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 of

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 Press.

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 of results.

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 function forms.

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:

Formula is an image

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 its square.

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)

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