Glossary

(or contiguity) Two polygons are either adjacent or not. Different criteria may be used to determine adjacency dependent on whether polygons must share an edge (Rook's case) or need only share a corner (Queen's case). Adjacency relations among a set of polygons or areas may be summarized in an adjacency matrix where each row-column entry is either 1 (for adjacent polygons) or 0 (for non-adjacent polygons).

A measure of the degree to which attribute values in a data set are related to one another over space. If locations near one another tend to have similar values, the data set is positively autocorrelated. If locations near one another tend to be different (a 'checkerboard' effect), the data set is negatively autocorrelated. Where there is no particular spatial pattern to the data there is no autocorrelation.

Lines on a surface joining points with the same value, used particularly for lines of equal elevation on earth's surface. A more general term is isoline, which can refer to lines of equal value of any surface or field phenomenon, such as atmospheric pressure, population density, soil pH, etc.

Any process used to measure the density or intensity of events in space, expressed in numbers per unit area. The most commonly used method uses kernel functions in kernel density estimation.

The spatial separation between two entities. Most simply, this is measured in a straight line or 'as the crow flies'. On the plane, this is the Euclidean distance, or on a globe the Great Circle distance. See also interaction.

A function in point pattern analysis based on the cumulative frequency of the shortest distance between events in a point pattern and a set of randomly placed locations in the study area. See also G function, K function.

First order variation in a spatial pattern is that part of the pattern that may be attributed to trends across the study area. The most obvious example is a steady (say) south-north decrease in average temperatures across a region. The part of a pattern that is considered first order is likely to vary with spatial and temporal scale. Marked first order effects in a pattern can be problematic for some methods such as kriging, when universal kriging should be used to account for the first order effect. First order components in a spatial pattern may be effectively modeled using trend surface analysis. See also second order spatial variation.

A function in point pattern analysis based on the cumulative frequency of the shortest inter-event distances between events in a point pattern. See also F function, K function.

In regression the variable (or variables) that are assumed to lead to changes in the dependent variable.

A generalization of other measures (such as distance and adjacency) of the degree to which spatial locations are related. Usually, interaction is measured on a scale of 0 to 1 where 0 indicates little or no relationship and 1 indicates a strong relationship.

A scale of measurement for attribute data that expresses the attribute numerically such that the differences between cases are directly comparable, that is, a given numerical difference is equivalent regardless of the relative values of the numbers. See also ordinal and ratio.

A function in point pattern analysis based on all the inter-event distances between events in a point pattern. See also G function, K function.

A method of density estimation making use of kernel functions. For each event to be included in the density estimates a kernel function is used to 'spread' its effect across space. A density surface is produced by summing all the individual functions across the study region.

A formalisation of the mathematical manipulation of values in GIS data layers. In map algebra values of attributes at map locations are altered by operations applied locally, focally, zonally or globally to individual map layers or between two or more.

A grid of numbers. There are mathematical rules for adding, multiplying and inverting matrices and their use is a key topic in modern statistics and algebra. In spatial analysis matrices are often used to represent relationships among spatial entities, such as distance, adjacency, and interaction.

A measure of central tendency in statistics based determined by summing all values in a dataset and dividing by the number of values. The me an gives an idea of the typical value in a dataset, but is prone to distortion by unusually high or low outlier values.

A statistical method of generating a sampling distribution for a statistic, usually in the absence of a well understood analytically derived method. In spatial analysis it is often difficult to derive expected distributions of statistical measures, so Monte Carlo simulation is often used. Based on an understanding of the processes at work in generating the spatial data under analysis, a computer simulation is used to generate a number of synthetic datasets, which are then analyzed using the measure under test. The results from multiple synthetic datasets provide a synthetic sampling distribution against which observed measurements can be assessed.

(or mean nearest neighbor distance) For any event in a point pattern one other event is its nearest neighbor. The distance to that event is the nearest neighbor distance. By determining nearest neighbor distance for all events in a pattern, the mean nearest neighbor distance can easily be determined, and may give an indication of whether the pattern is clustered or evenly-spaced.

The neighborhood of a spatial object is either a region of space considered for analysis to be associated with it, or a set of other objects considered as that object's neighbors. There is no standard way of defining neighborhoods for objects.

The value of the semivariogram function at zero distance. See also range, sill.

A scale of measurement for attribute data that expresses the attribute so that cases may be ranked in order, but precise differences are not calculable between the categories. See also interval and ratio.

Superimposing two or more maps registered to a common coordinate system, to show relationships between features in the same study area. In a GIS context the superimposition occurs digitally, although overlay analysis has its origins in the overlay of transparent map layers in landscape planning, where the method was used to identify areas suitable for different types of development. Overlay analysis is closely related to map algebra.

A characteristic arrangement of spatial objects, possibly produced by a spatial process.

Any of a number of methods of statistically assessing a point pattern. Classic point pattern analysis is concerned with determining whether a point pattern could have produced by a stochastic spatial process, and if not, whether it tends to be clustered or evenly spaced. See also "quadrat analysis," "F funtion," "G function," "K function," and "nearest neighbor distance."

A closed multi-point line, that is, one where the 'last' point on the line is the same as the 'first'. See also area.

A method of point pattern analysis in which the study region is sampled using a set of similar shapes (quadrats) and counting the number of events in each. Analysis of the resulting quadrat counts can help determine whether the pattern is evenly spaced or clustered. Quadrat analysis may be based on a set of randomly located quadrats (common in fieldwork) or on a census where the quadrats fill the study regions without overlaps.

(1) The range of a dataset is the difference between its highest and lowest values.

(2) A feature of the semivariogram. The range is the distance beyond which there is no particular relationship between data values that can be distinguished from the variance in the dataset. See also sill and nugget.

A term for a grid.

A scale of measurement for attribute data that expresses the attribute numerically such that the relative values of cases expressed as a ratio are meaningful across the full range of data values. See also interval and ordinal.

A statistical method that expresses average variation in one variable (attribute) in terms of one or more independent variables (or attributes). The result of a regression analysis summarizes how much we expect the value of the dependent variable to change given change in the independent variable(s). May also form the basis of a type of model-based overlay analysis.

A subset of the study population used as a basis study of the whole population. Statistics is concerned with understanding the relationships between measurements made on a sample and the likely values of those measurements for the population from which the sample was drawn.

Second order variation in a spatial pattern is that part of the pattern that may be attributed to interaction effects among elements in the pattern. Alternatively, it is what is left of the pattern once first order variation or trend effects have been removed. Against some back ground trend, the second order effects are more localized variations in pattern intensity.

A mathematical function that summarizes the relationship between spatial difference (distance) and attribute difference (variance) in a spatial data set. Derivation of the semivariogram is generally complex but may start with the variogram cloud. Features of the semivariogram are the nugget, sill, and range.

A feature of the semivariogram. The sill is the steady value of the semivariogram function at distances greater than the range. See also nugget.

See autocorrelation.

A trend surface summarizes the first order variation in spatial pattern. Trend surfaces may be used in kriging, and can be developed by applying regression with spatial coordinates as the independent variables.

A quantity having both size and direction. An example is wind which has both a speed and a direction. A two dimensional vector can be described by two values, while in general a quantity described by n numbers is a n-dimensional vector.

A method of overlay analysis based on the combined probability of different data attributes occurring at the same locations.