diagnostic measure

A diagnostic measure is a specific kind of statistical method used to evaluate model fit and identify problematic observations. Diagnostic measures (Cook's distance, leverage, etc.) are specialized statistical methods for diagnostics.

Leverage is a specific kind of diagnostic measure — the diagonal elements of the hat matrix that quantify each observation's potential influence on the fitted regression. A competent statistician would call leverage 'a diagnostic measure'.

A normalized residual IS a specific kind of diagnostic measure — it standardizes a residual (dividing by its estimated standard deviation) to flag observations with unusually large residuals, which is the core purpose of a diagnostic measure. Direction: specific→general. A competent statistician would call a normalized residual 'a diagnostic measure.'

Cook's distance IS a specific kind of diagnostic measure — it quantifies the influence of each observation on a regression model by measuring how much the fitted values change when that observation is removed. A competent statistician would call Cook's distance a diagnostic measure. Direction: specific→general.

Cook distance IS a diagnostic measure — it measures the influence of each observation on a regression model's fitted values. It is a specific kind of diagnostic tool that quantifies how much the model would change if that observation were removed.

Dfbetas IS a specific kind of diagnostic measure — it measures the standardized change in each regression coefficient when an observation is deleted. A competent speaker would call dfbetas a diagnostic measure. Direction: specific→general.

A leverage residual IS a specific kind of diagnostic measure — it computes a derived quantity (residual × sqrt((1-h_ii)/h_ii)) specifically to diagnose influential observations in regression. Direction: specific diagnostic construct → general category (diagnostic measure). Law 9 satisfied.

A studentized residual IS a specific kind of diagnostic measure — it quantifies how far an observation deviates from expectation in standard deviation units. A competent statistician would call it 'a diagnostic measure'. Specific→general under Law 9.

Influence diagnostics IS a specific kind of diagnostic measure: a statistical technique that quantifies how much individual observations affect regression model outputs (coefficients, predictions). It includes measures like Cook's distance, DFFIT, DFBETA. A competent statistician would classify it as a diagnostic measure. Nearest kind is diagnostic measure.

Model validation IS a specific kind of diagnostic measure: a structured practice of evaluating whether a model adequately represents its target phenomenon. Nearest kind per Law 11e — diagnostic measure is the general category, model validation is the specific practice.

Outlier detection IS a specific kind of diagnostic measure — a practice for diagnosing data quality by identifying anomalous observations. A practitioner would call it 'a diagnostic measure' for data integrity. Files against the nearest general kind per Law 11e.

Variance inflation factor (VIF) is a specific diagnostic measure used to detect multicollinearity in regression models. A competent speaker would call VIF 'a diagnostic measure' — it quantifies how much the variance of a regression coefficient is inflated due to collinearity, serving as a diagnostic tool for model health.