Description
Calculate nested first-stage partial R-squared and an ordinary homoskedastic partial F statistic from supplied sums of squares.
Instrumental-variable and moment calculations compare supplied regressors, instruments, residuals and first-stage quantities. A local moment or relevance statistic does not establish exclusion, exogeneity, identification or a complete estimator.
Calculate nested first-stage partial R-squared and an ordinary homoskedastic partial F statistic from supplied sums of squares.
When to use this tool
Use Weak Instrument First Stage Partial Ratio when checking one supplied first-stage or moment contribution.
How to use the tool and how it works
- Enter restrictedSse, unrestrictedSse, instruments, residualDf. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read partialR2, partialF. Use the output convention below.
Require positive restrictedSse and unrestrictedSse with restricted >= unrestricted and positive whole instruments and residualDf. partialR2 = (restricted-unrestricted)/restricted; partialF = (restricted-unrestricted)*residualDf/(instruments*unrestricted).1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| restrictedSse | Restricted Sse | Required. Finite number; strictly above 0. |
| unrestrictedSse | Unrestricted Sse | Required. Finite number; strictly above 0. |
| instruments | Positive whole count of restrictions tested in the nested first-stage comparison. | Required. Safe integer; minimum 1. |
| residualDf | Residual Df | Required. Safe integer; minimum 1. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| partialR2 | Partial R2 | Required. Finite number. |
| partialF | Partial F | Required. Finite number. |
{
"input": {
"restrictedSse": 100,
"unrestrictedSse": 80,
"instruments": 2,
"residualDf": 40
},
"output": {
"partialR2": 0.2,
"partialF": 5
}
}Limitations and assumptions
- The sums of squared errors must come from comparable nested first-stage models. No regressions, weak-instrument critical values or instrument validity are determined.
- 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
Fit an appropriate full model and examine identifying assumptions and diagnostics before interpreting an IV result.
References
Similar or alternative tools
- Two Stage Least Squares One Fitted Value Term
fittedEndogenous = intercept+sum(instrument*coefficient).
- Instrument Relevance One Moment Gap
covariance = meanProduct-instrumentMean*regressorMean; gap = covariance-referenceCovariance.