An ABA Ramsey RESET calculator asks whether powers derived from an existing model add explanatory structure that its original functional form did not capture. The fitted-power version can flag broad specification concerns, but it cannot name the missing variable, prove nonlinearity, or choose a better clinical model.

Clinicians & ABA Professionals / Data, Outcomes and Clinical Decision-Making.

An omnibus question about one fitted model

Start with a fixed ordinary least-squares model. RESET augments that model with nonlinear functions of fitted values or predictors, then jointly tests whether the added terms contribute. If they do, the original specification may be missing curvature, interactions, transformations, or other structure. The test does not reveal which explanation is correct.

This page uses fitted values raised to powers two and three. That choice corresponds to the current statsmodels settings testtype="fitted" and power=3. The fitted-value square and cube are appended to the original exogenous matrix, and their coefficients are tested jointly. The worked worksheet uses the classical nested-model F form, corresponding to an F output when usef is true.

Statsmodels also supports powers of exogenous columns and a principal-component route. It can use nonrobust or named robust covariance estimators, and its documented result is a Wald test. Those settings answer related questions, but their statistics are not interchangeable. An output record must say which augmentation, powers, covariance, and test form were used.

The question is fixed before the answer

An ABA Ramsey RESET calculator is reproducible only when the original and augmented specifications are both visible.

Record itemWhat to retainPause whenIntended useExploratory diagnosis or prespecified inferential reviewRESET will determine a treatment decisionRow unitSession, interval, client, provider, or another defined unitDependent units are treated as independentAuthorized row keyStable de-identified identifier linked to the sourceRows cannot be reconciled across fitsResponseOperational definition, unit, denominator, and windowMeasurement or opportunity changes are uncodedOriginal designEvery column, constant, interaction, offset, and transformationThe fitted values cannot be regeneratedInclusion rulesMissingness, exclusions, weights, and verified correctionsRows changed after the result was inspectedAugmentationFitted, exogenous, or principal-component routeThe software default is unknownPower planHighest power and included sequencePowers were searched until a preferred result appearedTest planWald or F, covariance rule, alpha, and multiplicity planResult labels from different plans are mixedSoftwarePackage, version, precision, and toleranceOnly a rounded probability remainsClinical contextDirect graph, phase labels, integrity, and setting eventsThe model is separated from observed behavior

If the plan includes several plausible original models, preserve all planned fits and explain their purposes. Selecting one only after RESET is known converts a diagnostic into an undocumented specification search.

Fitted powers and the nested-model F calculation

Let X contain the original design columns, including an intercept, and let y be the response. Fit the restricted model:

y = X*beta + e

Save the fitted values yhat_i. For a fitted-power test through power three, append two columns:

P2i = yhati^2

P3i = yhati^3

Fit the unrestricted model with [X, P2, P3]. Let SSER and SSEU be the restricted and unrestricted residual sums of squares. If q=2 added terms and the unrestricted design has k_U estimable columns, calculate:

F = ((SSER - SSEU) / q) / (SSEU / (n - kU))

The upper-tail reference is F(q, n-kU). The null restriction is that both added coefficients equal zero. The current statsmodels RESET documentation describes the augmentation routes, power sequence, covariance options, and optional F result. The implementation source shows construction of the expanded model and the joint coefficient test.

The formula requires nested fits on the same response and rows. A negative SSE difference beyond numerical tolerance, nonpositive denominator degrees of freedom, or rank-deficient augmented design is a stop condition. Do not clip an invalid result into a convenient range.

Blank fitted-power RESET worksheet

Keep a copy of the original fit and its residuals.

Row keyPredictor codingResponseRestricted fitted yhatRestricted residualyhat^2yhat^3Context

Then reconcile the two models.

FieldRestricted modelUnrestricted modelRowsEstimable columnsNumerical rankResidual degrees of freedomSSESoftware and precision

Joint-test fieldRecorded valueAugmentation routeHighest powerAdded terms qF statisticNumerator degrees of freedomDenominator degrees of freedomF upper-tail probabilityCovariance conventionPrespecified alpha, if applicableReviewer and date

Place the raw series, fitted line, residual-versus-fitted plot, residual sequence, and any phase markers beside the worksheet. A joint test does not show where the extra structure occurs.

Fictional eighteen-row calculation

The numbers below are an arithmetic fixture, not a client record or a recommended way to model a single-case series. The restricted design contains a constant and session index 1...18. The response values deliberately curve upward so the fitted-power calculation is easy to audit.

RowSessionResponseRestricted fittedRestricted residualFitted squaredFitted cubed114.82.85380116961.94619883048.144181115623.2418735929225.74.19518403851.504815961517.599569117173.8334314451336.15.53656690750.563433092530.6535731208169.7155585364447.56.87794977640.622050223647.3061931267325.3696204382558.08.2193326453-0.219332645367.5574291347555.2769827223669.29.5607155143-0.360715514391.4072811449873.9190109600779.710.9020983832-1.2020983832118.85574915731295.77707072298811.412.2434812521-0.8434812521149.90283317171835.33252758259912.213.5848641211-1.3848641211184.54853318842507.0667471103101013.814.9262469900-1.1262469900222.79284920723325.4610948779111114.916.2676298590-1.3676298590264.63578122824304.9969364568121216.117.6090127279-1.5090127279310.07732925135460.1556374185131318.018.9503955968-0.9503955968359.11749327666805.4185633345141419.420.2917784658-0.8917784658411.75627330408355.2670797763151521.821.63316133470.1668386653467.993669333610124.1825523156161623.322.97454420360.3254557964527.829681365312126.6463465237171726.124.31592707261.7840729274591.264309399214377.1398279722181828.625.65730994152.9426900585658.297553435216890.1443622327

The restricted intercept and session coefficients are 1.5124183007 and 1.3413828689. Its SSE is 30.0997179223. After fitted squared and fitted cubed are appended, the unrestricted coefficients for constant, session, fitted squared, and fitted cubed are 3.8938250501, 0.9219928517, -0.0129995921, and 0.0009810599. The unrestricted SSE is 0.8671809426.

