# How Do You Interpret Moran’s I Statistic?

How do you interpret Moran's I statistic? If the values in the dataset tend to cluster spatially (high values cluster near other high values; low values cluster near other low values), the Moran's Index will be positive. When high values repel other high values, and tend to be near low values, the Index will be negative.

## What does the Moran's I value mean?

Moran's I is a correlation coefficient that measures the overall spatial autocorrelation of your data set. In other words, it measures how one object is similar to others surrounding it. It is similar to correlation coefficients, it has a value from -1 to 1.

## How do you read Local Moran's I?

Interpretation. A positive value for I indicates that a feature has neighboring features with similarly high or low attribute values; this feature is part of a cluster. A negative value for I indicates that a feature has neighboring features with dissimilar values; this feature is an outlier.

## What does a negative Morans I mean?

While a positive Moran's I hints at data is clustered, a negative Moran's I implies data is dispersed.

## What is Local Moran's I?

Local Moran's I is a local spatial autocorrelation statistic that identifies local clusters or local outliers to understand their contribution to the 'global' clustering statistic. It was developed by Anselin (1995) as a class of local indicators called Local Indicators of Spatial Association (LISAs).

## Related faq for How Do You Interpret Moran's I Statistic?

### What is the statistic Moran's I used to measure?

In statistics, Moran's I is a measure of spatial autocorrelation developed by Patrick Alfred Pierce Moran. Spatial autocorrelation is characterized by a correlation in a signal among nearby locations in space.

### What is the difference between Moran's I and Geary's C?

Globals. Moran's I and Geary's c are well known tests for spatial autocorrelation. Moran's I is produced by standardizing the spatial autocovariance by the variance of the data. Geary's c uses the sum of the squared differences between pairs of data values as its measure of covariation.

### What is a Moran scatterplot?

The Moran scatter plot, first outlined in Anselin (1996), consists of a plot with the spatially lagged variable on the y-axis and the original variable on the x-axis. The slope of the linear fit to the scatter plot equals Moran's I.

### What is bivariate Local Moran's I?

Bivariate Moran's I is a global measure of spatial autocorrelation to measure the influence one variable has on the occurrence of another variable in close proximity. Whereas the original Moran's I statistic measured the degree of linear association of the values of a variable in neighbouring regions.

### What are Lisa clusters?

LISA Principle

Such clustering is a characteristic of the complete spatial pattern and does not provide an indication of the location of the clusters. The concept of a local indicator of spatial association, or LISA was suggested in Anselin (1995) to remedie this situation.

### What is Getis Ord Gi?

The Hot Spot Analysis tool calculates the Getis-Ord Gi* statistic (pronounced G-i-star) for each feature in a dataset. The resultant z-scores and p-values tell you where features with either high or low values cluster spatially. This tool works by looking at each feature within the context of neighboring features.

### What relationship does the Z score have to the Moran's I index?

When the z-score or p-value indicates statistical significance, a positive Moran's I index value indicates tendency toward clustering, while a negative Moran's I index value indicates tendency toward dispersion.

### What is positive spatial autocorrelation?

Positive spatial autocorrelation means that geographically nearby values of a variable tend to be similar on a map: high values tend to be located near high values, medium values near medium values, and low values near low values.

### What a moran means?

1 : a foolish or stupid person … once their business is over [clients] go right back to thinking you're either a crook or a moron.

### How does Local Moran's I work?

Local Moran's I is a local spatial autocorrelation statistic based on the Moran's I statistic. It was developed by Anselin(1995) as a local indicator of spatial association or LISA statistic. "the sum of LISAs for all observations is proportional to a global indicator of spatial association."

### What is a Lisa map?

The LISA Cluster Map shows the significant locations color coded by type of spatial autocorrelation. The above map shows p<.001 and 999 permutations. • High-high and low-low = spatial clusters. • High-low and low-high = spatial outliers. The spatial clusters on the map refer to the core of the cluster.

