An ABA VIF calculator measures how strongly one predictor can be reconstructed from the other predictors in a documented regression design. It converts that auxiliary regression into tolerance and a variance inflation factor. Variable selection and clinical-model design remain separate decisions.

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

VIF describes one predictor within one design matrix

Use the ABA VIF calculator for one declared target predictor xj. Regress it on the remaining predictor columns under the documented intercept convention. The resulting auxiliary Rj^2 measures how much of the target predictor's sample variation is explained by those other columns.

tolerancej = 1 - Rj^2

VIFj = 1 / tolerancej = 1 / (1 - R_j^2)

VIF is predictor-specific. A separate auxiliary fit is required for every predictor under review. One result is not a whole-model score, a measure of treatment effectiveness, or proof that a predictor should be retained, removed, combined, or interpreted causally.

Register the model and coding before the auxiliary fit

The same conceptual variable can produce a different design matrix after dummy coding, centering, interactions, transformations, or row exclusions. Preserve the actual columns used by the fitted source model.

Scope fieldRequired recordStop signalOutcome contextResponse, unit, population, phase, and intended source modelModel purpose is undocumentedTarget predictorExact column x_j and clinical meaningTarget chosen after preferred VIFs were seenComparison setEvery other design columnColumns added or removed without versioningCoding and unitsReference levels, transformations, interactions, and unitsCoding cannot be reconstructedIntercept ruleIncluded or excluded consistentlyAuxiliary rule differs without justificationRow setAligned rows and prespecified missing-data ruleMismatched or post hoc row selectionData versionImmutable extract or design-matrix versionInputs can change without traceIntended useNamed collinearity diagnostic reviewAutomatic feature selection or clinical decision

If the source model includes weights, clustered observations, regularization, or nonstandard coding, obtain method-specific review before assuming this simple auxiliary calculation answers the intended question.

Preserve the full row-aligned design

Keep the source design matrix under authorized access. The working table may minimize identifiers, but it must let a reviewer reproduce every column and verify that target and comparison values stayed on the same row.

RowAuthorized row keyTarget x_jOther predictor 1Other predictor 2Additional columnsIncluded?Coding or context note123...

Do not compare VIF values from different row sets or differently encoded designs as if only the target predictor changed. Preserve column names, meanings, reference categories, transformations, and the intercept.

Calculate the auxiliary fit and tolerance visibly

For target values xij, auxiliary fitted values xhatij, and target mean xbar_j under an intercept model:

SSEj = sum((xij - xhatij)^2)

SSTj = sum((xij - xbarj)^2)

Rj^2 = 1 - SSEj / SST_j

tolerancej = 1 - Rj^2

VIFj = 1 / tolerancej

The statsmodels VIF documentation defines VIF from a design matrix and a target column and describes the increase in coefficient variance associated with multicollinearity. Record the software version and standardization setting. This worksheet exposes the auxiliary arithmetic rather than relying on an unlabeled software output.

Copy one worksheet per target predictor

RowTarget x_jAuxiliary fitted xhatijAuxiliary residualSquared residualIncluded?Audit note123...

Summary fieldValueRequired noteTarget columnExact design-matrix nameComparison columnsAll other predictors used in this fitIntercept and standardizationVersioned conventionIncluded rows nSame rows across columnsSSE_jFull precisionSST_jMust be positiveR_j^2Reproduce from SSE and SSTTolerance1 - R_j^2VIF1 / tolerance

Repeat the table for each predictor whose VIF is reported. Preserve full precision until display, along with the analyst, reviewer, calculation date, source-model version, design version, code or spreadsheet version, and independent cross-check.

A fictional six-row example keeps each step inspectable

Suppose the target predictor is x1 = [1, 2, 3, 4, 5, 6] and the only comparison predictor is x2 = [1, 3, 2, 5, 4, 7]. Both columns and an intercept were prespecified for a fictional design.

The auxiliary fit is x1_hat = 0.6714285714 + 0.7714285714*x2.

Rowx1x2x1_hatAuxiliary residual1111.4428571429-0.44285714292232.9857142857-0.98571428573322.21428571430.78571428574454.5285714286-0.52857142865543.75714285711.24285714296676.0714285714-0.0714285714

The target mean is 3.5, SSEj = 3.6142857143, and SSTj = 17.5. Therefore Rj^2 = 0.7934693878, tolerance is 0.2065306122, and VIFj = 4.8418972332.

