Description
adjacentLogOdds = discrimination*(ability-stepDifficulty); odds = exp(adjacentLogOdds).
Item-response models link a latent ability scale to response probabilities, odds and information. Parameters must share the intended calibrated scale, and one item or category term is different from a full test model or parameter estimate.
adjacentLogOdds = discrimination*(ability-stepDifficulty); odds = exp(adjacentLogOdds).
When to use this tool
Use Partial Credit One Step Logit Term when checking one supplied item-response model term.
How to use the tool and how it works
- Enter ability, stepDifficulty, discrimination. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read adjacentLogOdds, odds. Use the output convention below.
Require positive discrimination. adjacentLogOdds = discrimination*(ability-stepDifficulty); odds = exp(adjacentLogOdds).1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| ability | Ability | Required. Finite number. |
| stepDifficulty | Step Difficulty | Required. Finite number. |
| discrimination | Discrimination | Required. Finite number; strictly above 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| adjacentLogOdds | Adjacent Log Odds | Required. Finite number. |
| odds | Adjacent-category odds from one supplied step logit, not normalized response probability. | Required. Finite number. |
{
"input": {
"ability": 2,
"stepDifficulty": 1,
"discrimination": 1
},
"output": {
"adjacentLogOdds": 1,
"odds": 2.718281828459045
}
}Limitations and assumptions
- This is one adjacent-category step term, not a normalized category probability or complete partial-credit model. Parameter calibration and model suitability are not established.
- Inputs must satisfy both the field types and the cross-field conditions above. Invalid input causes an error; a successful false flag or documented placeholder is a different result.
- Numeric calculations use binary floating point unless exact decimal-integer arithmetic is explicitly stated. No hidden measurement tolerance or decimal rounding is added; nonfinite or out-of-contract results are rejected. Numeric signed-zero results are exported as zero.
Alternative or Complementary methods
Use a fitted, validated measurement model with appropriate item and population evidence for interpretation of ability or test precision.
References
Similar or alternative tools
- Item Response Rasch Logit One Point
Calculate a dichotomous Rasch response probability from supplied ability and item difficulty.
- Test Information One Item Term
information = probabilityDerivative²/[probability*(1-probability)].