### What does a Lisa map show?

LISA Significance Map

This display shows the statistical significance level at which each region can be regarded as making a meaningful contribution to the global spatial autocorrelation outcome. Note that a statistically significant result may be either very high or very low.

### What is a spatial weights matrix?

A spatial weights matrix is a representation of the spatial structure of your data. It is a quantification of the spatial relationships that exist among the features in your dataset (or, at least, a quantification of the way you conceptualize those relationships).

### What does negative spatial autocorrelation mean?

Negative spatial autocorrelation refers to a geographic distribution of values, or a map pattern, in which the neighbors of locations with large values have small values, the neighbors of locations with intermediate values have intermediate values, and the neighbors of locations with small values have large values.

### What is spatial lag model?

A spatial lag (SL) model. Assumes that dependencies exist directly among the levels of the dependent variable. That is, the income at one location is affected by the income at the nearby locations.

### What is bivariate Lisa?

Bivariate LISA examines the spatial relationship between the exposure and the outcome variable for the geographic regions of India.

### What is global spatial autocorrelation?

Global Spatial Autocorrelation. Positive spatial autocorrelation means that the locations close together have similar values, while negative spatial autocorrelation means that locations close together have more dissimilar values than those locations further away.

### What is local indicators of spatial association?

Local indicators for spatial association (LISAs) are a class of local statistics that measure spatial association in sub-regions of the study region. They are also used to identify spatial outliers and local clusters (Anselin, 1995).

### What is a Semivariogram?

The semivariogram is a statistic that assesses the average decrease in similarity between two random variables as the distance between the variables increases, leading to some applications in exploratory data analysis.

### What is spatial Correlogram?

Spatial correlograms are great to examine patterns of spatial autocorrelation in your data or model residuals. They show how correlated are pairs of spatial observations when you increase the distance (lag) between them – they are plots of some index of autocorrelation (Moran's I or Geary's c) against distance.

### What is local spatial autocorrelation?

Local measures of spatial autocorrelation focus on the relationships between each observation and its surroundings, rather than providing a single-number summary of these relationships across the map.

### What does high high cluster mean?

Only High-High Cluster. A location where the only statistically significant type throughout time has been High-High Clusters. Only High-Low Outlier. A location where the only statistically significant type throughout time has been High-Low Outliers.

### What is a hot spot analysis?

Hotspot analysis is a spatial analysis and mapping technique interested in the identification of clustering of spatial phenomena. These spatial phenomena are depicted as points in a map and refer to locations of events or objects.

### What is spatial geography?

Spatial information is the digital connection between location, people and activities. This information can graphically illustrate what is happening where, how and why to show the insight and impact of the past, the present and the likely future.

### What is Getis Ord statistic?

The Getis–Ord Gi statistic is a distinct perspective on the question of geographical clustering from other measures, like the Local Geary's ci or Local Moran's Ii statistics. The Getis–Ord Gi statistic measures whether the area around site i tends to be larger (or smaller) than areas that are not near site i.

### How do you read a hotspot analysis?

A high z-score and a low p-value for a feature indicates a significant hotspot. A low negative z-score and a small p-value indicates a significant cold spot. The higher (or lower) the z-score, the more intense the clustering. A z-score near 0 means no spatial clustering.

### What is spatial autocorrelation GIS?

Spatial autocorrelation is simply looking at how well objects correlate with other nearby objects across a spatial area. Positive autocorrelation occurs when many similar values are located near each other, while negative correlation is common where very different results are found near each other.

### What is point pattern analysis in GIS?

Point pattern analysis (PPA) is the study of the spatial arrangements of points in (usually 2-dimensional) space. The simplest formulation is a set X = x ∈ D where D, which can be called the 'study region,' is a subset of Rn, a n-dimensional Euclidean space.

### What is spatial statistics in GIS?

The GIS dictionary (Wade and Sommer, 2006) define spatial statistics as "the field of study concerning statistical methods that use space and spatial relationships (such as distance, area, volume, length, height, orientation, centrality and/or other spatial characteristics of data) directly in their mathematical