Table 21.7 (adapted from Pampel, 2000) shows how values of pi are related to values of odds and values of the logit Li. To do this exercise, you will either need a calculator that has the natural log function or you can find a calculator that does this function online (e.g., at eri.gg.uwyo.edu/toolbar/calculator/natlog.htm).
a. Fill in the values in the empty cells in Table 21.7.
b. Consider the set of scores on pi. Do these scores satisfy the assumptions that are generally required for scores on a Y outcome variable in a multiple linear regression? In what way do these scores violate these assumptions?
c. An odds of 1.00 corresponds to values of p = _________ and (1 – p) = _________.
d. An odds of 1.00 corresponds to a logit Li value of _____.
e. Look at the column of scores for Li, the logit. Do these scores satisfy the assumptions that are generally required for scores on a Y outcome variable in a multiple linear regression? Can you see any way that these scores violate these assumptions?
f. Based on this table, what advantages are there to using Li, rather than pi, as the dependent variable in a logistic regression? You might want to graph the values in the last column of Table 21.7 to see what distribution shape they suggest.