Building the Logit Spreadsheet, Page 1, Parameter Estimates:

The example here uses only a location, L, and scale, S, but the technique is general and can be used with more than one explanatory variable. Let x=log(cracksize) be the independent variable, and inspection outcome the dependent variable, with a logit link. Log10 of cracksize is used to be consistent with NDE engineering practice.

First, select two cells in which to place initial "guess" values of the link function parameters L and S. (These are in the upper right of Page 1 of the sample spreadsheet(), cells J6 and K6.) Use column A for the specimen number, and enter the data in the next two columns, the first containing ai and the adjacent column with the experimental outcome, 0 if crack ai was missed, 1 if it was found. Use the next three columns for xi=log( ai ), (xi-L)/S, and exp( (xi-L)/S ) in columns D, E, and F. Put the link (POD, in this example) in column G. Finally, make column H the lnlikelihood values (ln of equation 1). Since li = p when yi = 1, and li = (1-p) when yi = 0, it is easier to use an IF than to perform the two exponentiations and a multiplication required by equation 1. The formula for an individual lnlikelihood for row 6 is shown in Table 1 where column G contains POD evaluated using the current values of L and S and column C holds either a zero or one.