I have two variables. From these two variables, I want to produce one weight variable. The first (A) is a percentage, 0.0 - 1.0. The second variable (B) is a count, 0 to infinity. I want to weight the first variable by the second. For variable A, closer to 1.0 is considered negative and closer to 0.0 is positive. However, for variable B, closer to 0.0 is negative and approaching infinity (real max is probably ~2,000) is considered positive. I want to find observations that have the lowest of variable A and the highest of variable B as a "best" value and the inverse as a "worst" value.
When I use a simple weighted arithmetic mean, I produce the following the results:
| A | B | C |
|---|---|---|
| 0.4 | 100 | 40 |
| 0.3 | 100 | 30 |
| 0.2 | 100 | 20 |
| 0.1 | 100 | 10 |
| 0.4 | 20 | 5 |
| 0.3 | 20 | 6 |
| 0.2 | 20 | 0.4 |
| 0.1 | 20 | 0.2 |
Both the highest (40) and lowest (0.2) are not descriptive of necessarily the "best" or "worst" values. However, the value 10 (A = 0.1, B = 100) is the "best" value.
How can I adjust the variables so that maximum and minimum values are indicative of positive and negative?
Three methods come to mind:
Determine the "best" value then calculate the absolute difference from of each value in variable C from that value.
Calculate the percentiles for variable A and variable B. The top percentile (100) would be for the best variable in each category, the lowest value in variable A and the greatest value in variable B. I would then multiply the percentiles.
Invert the values in one of the variables. For example, the value in the 95th percentile would be the value for the observation at the 5th percentile. I would then use a simple arithmetic weight.
What method can be applied to weight the variable as described? Is there another method I should use? If yes, what is it and why?
Edit: Variable A is a wildfire risk index. Overall, it ranges from 0.0 to 1.0 with 1.0 being extremely high risk. However, for the area of study, the top value is around 0.7. Variable B is a the number of trees of a specific species of concern. Each observation in the table is a census block group.
