Spatial Autocorrelation

The global Morans statistic is used to evaluate whether a feature represents a clustered, discrete, or random pattern based on the specified feature and associated attributes.

Principles of analysis

The statistical value of Spatial Autocorrelation can be calculated according to the following formula:

The mathematical formula on which the Global Moran's I statistic is based is shown above. The tool calculates the mean and variance of the evaluated attribute. The mean is then subtracted from each element value to obtain the deviation from the mean. The numerator of the Global Moran's I statistic is the sum of the difference products obtained by multiplying the deviation values of all neighboring features, such as features located within a specified distance.

After the Global Moran's I tool calculates the index value, it calculates the Expectations Index: value. The Expectations Index: value is then compared to the observation index value. Given the number of features in the Dataset and the variance of all data values, the tool calculates a z-score and a p-value to indicate whether the difference is statistically significant. The index values cannot be interpreted directly, but only in the context of the null hypothesis.

Application case

By finding the distance (i.e., the distance corresponding to the location where Spatial Autocorrelation is strongest), the appropriate proximity distance can be determined for the various Spatial Analysis methods.
Measures the overall trend of racial or ethnic separation over time-is the degree of separation increasing or decreasing?
Summarize the spread of an idea, disease, or trend over space and time-does the idea, disease, or trend remain quarantine and concentrated, or does it spread and become more dispersed?

Function entrance

Spatial Statistical Analysis tab-> Analysis Mode-> Spatial Autocorrelation. （iDesktopX）
Toolbox, Spatial Statistical Analysis, Analysis Mode, Spatial Autocorrelation. (iDesktopX)

Main parameters

Source Data: Set the Vector Dataset to be analyzed, which supports three types of Dataset: point, line and surface. A Object CountGreater than or equal of to 30 in the source data is recommended to ensure the reliability of the results.
Evaluation Field: Set the Property Field value of the analysis element involved in the analysis. Only numerical fields are supported.
Conceptual Model: The selection should reflect the inherent relationships between the features to be analyzed. Set the way features interact with each other in space. The more realistic the model, the more accurate the results will be.
- Fixed Distance: Applicable to point data and face data with large size change.
- Polygon Adjacent (Common Edges/Intersect): Applies to face data with adjacent edges and intersections.
- Polygon Adjacent (Node/Common Edges/Intersect): Applies to face data with adjacent points, adjacent edges, and intersections.
- Inverse Distance: All features are treated as neighbors to all other features. All features contribute to the target feature, but the contribution decreases as the distance increases. Features are weighted as a fraction of the distance. Applies to continuous data.
- Inverse Distance Square: Similar to the Inverse Distance ", influence decreases more rapidly as distance increases, and the weight between elements is one part of the square of the distance.
- K Nearest Neighbors: The K elements closest to the target element are included in the calculation of the target element (with a weight of 1), and the remaining elements are excluded from the calculation of the target element (with a weight of 0). This option is useful if you want to ensure that you have a minimum number of adjacent features for analysis. This method works well when the distribution of the data varies over the study area such that some elements are distant from all others. When the proportion of fixed analysis is not as important as fixed adjacent Records, the K nearest neighbor method is more suitable.
- Spatial Weight Matrix: a Spatial Weight Matrix File is required. Spatial weights are numbers that reflect the distance, time, or other costs between each element and any other element in the Dataset. If you want to model the accessibility of urban services, for example, to find areas of urban crime concentration, it is a good way to model spatial relationships with the help of networks. You can select an existing Spatial Weight Matrix File (.swmb) or create a new one based on the Source Dataset.
- Undifferentiated Region: This model is a combination of Inverse Distance "and Fixed Distance" that treats each feature as an adjacent feature to each other. This option is not suitable for large Datasets. Features within the specified fixed distance range have equal weight (weight of 1); features outside the specified fixed distance range have less influence as the distance increases.
Break Distance Tolerance: "-1" indicates that the default distance is calculated and applied. This default value is to ensure that each feature has at least one adjacent feature. "0" indicates that no distance is applied, and each feature is an adjacent feature. A non-zero positive value indicates adjacent features when the distance between features is less than this value.
Inverse Distance Power Index: An index that controls the importance of the distance value. The higher the power value, the smaller the influence of the distance.
Number of Adjacent Elements: Set a positive integer, indicating that the nearest K elements around the target element are adjacent elements. This parameter needs to be set when "K Nearest Neighbors" "is selected for the conceptual model.
Measure Distance Method: The Measure Distance method uses Euclidean distance and Manhattan distance. Detail Description for Euclidean Distance and Manhattan Distance. Refer to the Basic Vocabulary of Spatial Statistical Analysis .
Spatial Weights Matrix Standard ization: Spatial Weights Matrix Standard ization is recommended when the distribution of features may deviate due to sampling design or imposed aggregation scheme. When you select a Spatial Weights Matrix Standard ization, each weight is divided by the sum of the rows (the sum of the weights of all adjacent features). Weighting of Spatial Weights Matrix Standard ization is typically used in conjunction with fixed distance neighboring features, and is almost always used for neighboring features based on face adjacency. This reduces the bias that occurs when an element has a different number of adjacent elements. The Spatial Weights Matrix Standard ization will scale all weights between 0 and 1, creating a relative (rather than absolute) weight scheme. You may want to select the Spatial Weights Matrix Standard ization "option whenever you are working with a face feature that represents an administrative boundary.

Explanation of results

Analyst Result is a CAD Dataset and will be displayed in a Map.

The Spatial Autocorrelation Analyst Result includes five parameters: Moran's I index, expected value, variance, Z score and P value. When z-score or p-value is used to indicate statistical significance, Reject the null hypothesis can be used. If the Moran's I index value is positive, it means that the data has a positive spatial correlation. The value used by Dataset for analysis is proportional to the degree of spatial aggregation; A negative Moran's I index value indicates a dispersion trend. As shown in the following figure:

Instance

Case data: Click here to download the case data . After downloading, unzip it for use.

For the existing data of viral hepatitis in a province in a year, the incidence of viral hepatitis (Pneumonia) was analyzed by Spatial Autocorrelation, and the evaluation fields were set as incidence, and the conceptual model was Inverse Distance. The Measure Distance method is Euclidean Distance, which standardizes the spatial weight matrix and defaults to other methods. Analyst Result is as follows:

The following conclusions can be drawn from the Analyst Result:

在Random Distribution的假设下，P值 < 0.01 且 z得分 > 2.58, 该省当年肝炎发病数的Analyst Result具有99%的置信度是具有显著性的。Moran’s I > 0 ，该省当年病毒性肝炎发病数呈空间正相关性，具有一定空间聚集度。