Bivariate Moran’s I

Introduction

The Bivariate Moran’s I is very similar to the Moran’s I tool, except that rather than determining the level of spatial autocorrelation within one variable (that is, how clustered in space one variable is in terms of high and low values), the bivariate tool determines whether there is spatial autocorrelation between two variables (that is, how clustered in space two variables are in terms of high and low values.)

Like the Moran’s I, the range of possible Moran’s I is between -1 and 1. An estimate of 0 implies no spatial autocorrelation. For a significant estimate the closer it gets to 1, the greater the degree of positive spatial autocorrelation; while the closer it is to -1 indicates stronger negative spatial autocorrelation.

Inputs

In this example, we will determine how much spatial autocorrelation there is between socio-economic disadvantage and the rate of Type II diabetes across Melbourne. To do this:

  • Select Melbourne GCCSA as you area
  • Select the following datasets:
    • SA2 Summary Measure of Disadvantage, selecting all variables
    • SA2 Chronic Disease – Modelled Estimate, selecting Statistical Area 2 Name, Statistical Area 2 Code and Diabetes – Rate per 100
  • Merge the two datasets together
  • Spatialise the merged dataset
  • Generate a spatial weights matrix for the spatialised dataset

Once you have done this, open the Bivariate Moran’s I tool (Tools → Spatial Statistics → Bivariate Moran’s I) and enter the parameters as shown below. Each of these parameters is explained more fully underneath the image

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  • Dataset Input:  The dataset that contains the variable(s) to be tested. This dataset must be a spatialised dataset. In this instance, it is a merged dataset that has been spatialised, which we have called SPATIALISED MERGED Chronic Disease and Disadvantage
  • Spatial Weights Matrix: The spatial weights matrix generated from your spatialised dataset, used to determine the level of spatial proximity amongst your areas of interest. In this instance we have generated a contiguous spatial weights matrix named Cont SWM Chronic Disease and Disadvantage
  • Key Column: This is the column that contains the unique codes for each of the areas in the dataset. In this instance it is the column called Statistical Area Level 2 Name
  • X Variable: This is the first of the two variables being tested for spatial autocorrelation (one against the other). This will be the non lagged variable. In this instance we specify SEIFA Index of Relative Socio-Economic Disadvantage – Index Score as the X variable
  • Y Variable: This is the second of the two variables being tested for spatial autocorrelation (one against the other). This will be the lagged variable. In this instance we specify Diabetes – Rate per 100 as the Y variable
  • Alternative Hypothesis – indicates the alternative hypothesis, can be two sided, greater than or less than. In this instance we have selected two.sided
  • Inference – a tick box indicating the assumption under which the variance should be calculated. A tick indicates randomisation, blank indicates normality.

Once you have entered your parameters click Add and Run

Outputs

Once your process has run you will get a pop up box looking like the one below. Check both boxes and click Display. This will bring up two outputs

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  • A table named Output: BivariateMoranI-Workflow XXX which, when opened, should look something like the table displayed below. This table contains for each row, the X variable (i.e. the IRSD Score of the SA2) value, the Y variable (i.e the per 100 rate of diabetes for the SA2), the lagged Y value (i.e. the mean value of type 2 diabetes for all of the SA2s which surround that particular SA2), the scaled X value (i.e. the Z score for the IRSD score of the SA2) and the scaled lagged Y variable (i.e. the Z score for the mean value of the type 2 diabetes of for all the SA2s which surround that particular SA2).
  • A text file named Text: BivariateMoranI-Workflow XXX which, when opened should look something like the image displayed below. This file contains the outcome of the Bivariate Moran’s I workflow with the value of Moran’s I for the two variables, together with its significance. In this instance, the Moran’s I value is -0.5396 with a P value of ~0 , indicating a highly significant negative relationship between the IRSD score and the rate of type II diabetes. This indicates that high IRSD scores (low disadvantage) tended to be clustered in space with low rates of type II diabetes
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