That value describes this target column, comparison column, row set, intercept rule, and coding. Neither source-model adequacy nor either predictor's clinical value follows from it.

One changed row can move the diagnostic

Replace the last two x2 values in the fictional design so x2 = [1, 3, 2, 5, 5, 6], while keeping x1 fixed. The auxiliary R_j^2 becomes 0.8541871921, tolerance becomes 0.1458128079, and VIF becomes 6.8581081081.

This is a sensitivity demonstration, not evidence that either row should be deleted or corrected. Investigate provenance, coding, entry errors, phase differences, and substantive meaning. A defensible unusual row belongs in the analysis even when it changes VIF.

Higher-order collinearity is not only pairwise correlation

The NIST regression-diagnostics reference describes multicollinearity as interdependence among explanatory columns and notes that pairwise correlations do not capture all higher-order relationships. A target predictor may be reconstructed from a combination of columns even when no single pairwise correlation appears decisive.

Inspect the actual design matrix, coding, coefficient uncertainty, and substantive role of each term. Interactions and derived columns can be structurally related to their components. That relationship may be expected by design rather than an error, but it still needs explicit interpretation.

Do not turn a rule of thumb into a universal ABA cutoff

The statsmodels page mentions a VIF threshold as a recommendation. That statement is not an ABA validation study, and it does not account for the purpose of a model, planned contrasts, sample size, design coding, measurement quality, coefficient precision, or costs of removing a clinically meaningful predictor.

Report the value, design, tolerance, uncertainty context, and sensitivity checks. A qualified analyst may use several diagnostics and substantive constraints when evaluating a model. This page does not output low, moderate, high, acceptable, or unacceptable labels.

Run invariance and failure-boundary checks

CheckExpected arithmetic behavior with an interceptWhat it cannot establishPermute every design row togetherR_j^2, tolerance, and VIF stay the sameOrder is irrelevant to all other analysesAdd a constant to one predictorVIF stays the sameCoding changes never affect interpretationMultiply one predictor by a nonzero constantVIF stays the sameUnits are clinically interchangeableChange one comparison valueVIF may change, as in the sensitivity exampleThe changed row is erroneousConstant target columnSST_j = 0; VIF is undefinedThe column can be silently removedExact reconstruction of targetR_j^2 = 1, tolerance = 0, VIF tends to infinitySoftware output resolves rank deficiencyDuplicate or derived columnsDesign may be rank deficientOne arbitrary deletion is clinically justified

Translation and scaling invariance depend on a compatible intercept and unchanged row set. If the intercept is omitted, those properties can differ. Record the convention instead of applying an invariance claim mechanically.

Read VIF within model validation, not in isolation

The NIST model-validation guidance emphasizes residual plots and multiple checks rather than a single summary. VIF addresses coefficient variance associated with linear dependence among predictor columns. Residual shape, variance, autocorrelation, influence, outcome measurement, omitted nonlinear structure, and clinical importance remain outside this diagnostic.

Review the source graph and model purpose, coefficient estimates and uncertainty, residual plots, influential rows, phase context, and whether the design can answer the stated question. A low VIF cannot validate these other features. A high VIF cannot by itself identify which representation best serves the client or decision.

Stop when the design cannot be reconstructed

Stop when the target, comparison set, coding, intercept, row alignment, missing-data rule, or data version is undocumented. Stop as well for constant targets, exact collinearity, silent software column-dropping, mixed populations or models, or predictor selection after preferred values are known.

Seek qualified methods review for near rank deficiency, complex categorical coding, interactions, clustered or repeated observations, weighted designs, regularization, small samples, formal inference, or a request to change clinical care from VIF alone. Preserve exploratory checks as exploratory rather than rewriting the original plan.

Professional, privacy, and accessibility gates stay open

The BACB Ethics Codes page supplies the current official ethics source. The BCBA Test Content Outline addresses measurement, graphing, interpreting data, and experimental design. Broader evidence and interpretation principles appear in the Standards for Educational and Psychological Testing. None validates this VIF worksheet, defines competence, or supplies a clinical threshold.

Use synthetic or appropriately de-identified matrices for training and testing. For authorized identifiable data, minimize fields and use approved access, storage, retention, and version controls. HHS publishes separate Privacy Rule and Security Rule summaries. Applicability and safeguards require organizational and legal review.

Related resources

Sources