Item Information Function Peak Calculator
Explicit2PL logistic item information peak a²/4atθ=bwith no guessing/lapseandD=1. Not3PLpeak or independently fitted curve. Actual independently qualified instrument/cohort/matching units; no diagnosis, causal outcome, validated personal prediction or universal clinical cutoff.
Description
A two-parameter logistic item's information peaks when its correct-response probability is one half.
A two-parameter logistic item's information peaks when its correct-response probability is one half.1
Under the D=1, no-guessing convention the peak depends on discrimination alone. The calculation and input requirements are explained below.
When to use Item Information Function Peak Calculator
Enter positive calibrated two-parameter logistic discrimination.
How to use Item Information Function Peak Calculator 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 Item Information Function Peak Calculator.
- 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 |
|---|---|---|---|
| callerCalibratedTwoPlDiscrimination | Caller Calibrated Two Pl Discrimination. Use the units and matching context stated in the calculation below. | number | Required; strictly positive; finite; other constraints below |
Enter positive calibrated two-parameter logistic discrimination. Return its square divided by four as information at theta equal to item difficulty, under D=1 and no guessing or lapse.
peakInformation=a^2/4 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.value | Numeric result under the formula and output units explained above. | number |
{
"input": {
"callerCalibratedTwoPlDiscrimination": 2
},
"output": {
"result": {
"value": 1
}
}
}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 Wright Map Item Position Lookup for a complementary operation: A Wright map places person measures and item locations on a common calibrated scale.
Use Rasch Item Difficulty Logits Calculator for a complementary operation: A restricted Rasch difficulty estimate transforms an observed correct-response fraction into logits.
References
Similar or alternative tools
- Wright Map Item Position Lookup
A Wright map places person measures and item locations on a common calibrated scale.
- Rasch Item Difficulty Logits Calculator
A restricted Rasch difficulty estimate transforms an observed correct-response fraction into logits.