Test for Spatial Join Count Statistics

The function join_count calculates spatial join count statistics for a binary matrix, identifying patterns of aggregation or randomness.

Usage

join_count(matrix_data)

Arguments

matrix_data: A binary matrix (with elements 0 and 1) representing the spatial distribution of two types of points: 0 for healthy plants (H) and 1 for diseased plants (D). This matrix reflects the geographical distribution or layout of plants in the studied area.

Value

A comprehensive, rich-text formatted string of results that includes:

Statistical counts of specific binary sequences (e.g., "01 or 10", "11")
Expected counts under the assumption of Complete Spatial Randomness (CSR)
Standard deviations and Z-scores (ZHD for "01 or 10" sequences, ZDD for "11" sequences)
Interpretation of whether the spatial distribution for each sequence type is "Aggregated" or "Not Aggregated" based on Z-scores
A summary explaining the implications of these statistics and patterns

The return value aims to provide a clear understanding of the spatial arrangement's characteristics, aiding in further spatial analysis or research.

Details

The function conducts an analysis by first counting the occurrence of specific sequences ("01 or 10" and "11" - equivalent to HD and DD) in the binary matrix. It then calculates expected values, standard deviations, and Z-scores to determine the spatial randomness or aggregation. The analysis considers both horizontal and vertical adjacency (rook case) in the matrix.

References

Madden, L. V., Hughes, G., & van den Bosch, F. (2007). The Study of Plant Disease Epidemics. The American Phytopathological Society.

Examples

if (FALSE) {
matrix_data <- matrix(c(1,1,1,0,0,
                        1,1,1,0,0,
                        1,1,1,0,0,
                        1,1,1,0,0,
                        0,0,0,0,0),
                        ncol = 5, byrow = TRUE)
result_text <- join_count(matrix_data)
cat(result_text)  # Print the rich text output
}