Hoctests

Hoctests is a term used in statistics and data analysis to describe a family of tests designed to assess higher-order relationships among variables, particularly interactions and conditional effects that extend beyond main effects.

The label is not universally standardized; in some texts hoctests stands for Higher-Order Conditional Tests, while others use it as an umbrella for procedures that evaluate nonlinearity, interaction terms, or conditional independence in regression, classification, and observational studies.

Common practice involves specifying a base model and an extended model that adds higher-order terms or conditional terms; the hypothesis tested is whether the additional components improve fit or explain outcomes beyond the base model. Test statistics include likelihood ratio tests, Wald tests, and score tests; p-values are obtained from asymptotic distributions or resampling methods such as permutation tests. In complex models, information criteria or cross-validation may accompany inference.

Applications span social sciences, economics, epidemiology, genetics, and machine learning pipelines where detecting interactions and conditional relationships is important. Hoctests are useful for identifying moderation effects, epistasis in genetics, or nonlinear relationships that standard main-effect tests might miss.

Limitations and best practices include risks of overfitting as model complexity grows, multiple testing concerns, and interpretability challenges for higher-order terms. Practitioners often pre-specify candidate interactions, apply regularization, or rely on domain knowledge to guide which higher-order components to test.