Meaning
Statistical transformations linearize the relationship between point density and distance to simplify the detection of spatial clustering or dispersion. Applying the besag l-function converts the quadratic output of a k-function into a linear plot where the expected value under randomness is zero. This adjustment allows for a more intuitive visual assessment of whether points are more grouped or more spread out than a random process would suggest.
Linear Variance
Transforming the square root of the estimated k-function stabilizes the variance of the estimator. This linear variance makes it easier to compare patterns across different scales.
Pattern Interpretation
Graphical output shows deviations from a horizontal line. When the besag l-function remains near zero, the data follows a random distribution. A positive value indicates clustering, where the observed density of points exceeds the expected density at that radius.
Negative values suggest a regular or inhibited pattern where points appear to avoid one another. Statistical envelopes are often plotted alongside the function to determine if the observed deviations are larger than what chance alone could produce.
Analytical Confidence
Confidence intervals depend on the number of points in the sample. A pattern interpretation becomes more reliable as the sample size increases.
