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Logistic Regression. Subscribe.

Special form of regression in which the dependent variable is nonmetric, dichotomous (binary) variable..

Suppose we want to study the labor force participation (LFP) decision of adult males. Since an adult is either in the labor force or not, LFP is a yes or no decision. Hence, the response variable, or dependent variable, can take only two values, say, 1 if the person is in the labor force and 0 if he is not. In other words, the dependent variable is a binary, or dichotomous, variable. Labor economics research suggests that the LFP decision is a function of the unemployment rate, average wage rate, education, family income, etc. we do not have to restrict our response variable to binary variables only (two categories). It may be multiple-categories..

Identify the independent variables that impact group membership in the dependent variable..

Why we use logistic instead the discriminant?. When our data is from multivariate normal distribution we prefer to discriminant analysis. If this case is violated we tend to logistic regression..

It does not require any specific distributional form of the independent variables..

Applications of logistic Regression. Medical field Engineering Marketing Economics Social sciences.

Logistic regression contain. Causal relationship Medically: Do body weight, calorie intake fate intake and age have an influence on heart attack...? Biologically: Does the herbicides and oxygen level in water kill the plants..? Management: Do customer satisfaction, brand perception, price perception influence the purchase decision..? Forecasting Will a subject who smokes X cigarettes a day and works Y hours get lung cancer?.

If we choose the normal distribution as the appropriate probability distribution, than we can use the probit model..

Yi =βo+ β1X or Ii = βo+ β1X. where I is known as unobservable utility index(a latent variable)..

Consider a home ownership example.. Suppose Y=1 a family own a house and Y=0 it does not..

Model for the example. I i = β o+ β 1 X i Where X i is the income of the ith family. Now it is reasonable to assume that there is a critical level of the index, call it I i *, such that if I i exceeds I i * the family will own a house otherwise it will not..

Explanation. Subscribe.

Zi is the Stander normal vaiable. F is the stander normal CDF. P is the probability that an event will occur. The CDF of Normal Distribution is given by F(x) = fx_0æe-7 dz Replace X with latent variable F(li) = f!'oo d ß1+ß2Xi - F(li) = f-00.

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