Method
Response surface analysis
Surface statistics are computed from the second-order regression coefficients under the Edwards (2002) parameterization:
a1 = b1 + b2 slope along the congruence line X = Y
a2 = b3 + b4 + b5 curvature along the congruence line
a3 = b1 - b2 slope along the incongruence line X = -Y
a4 = b3 - b4 + b5 curvature along the incongruence lineInterpretation rules applied:
| Condition | Reading |
|---|---|
| a1 > 0, significant | Outcome rises monotonically as T and E rise together |
| a2 < 0 | An optimum exists along the congruence line — a concave ridge |
| a3 different from 0 | The two directions of misfit are not equivalent |
| a4 < 0 | Incongruence imposes a curvature penalty — the P-E Fit signature |
Stationary point and its uncertainty
The stationary point of the fitted surface is a derived quantity with no closed-form standard error, so it is bootstrapped:
boot_sp <- boot(
data,
statistic = function(d, i) {
fit <- rsm(Y ~ SO(T, E), data = d[i, ])
canonical(fit)$xs
},
R = 1000
)
boot.ci(boot_sp, type = "perc")Reporting the stationary point without an interval would overstate its precision; the interval is what determines whether the located optimum is interpretable at all.
Configurational analysis
| Parameter | Setting |
|---|---|
| Outcome | Upper quartile of the outcome measure |
| Conditions | T, E, organizational size, training exposure |
| Calibration | Theoretical anchors at the scale endpoints and midpoint |
| Frequency threshold | 2 |
| Consistency cutoff | 0.80, with a 0.85 strict sensitivity re-run |
| Bootstrap | 5,000 samples |
Calibration anchors are theoretical rather than sample-derived, and anchor sensitivity is reported rather than assumed away — configurational results are known to move under anchor perturbation, and a solution that survives only at one calibration is not a finding.
Robustness
- HC3 standard errors on all surface models
- Bootstrap intervals on derived quantities
- Subgroup estimation across size bands
- Multi-threshold sensitivity on configurational cutoffs
- Model comparison by information criterion alongside explained variance
Revisions in progress
The four items identified by internal review are being addressed in dependency order: the outcome measure first, then the panel restriction, then the common-method diagnostic, then multiple-comparison correction. The last is re-tabulation rather than re-analysis, which is why it is sequenced last despite being the least effortful.