:

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 .

3. Transforming the dependent variable:

3. Transforming the dependent variable S-shaped Range (0-1)

What is p?:

What is p? p = probability (or proportion)

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Failure Success Total 1 - p p (1 - p ) + p = 1 What is the p of success or failure?

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Failure Success Total 250 750 = 1000 What is the p of success or failure?

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Failure Success Total 250/1000 750/1000 = 1000/1000 What is the p of success or failure?

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Failure Success Total .25 .75 1 What is the p of success?

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Failure Success Total .25 = 1 - p .75 = p 1 = (1 - p ) + p What is the p of success?

What are odds?:

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 (ω) = p/(1-p)

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Failure Success Total .25 = (1 - p ) .75 = p 1 = (1 - p ) + p What are the odds of success? omega (ω) = p /(1- p ) ω = .75/ (1 - .75) ω = .75/.25 = 3

What is an odds ratio?:

What is an odds ratio? The odds ratio compares the odds of success for one group to another group. Theta (θ) = ω groupA = p A /(1- p A ) ω groupB p B /(1- p B )

How can we compare the odds (ω) of males versus females:

Group Failure Success Total A (Male) 182 368 550 B (Female) 75 375 450 250 750 1000 How can we compare the odds (ω) of males versus females

How can we compare the odds (ω) 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 How can we compare the odds (ω) of males versus females

How can we compare the odds (ω) of males versus females:

Group Failure Success Total A (Male) .33 .67 1 B (Female) .17 83 1 250 750 1000 How can we compare the odds (ω) of males versus females

How can we compare the odds (ω) 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 How can we compare the odds (ω) of males versus females

How can we compare the odds (ω) 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 How can we compare the odds (ω) of males versus females ω groupA = p A /(1-p A ) ω groupB = p B /(1-p B )

How can we compare the odds (ω) of males versus females:

Group Failure Success Total Male .33 .67 1 Female .17 .83 1 How can we compare the odds (ω) of males versus females ω male = .67/.33 ω female = .83/.17

How can we compare the odds (ω) of males versus females:

Group Failure Success Total Male .33 .67 1 Female .17 .83 1 How can we compare the odds (ω) of males versus females ω male = .67/.33 = 2.03 ω female = .83/.17 = 4.88 Theta (θ) = ω groupA / ω groupB

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Theta (θ) = ω group A / ω group B ω male / ω female = 2.03 / 4.88 ω male / ω female = .4160 The odds that males succeeds compared to females are only .416 times that of females How can we compare the odds (ω) of males versus females

4. Estimating the coefficients:

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.

Stage 5 interpretation of the results :

Stage 5 interpretation of the results

Lets go through an example:

Lets go through an example

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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 :