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In contemporary causal inference, regression-based strategies remain popular because they offer a transparent way to adjust for confounding and to estimate the effect of an exposure or treatment on an outcome. Yet these methods hinge on a set of functional form assumptions about how the outcome relates to covariates and the treatment, often expressed as linearity, additivity, or specific interaction patterns. When these assumptions align with reality, estimates can be precise and interpretable; when they do not, bias and inefficiency creep in. Understanding the sensitivity of results to these modelling choices is essential for credible inference, particularly in observational studies where randomization is absent and researchers must rely on observational proxies for treatment.

The core issue is not simply whether a model is correct in a mathematical sense, but whether its implied relationships accurately capture the data-generating process. Regression coefficients are abstractions of conditional expectations, and their interpretation as causal effects depends on untestable assumptions about confounding control and temporal order. Practically, analysts choose a functional form to map covariate patterns to outcomes, and this choice directly shapes the estimated contrast between treated and untreated groups. Exploring alternative specifications, such as flexible functional forms or nonparametric components, helps gauge whether conclusions hold under different plausible structures.

When researchers specify a model with a particular form—say, a quadratic term for a continuous covariate or a fixed interaction with treatment—they impose a structure that may or may not reflect how variables actually interact in the world. If the true relationship is more nuanced, the estimator may misattribute effects to the treatment rather than to covariate dynamics. Conversely, overly cautious models that aggressively bend to data complexity can dilute statistical power and produce unstable estimates with wide confidence intervals. The balancing act is to preserve interpretability while remaining faithful to potential nonlinearities and varying treatment effects across subgroups.

A practical approach begins with a transparent baseline specification and a principled plan for model expansion. Analysts can start with a simple, well-understood form and then incrementally introduce flexible components, such as splines or piecewise functions, to relax rigidity. Parallel analyses with alternative link functions or different interaction structures offer a clearer map of where conclusions are robust versus where they are contingent on particular choices. Importantly, these steps should be documented in a way that allows readers to follow the logical progression from assumption to inference, rather than presenting a black-box result as if it were universally valid.

An effective way to manage functional form concerns is to employ a menu of models that share the same causal estimand but differ in specification. For example, one could compare a linear specification with a generalized additive model that allows nonlinear effects for continuous covariates, while keeping the treatment indicator constant. If both models produce similar estimates, confidence grows that the treatment effect is not an artifact of a rigid form. If results diverge, researchers gain insight into how sensitive conclusions are to modelling choices, prompting further investigation or caveats in reporting.

Beyond model choice, diagnostic checks play a crucial role. Residual analyses, goodness-of-fit statistics, and cross-validation help assess whether the chosen form captures patterns in the data without overfitting noise. When feasible, semiparametric or nonparametric strategies can be used to verify core findings without imposing strict parametric shapes. In addition, leveraging domain knowledge about the likely mechanisms linking exposure to outcome can inform which interactions deserve attention and which covariates merit nonlinear treatment. The end goal is to prevent misinterpretation caused by convenient but misleading assumptions.

Another avenue is the use of doubly robust estimators that combine modelling of the outcome with modelling of the treatment assignment. This class of estimators can provide protection against certain misspecifications, because a correct specification in at least one component yields consistent estimates. Nevertheless, the performance of these methods can still depend on how the outcome model is structured. In practice, researchers should assess the impact of different functional forms within the doubly robust framework, ensuring that conclusions are not unduly driven by a single modelling path.

Sensitivity analyses are essential complements to fitting a preferred model. Techniques such as partial identification, bounding approaches, or local sensitivity checks enable researchers to quantify how much the estimated causal effect would have to shift to reverse conclusions under plausible departures from the assumed form. These exercises do not pretend to prove neutrality of model choices; rather, they illuminate the boundary between robust findings and contingent results. A transparent sensitivity narrative strengthens the overall scientific claim and invites scrutiny from the broader community.

Clear documentation of modelling decisions, including the rationale for chosen functional forms and any alternatives considered, helps others evaluate the credibility of findings. Presenting side-by-side comparisons of key estimates across a spectrum of specifications makes the robustness argument tangible rather than theoretical. Visualizations, such as marginal effect plots across covariate ranges, can illustrate how treatment effects vary with context, which often reveals subtle patterns that numbers alone might obscure. Coupled with explicit statements about limitations, these practices support responsible use of regression-based causal estimates.

The interpretive burden also falls on researchers to communicate uncertainty honestly. Confidence intervals that reflect model-based uncertainty should accompany point estimates, and when feasible, Bayesian approaches can provide a coherent uncertainty framework across multiple specifications. It's important to distinguish between statistical uncertainty and epistemic limits arising from unmeasured confounding or misspecified functional forms. By acknowledging both, scholars create a more nuanced narrative about when causal claims are strong and when they remain provisional.

In the end, the central question is whether the chosen functional form faithfully represents the dependencies among variables without distorting the causal signal. This balance requires humility, methodological pluralism, and rigorous testing. Researchers should treat regression-based estimates as provisional until consistent evidence emerges across a range of thoughtful specifications. The discipline benefits from openly exploring where assumptions matter, documenting how conclusions shift with specification changes, and resisting the temptation to declare universal truths from a single model. Responsible practice advances both methodological rigor and practical applicability.

As methods evolve, a transparent culture of model comparison and robustness checks remains the best antidote to overconfidence. By embracing flexible modeling options, validating assumptions with diagnostics, and communicating uncertainty with clarity, investigators can derive causal insights that endure beyond specific datasets or analytic choices. Ultimately, the most credible analyses are those that reveal the contours of what we know and what we still need to learn about how functional form shapes regression-based causal effect estimation strategies.