Prospect Value Function Alpha/Beta Estimator
OLS log positive utility magnitudes versus log actual outcomes for ONE separately identified gain/loss branch, not infer bothα/βfrom one branch or validate subjective utility model.
Description
A power-value model becomes a straight line after logarithmic transformation.
A power-value model becomes a straight line after logarithmic transformation.1
Fitting one independently identified gain or loss branch estimates that branch's exponent and log scale. The calculation and input requirements are explained below.
When to use Prospect Value Function Alpha/Beta Estimator
Enter aligned positive outcome magnitudes and independently elicited positive values with at least two observations and nonzero variance in logged magnitude.
How to use Prospect Value Function Alpha/Beta Estimator and how it works
- Prepare the measurements or independently established model inputs described below, with matching units and observation scope.
- Enter the required fields and run Prospect Value Function Alpha/Beta Estimator.
- Read the result fields using the formula, output units, signs and ordering explained below.
- Correct any rejected inputs and rerun; interpret the result within the stated model and its assumptions.
| Input field | Meaning | Value type | Requirement |
|---|---|---|---|
| actualPositiveOutcomeMagnitudes | Actual Positive Outcome Magnitudes. Use the units and matching context stated in the calculation below. | array of number | Required; other constraints below |
| actualIndependentlyElicitedPositiveValues | Actual Independently Elicited Positive Values. Use the units and matching context stated in the calculation below. | array of number | Required; other constraints below |
Enter aligned positive outcome magnitudes and independently elicited positive values with at least two observations and nonzero variance in logged magnitude. Fit ordinary least squares to ln(value) versus ln(magnitude). Return slope as power exponent and intercept as log scale. Only the separately identified branch is fitted.
ln(value)=logScale+exponent*ln(magnitude) Apply the input ordering, units and branch conditions stated above.
| Output field | Meaning | Value type |
|---|---|---|
| result | Object containing the calculated or selected fields below. | object |
| result.fittedPowerExponent | Fitted Power Exponent. Interpret its unit, sign, order or availability flag as explained above. | number |
| result.fittedLogScale | Fitted Log Scale. Interpret its unit, sign, order or availability flag as explained above. | number |
{
"input": {
"actualPositiveOutcomeMagnitudes": [
1,
2,
4
],
"actualIndependentlyElicitedPositiveValues": [
1,
2,
4
]
},
"output": {
"result": {
"fittedPowerExponent": 1,
"fittedLogScale": 0
}
}
}Limitations and assumptions
The calculation uses the supplied observations and model inputs. It does not collect measurements, select a reference population or coefficient, or establish that the model applies to the actual case. The stated branch conditions and output units remain part of the result.
All fields require explicit values. Unexpected fields, wrong types, nonfinite numbers and sparse arrays are rejected. Alignment, bounds and supported-token rules are explained above; extremely large inputs or nonfinite results can also fail. Input errors differ from successful false comparisons, unavailable-domain flags and empty match lists.
Alternative or Complementary methods
Use Thurstone Case V Scale Value Calculator for a complementary operation: Thurstone Case V scaling converts pairwise preference probabilities to normal deviates.
Use Prelec Probability Weighting Gamma Estimator for a complementary operation: The one-parameter Prelec model relates objective probability to a decision weight.
References
Similar or alternative tools
- Thurstone Case V Scale Value Calculator
Thurstone Case V scaling converts pairwise preference probabilities to normal deviates.
- Prelec Probability Weighting Gamma Estimator
The one-parameter Prelec model relates objective probability to a decision weight.