Raykov Composite Reliability Calculator
Explicit Raykov composite reliability with independent latent variance and FULL residual sum variance inclcovariances, not force residual independence or unit factor variance. Actual independently qualified instrument/cohort/matching units; no diagnosis, causal outcome, validated personal prediction or universal clinical cutoff.
Description
Composite reliability depends on factor variance, loadings and residual variance of the summed score.
Composite reliability depends on factor variance, loadings and residual variance of the summed score.1
Including residual covariances changes the denominator from the independent-residual model. The calculation and input requirements are explained below.
When to use Raykov Composite Reliability Calculator
Enter positive latent variance, nonempty finite loadings and nonnegative residual variance of the summed score including covariances.
How to use Raykov Composite Reliability 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 Raykov Composite Reliability 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 |
|---|---|---|---|
| callerLatentVariance | Caller Latent Variance. Use the units and matching context stated in the calculation below. | number | Required; strictly positive; finite; other constraints below |
| actualFactorLoadings | Actual Factor Loadings. Use the units and matching context stated in the calculation below. | array of number | Required; other constraints below |
| actualResidualSumVarianceIncludingCovariances | Actual Residual Sum Variance Including Covariances. Use the units and matching context stated in the calculation below. | number | Required; nonnegative; finite; other constraints below |
Enter positive latent variance, nonempty finite loadings and nonnegative residual variance of the summed score including covariances. Require positive total variance. Return common variance divided by common plus residual variance.
reliability=latentVariance*(sum(loadings))^2/(latentVariance*(sum(loadings))^2+residualSumVariance) 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": {
"callerLatentVariance": 2,
"actualFactorLoadings": [
1,
1
],
"actualResidualSumVarianceIncludingCovariances": 2
},
"output": {
"result": {
"value": 0.8
}
}
}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 Standard Error of Measurement Calculator for a complementary operation: Classical measurement error combines score variability and applicable reliability.
Use Spearman-Brown Split-Half Reliability Calculator for a complementary operation: The Spearman–Brown equal-half correction transforms a split-half correlation.
References
-
Raykov Composite Reliability Calculator — tool.io
Similar or alternative tools
- Standard Error of Measurement Calculator
Classical measurement error combines score variability and applicable reliability.
- Spearman-Brown Split-Half Reliability Calculator
The Spearman–Brown equal-half correction transforms a split-half correlation.