INTRODUCTION 



The procedure discussed in this paper evolved from efforts to develop a model for 

 estimating the probability of mortality for an individual tree, as a function of indi- 

 vidual tree and crown characteristics. However, the algorithm discussed may be applied 

 to describe the relationship between dependent and independent variables when the de- 

 pendent variable is dichotomous. 



In mathematics, a dichotomous variable is one that may assume only one of two 

 distinct values. For estimating the probability of individual tree mortality, the 

 dichotomous dependent variable assumes the value 1 when a tree dies during the measure- 

 ment interval and otherwise assumes the value 0. The independent variables are diam- 

 eter at breast high (d.b.h.), crown ratio, crown width, tip character, and insect or 

 disease damage. 



A dichotomous dependent variable may pose difficulties in the analysis of data.— 

 The model frequently applied in this situation is a linear regression model of the form 



E(y\xi,...,x n ) = 6 + 81x1 +...+ 8 n x n 



where 



x. = ith independent variable {i = l,...,n) 



8- = Jth regression coefficient (j = 0,1,..., n) 



E(y I ,x n ) = P(y=l\x l , . . . ,x n ) 



A-major difficulty in using a linear regression model is that probabilities greater 

 than 1 or less than may occur. This is most likely to occur when an independent 

 variable assumes a value near or outside the limits of the initial data set. 



— This analysis is different from discriminant analysis, which is used to assign 

 individual observations to one of a finite number of classes. The analysis discussed 

 in this paper, however, is designed to estimate the probability that any given observa- 

 tion will assume one of two distinct classes. 



1 



