Check the Functional Form of a Continuous Predictor

Specify the model scale

A linear predictor term assumes a straight-line contribution on the model’s relevant scale. In linear regression that is the conditional mean scale; in logistic regression it is the log-odds scale. A straight line on one scale can be curved after transformation, so identify the assumption before assessing it.

NIST’s model-validation guidance supports graphical assessment of model adequacy. Use plots and scientifically informed alternative forms rather than assuming that a high overall fit statistic proves each predictor’s shape is correct.

Inspect coverage and possible shape

Plot the predictor distribution and identify sparse regions, extreme values and measurement limits. Consider the scientific mechanism and whether a threshold, plateau or smooth curve is plausible. A categorical split at the sample median discards information and creates a discontinuity that may have no scientific basis.

Assess the conditional relationship while accounting for other planned predictors. A raw scatterplot can be useful, but its shape may differ from the adjusted association if covariates vary across the predictor range.

Compare a hypothetical specification

Suppose a model uses age in years with coefficient 0.2 on the outcome scale. It implies the same two-unit difference for ages 30 versus 40 as for ages 70 versus 80, holding other modeled variables fixed. If the scientific relationship accelerates at older ages, that constant-increment assumption may be inadequate.

A flexible alternative can estimate different slopes across the range, but it needs enough data and a declared complexity choice. Inspect predictions at meaningful ages, not just the p-value of an added nonlinear term. A flexible curve that oscillates in a region with two observations is not automatically a better representation.

Report the chosen form

State transformations, knots or polynomial terms and preserve the exact prediction formula. Explain whether the form was prespecified or selected after inspecting the data. If model selection is part of prediction development, include it within the validation process to avoid optimistic performance estimates.

Show an adjusted curve or meaningful contrasts with uncertainty when that communicates the result better than a list of basis coefficients. Keep unsupported extrapolation distinct from interpolation. The practical goal is a model contribution that represents the scientific question across the observed range, with enough documentation that another analyst can reproduce its shape and recognize where evidence is sparse.

Source verification: 6 November 2026. Examples are hypothetical.