Nearbyvaries

Nearbyvaries is a conceptual term used in spatial analysis to describe a local measure of how much a variable changes among observations that are geographically close to each other. It is not a universally standardized metric, but rather a generic way to refer to nearby or local variation in a dataset.

Definition and calculation

For each observation i, with value y_i and location, define a neighborhood N(i) using a radius-based approach or a set of k nearest neighbors. The nearbyvaries value at i can be defined as a local variance: nearbyvaries_i = Var({ y_j : j in N(i) }). Other common choices include the local standard deviation or a robust dispersion measure. Weights can be applied, resulting in a weighted local variance that emphasizes closer neighbors.

Applications

Nearbyvaries is used to identify areas with high or low local variability, which can aid in hotspot detection, anomaly identification, and spatial smoothing decisions. It is applicable in environmental monitoring (e.g., soil or air quality), urban planning, agriculture, and ecology, where understanding spatial heterogeneity complements mean-level analyses. The measure is often considered alongside global metrics of spatial association to diagnose whether local variability patterns align with broader spatial trends.

Relation to related concepts

Nearbyvaries is related to local indicators of spatial association (LISA) and local Moran’s I, which assess spatial clustering of similar values. Unlike these statistics, which focus on autocorrelation, nearbyvaries emphasizes the dispersion of values within a neighborhood. The exact interpretation depends on the chosen neighborhood definition and scale.

Status and terminology

The term nearbyvaries is not a fixed, widely standardized statistic. In practice, researchers may use local variance or local dispersion as a proxy for nearbyvaries, with definitions tailored to their specific spatial context and data.