# Moran's I: Selecting the best option for conceptualizing the spatial relationship between # births & county locations

I'm using Moran's I to see whether there are clusters of births rates present among the 83 Michigan counties, and, if so, whether the clustering is statistically significant.

The inputs are the feature locations (counties) and the feature values (the total fertility rate values we've calculated for each county).

But now I'm stuck because I'm unsure which method I should use to model the spatial relationship. It seems like "polygon continuity", "K nearest neighbors", or the option to "generate spatial weights matrix file" could apply.

Should I select the option to generate a spatial weights matrix, since the total fertility rates for all 83 counties would likely need to be assessed entirely in order to determine the boundaries for clusters?

• For discrete units (polygons) you should be using kNN contegency in defining the Wij weights matrix. Are you using the global or local (LISA) index? The specification of neighbor contingency may vary based on your hypothesis and which index is used. – Jeffrey Evans Aug 27 '18 at 14:07
• @JeffreyEvans I'm using global moran's I to start. Since the county polygons are relatively the same size, I believe using the edge and corner contiguity would be sufficient. This criteria would fall under K nearest neighbors method, correct? – Ashley Aug 27 '18 at 14:55

Opt for spatial weight matrix while performing autocorrelation.

Let's start with K nearest neighbours: It isn't a suitable option in your case because it is used in distance references and you want to perform spatial statistics between birth and country location which doesn't make sense.

Polygon Continuity: It will provide you with the following results:

1. Area of overlaps

2. The length of coincident edges (edge neighbors)

3. The number of times boundaries cross or touch at a point (node neighbors) between source polygons and neighbor polygons, neighbors of neighbors (second-order contiguity) are not examined.

Spatial weight matrix: a key component in any cross-sectional analysis of spatial dependence. They are an essential element in the construction of spatial autocorrelation statistics and provide the means to create spatially explicit variables, such as spatially lagged variables and spatially smoothed rates.

I don't know what software are you working on but I would suggest using GeoDa, it is a free and open source software tool that serves as an introduction to spatial data analysis. It is designed to facilitate new insights from data analysis by exploring and modelling spatial patterns.

• Not clear on your definitions here. The Wij matrix can be derived using contingency or distance. In the case of polygons, the weights matrix needs to be based on contingency due to variability in areas of the spatial units. In the literature, this contegency is often reffered to as Nth order nearest neighbors. – Jeffrey Evans Aug 27 '18 at 14:01
• I am unable to understand that sir @JeffreyEvans still, as far as I know, Contiguity-based weights matrices include rook and queen. Areas are neighbors under the rook criterion if they share borders, not vertices. Under the queen criterion, areas are neighbors if they share either a border or point and Distance-based weights matrices include distance bands and k nearest neighbors but they are all under the weight matrix itself. – Swarley Aug 27 '18 at 14:12
• You really need to read some of the primary literature on spatial statistics. – Jeffrey Evans Aug 27 '18 at 14:40
• A queen contingency, on lattice data, merely means that if a common vertex representing an intersection with a zero-length boundary is encountered, the neighbor is included. In the context of a Wij matrix this would rarely change the result of an autocorreation statistic and is mostly operational. Where this would matter is on a square lattice where each corner would represent a queens contingency. The important consideration in specifying contingency is the neighbor order included (ie., 1st = neighbors, 2nd = neighbors of 1st order neighbors, 3rd = neighbors of 2nd order neighbors, ...). – Jeffrey Evans Aug 27 '18 at 19:52
• BTW, unless all of your polygons are square, vertices make up edges! The definition of rooks case is common boundary and queens is the addition of neighbors intersecting with a zero length boundary. – Jeffrey Evans Aug 27 '18 at 19:56