Neter and Maynes (1970) have cited several reasons for expecting a curvilinear 

 rather than a linear relationship when the dependent variable is dichotomous . Thus, 

 a nonlinear model appears to be preferable. 



Neter and Maynes have also questioned the meaning or usefulness of the correlation 

 coefficient when the dependent variable is dichotomous. When the true relationship is 

 nonlinear, the correlation coefficient does not apply. Even when the true relationship 

 is linear, the meaning of the correlation coefficient is not clear. Neter and Maynes 

 (1970) have demonstrated that when the dependent variable is dichotomous the correlation 

 coefficient can attain a value of 1 only when the independent variable is also dichoto- 

 mous. Thus, we are usually unable to judge an estimated correlation coefficient against 

 the maximum value 1 that indicates a perfect relationship. 



Walker and Duncan (1967) , and others have suggested the logistic function in place 

 of the linear model. This model has the form 



and restricts probability estimates to the closed interval [0,1]. 



Another difficulty in analyzing a dichotomous dependent variable is that we must 

 assume that the variance is nonhomogeneous . Thus, weighted regression n.ust be used to 

 estimate the regression coefficients. 



Walker and Duncan (1967) have suggested an algorithm and computer program for 

 fitting the logistic model. Modifications of the computer program and of the algorithm 

 to handle data sampled with unequal probability and four sample analyses are discussed 

 in this paper. 



The discussion of the algorithm will utilize matrix notation. Equation (1) is 

 rewritten in matrix notation as 



E(y \x 1 , . . . ,x ) = {1 + exp[-(3o + Si^i + 



. .+ B x )]} 



n n J 



-1 



(1) 



P = [1 + exp(-x'B)] 



-1 



(2) 



+ e 



where 



P = 



probability of the occurrence of an event 



P = 



estimate of P 



x 



vector of independent variables 



vector of regression coefficients 



£(0 



= o 



Var (e) = P(l-P) 



2 