There are q=2 restrictions and 18 - 4 = 14 denominator degrees of freedom. Therefore:

F = ((30.0997179223 - 0.8671809426) / 2) / (0.8671809426 / 14)

F = 235.9689296857

The F(2,14) upper-tail probability is 0.0000000000164752. This small number says the fitted-power additions improve this synthetic nested fit relative to the classical reference. It does not prove that a polynomial is the correct explanation, that the response is generated by a cubic function, or that any change is clinically meaningful.

Sensitivity when the last value changes

Change only row 18's fictional response from 28.6 to 25.5. Then refit the restricted model, rebuild its fitted squared and fitted cubed columns, and refit the unrestricted model. The restricted SSE becomes 19.4980804954, while the unrestricted SSE becomes 4.0832043344. The resulting F statistic is 26.4263368401, with upper-tail probability 0.0000176630.

Both probabilities are small under a conventional 0.05 comparison, yet the F statistic changes almost ninefold. Reporting only a binary label would hide that sensitivity. Neither value establishes that the original last observation is wrong, and neither licenses its deletion. Verify provenance and retain both analyses when a correction or planned sensitivity analysis is appropriate.

With an intercept, translating the response by a constant or multiplying it by a nonzero constant preserves the span of the fitted-power augmentation and the nested F result, subject to numerical precision. An affine recoding of the sole predictor also preserves the original linear fitted values when the intercept remains. These are implementation checks, not promises for every model, weighting scheme, covariance choice, or software tolerance.

A flag does not name the missing structure

RESET may respond to omitted curvature, an interaction, a transformed predictor, a missing variable, an outlier, leverage, changing variance, dependence, or another form of misspecification. The fitted-power basis can approximate several patterns, which is why a rejection is intentionally nonspecific.

Do not automatically add squared and cubed fitted values to the clinical model. Those columns are diagnostic devices in this worksheet. A substantive model revision needs a plausible mechanism, interpretable terms, enough data, prespecified evaluation, and qualified review. A new specification should be checked on its own assumptions and retained alongside the original.

The statsmodels diagnostics index lists RESET among several linear-regression checks. NIST's analysis of residuals shows why residual structure is examined graphically, and its discussion of assessing the fit combines numerical summaries with graphical evidence. A model can pass one diagnostic and still fail another important check.

Boundaries that should halt or redirect use

Stop when the original fitted values cannot be reproduced, the restricted and unrestricted row sets differ, the augmented design is rank deficient, or the denominator degrees of freedom are not positive. Nonfinite fitted powers, extreme numerical scaling, undocumented weights, and a covariance result that cannot be matched to the stated test are also reasons to pause.

Repeated clients, providers, or sites require dependence-aware reasoning. Ordered series may retain serial correlation. Residual spread may change. A fitted-power test cannot repair either issue. Review influence, leverage, residual sequence, phase fit, opportunity and denominator changes, treatment integrity, schedule gaps, setting events, and measurement drift before assigning a cause.

Avoid trying several powers, transformations, phase definitions, exclusions, and models until one crosses a chosen probability threshold. If multiple diagnostics were planned, keep the entire family of results and address selection and multiplicity. A high probability is not proof that the original form is correct, just as a low one is not proof that a particular alternative is right.

Clinical interpretation stays with people and direct data

Ramsey RESET cannot establish treatment effect, functional relation, causation, experimental control, social validity, or clinically important change. A line or curve fitted across phase-structured data does not create the logic of a single-case experimental design. Direct graphs, level, trend, variability, immediacy, overlap, consistency, integrity, and client priorities remain visible in the clinical review.

The BACB Ethics Code materials support professional competence and data-based decision-making. The BCBA Test Content Outline addresses measurement, graphing, interpretation, and experimental design. The Standards for Educational and Psychological Testing frame evidence around an intended use. None prescribes RESET or validates this fictional calculation.

A statistician or regression-specification specialist should review the augmentation, power plan, rank, covariance, test form, sample size, and inferential interpretation. The responsible clinician should review measurement, design logic, direct graphs, treatment integrity, and client significance. Client and caregiver perspectives belong in decisions that could affect goals or services. External clinical and methods review remains pending.

Privacy, security, and accessible implementation

Use authorized de-identified row keys, and keep any re-identification material separate in an approved system. The HHS Privacy Rule summary and HHS Security Rule summary provide federal context for covered entities and business associates. They are not organization-specific legal advice.

Do not submit protected data to an unapproved public calculator. Save the original model, fitted values, power columns, both fits, test configuration, software version, reviewer notes, and any corrections together. An accessible implementation should have persistent labels, keyboard operation, visible focus, readable error text, text alternatives for plots, downloadable tables, and conclusions that do not rely on color.

Related resources

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