Description
density = exp(-0.5*(linearPredictor/scale)²)/(sqrt(2*pi)*scale); effect = coefficient*density.
Regression model terms depend on the response link, variable scale and the meaning of coefficients. A local marginal effect, elasticity or model mean computed from supplied parameters does not estimate those parameters or establish causality.
density = exp(-0.5*(linearPredictor/scale)²)/(sqrt(2*pi)*scale); effect = coefficient*density.
When to use this tool
Use Probit Density Scale One Parameter when checking one stated regression-model contribution.
How to use the tool and how it works
- Enter linearPredictor, coefficient, scale. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read density, effect. Use the output convention below.
Require positive scale. density = exp(-0.5*(linearPredictor/scale)²)/(sqrt(2*pi)*scale); effect = coefficient*density.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| linearPredictor | Linear Predictor | Required. Finite number. |
| coefficient | Coefficient | Required. Finite number. |
| scale | Positive output-length units per source-coordinate unit. | Required. Finite number; strictly above 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| density | Density | Required. Finite number. |
| effect | Effect | Required. Finite number. |
{
"input": {
"linearPredictor": 0,
"coefficient": 2,
"scale": 1
},
"output": {
"density": 0.3989422804014327,
"effect": 0.7978845608028654
}
}Limitations and assumptions
- This is a scaled-normal probit derivative term. Predictor, coefficient and scale must share a specified model basis; no parameter estimation, probability or uncertainty is returned.
- 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 model, suitable data and defensible identification for prediction, inference and causal interpretation.
References
Similar or alternative tools
- Omitted Variable Bias Supplied Covariance Term
bias = omittedEffect*covariance/includedVariance.
- Measurement Error Attenuation Factor Term
reliability = signalVariance/sum; expectedSlope = trueSlope*reliability.