STATISTICAL CRITERIA FOR 

 GOODNESS-OF-FIT 



When the dependent variable is dichotomous, mean square error (the customary 

 measure of goodness-of-fit for regression relationships) is not appropriate. The 

 definition of mean square error demonstrates its inappropriateness as a measure of 

 goodness-of- fit . 



MSE = l — — — 

 i=l N-r 



where N is the population size and r is the number of parameters to be estimated in the 

 regression, y^ is always either or l while y^ is a continuous variable in the range 

 (0<p£<l) . The following proof shows that as N increases, the limiting value for the 

 mean square error is l rather than 0, as is expected in most regression relationships. 



N N 

 When ¥ is a (0,1) variable, Y = I y./N = P and j (y . - I) 2 = NPQ 

 (Cochran 1963) . i=l t i=l 



in 



