
 Problems in moving from
quantitative (continuous) data to
qualitative (categorical) data
 The common case of a dichotomous
dependent variablevoting for candidates A or B.
 Standard regression produces a
linear probability model
 Coefficients are read as
probabilitiesincreasing or decreasing the
dependent variable.
 These estimates are unbiased
but inefficient, actually instable.
 They can range nonsensically
above 1.0 or below 0.
 Alternative, nonlinear forms for
probability exist.
 Logistic transformations of
proportions, p
 A logistic
probability unitlogitis
computed by taking the natural logarithm of the ratio
of p_{i} to its reciprocal
1p_{i}, that is L_{i} =
log_{e} (p_{i} /
1p_{i}).
 The resulting value, the
logit, is symmetrically distributed around the
central value of p=.50.
 When p=.50, the value of
the log =0.
 But as p departs from .5
in either direction, the corresponding logit values
depart from 0 (positive and negative) at an
increasing rate.
 Thus, as a dichotomous variable
becomes skewed in either direction, the nonlinear
function of the logistic transformation differs
dramatically from the linear function.
 Moreover, logit transformations
are undefined when p_{i} = 0 or
1.
 Knoke and Bohrnstedt (1994) graph
linear probability against logistic regression (p.
340):
