Calculating Relative Weights
The Policy PC program does a standard linear regression analysis. Predictors
are the cues and quadratic terms--(cue - mean)**2 (for those allowed to be
nonlinear). The relative weights are calculated using the formula on p. 282
Hammond, K.R., Stewart, T.R., Brehmer, B., and Steinmann, D. (1975). Social
judgment theory. In M.F. Kaplan and S. Schwartz (Eds.), Human Judgment and
Decision Processes: Formal and Mathematical Approaches. New York: Academic
An equivalent approach (not used by policy PC, but would give same results)
is described in the appendix of:
Stewart, T.R., Moninger, W.R., Grassia, J., Brady, R.H. and Merrem, F.H.
(1989). Analysis of expert judgment and skill in a hail forecasting experiment,
Weather and Forecasting, 4, 24-34.
The Policy PC program is not recommended for statistical analysis of judgments
because it is designed primarily for case presentation and rapid feedback
Relative weights can be calculated using any standard statistical package
and a spreadsheet by the following procedure:
1. Calculate raw regression weights
Do a standard multiple regression analysis. If you want nonlinear function
forms for any of the cues, include quadratic terms. It is a good idea to
subtract the mean of the cue from each cue value before squaring to obtain
the quadratic cue. If no quadratic function forms are used, go to step 3.
Otherwise, combined beta weights must be calculated.
NOTE: The use of quadratic functions of the cues has been standard for fitting
functions forms for 20 years, but there are better methods available now.
Quadratic functions often provide a poor representation, particularly when
the function forms are monotonic. We need to explore better ways of fitting
2. Calculate combined weights
The two regression coefficients from the regression equation obtained in
Step 1 for the linear and quadratic terms determine the function form for
the cue. In order to obtain a single weight for each cue, "combined weights,"
which are standardized regression weights for the function forms should be
computed. Combined weights can be obtained by using the raw regression weights
to transform the cue and its square into a new variable and then using the
new variable in a regression. The following calculation gives the same result
and does not require a new regression:
where the b is a raw regression weight, s is a standard deviation, y is the
judgment, the subscript 1 refers to the cue and the subscript 2 refers to
3. Calculate relative weights
Relative weights are calculated by simply adjusting the combined beta weights
to sum to 100 for each person's judgment. Since combined beta weights are
always positive, relative weights will be positive also.
Contributed by Tom Stewart (1/3/95)