- Problems in moving from
quantitative (continuous) data to
qualitative (categorical) data
- The common case of a dichotomous
dependent variable--voting for candidates A or B.
- Standard regression produces a
linear probability model
- Coefficients are read as
probabilities--increasing or decreasing the
- These estimates are unbiased
but inefficient, actually instable.
- They can range nonsensically
above 1.0 or below 0.
- Alternative, nonlinear forms for
- Logistic transformations of
- A logistic
computed by taking the natural logarithm of the ratio
of pi to its reciprocal
1-pi, that is Li =
loge (pi /
- 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
- 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 pi = 0 or
- Knoke and Bohrnstedt (1994) graph
linear probability against logistic regression (p.