it has found values for a and b which maximize LL. When we click on the Solve button we get a message that Solver has successfully found a solution, i.e. Our objective is to maximize the value of LL (in cell L14) by changing the coefficients (in cells O5 and O6). It is important, however, to make sure that the Make Unconstrained Variables Non-Negative checkbox is not checked. We now use Excel’s Solver tool by selecting Data > Analysis|Solver and filling in the dialog box that appears as described in Figure 2 (see Goal Seeking and Solver for more details). Cell L14 contains the value of LL using the formula =SUM(L4:L13) where L4 contains the formula =(B4+C4)*(J4*LN(K4)+(1-J4)*LN(1-K4)), and similarly for the other cells in column L. cell K4 contains the formula =1/(1+EXP(-O5–O6*I4)) and initially has value 0.5 based on the initial guess of the coefficients a and b given in cells O5 and O6 (which we arbitrarily set to zero).
Column K contains the values of each p i. Column J contains the observed probability of survival for each interval (copy of column F). We capture this information in the worksheet in Figure 1 (based on the data in Figure 2 of Basic Concepts of Logistic Regression).įigure 1 – LL based on an initial guess of coefficientsĬolumn I contains the rem values for each interval (copy of columns A and E).
Where y i is the observed value of survival in the ith of r intervals and y i = the fraction of subjects in the ith interval that survived). Since we are aggregating the sample elements into intervals, we use the modified version of the formula, namely Where y i is the observed value for survival in the ith interval (i.e.
The log-likelihood statistic as defined in Definition 5 of Basic Concepts of Logistic Regression is given by We start with Example 1 from Basic Concepts of Logistic Regression.Įxample 1 (Example 1 from Basic Concepts of Logistic Regression continued): From Definition 1 of Basic Concepts of Logistic Regression, the predicted values p i for the probability of survival for each interval i is given by the following formula where x i represents the number of rems for interval i. We now show how to find the coefficients for the logistic regression model using Excel’s Solver capability (see also Goal Seeking and Solver).
0 kommentar(er)
