Vernacular spatial Statistics 14: Clustering of high/low values (upper)

From the last 0 hypothesis, we all know that we have to go into all sorts of magical statistical theory stages, but because of the Wu Dao, I try not to write the official flavor of the white paper.

today we're going to talk about an advanced measure of spatial autocorrelation: High / clustering of low values.

Previously, the relationship between spatial data is nothing more than three possible-discrete, random, aggregated, as follows:

So when we get the data, we first determine whether it's discrete or aggregate, because random is worthless. Only after the determination, we can absolutely how to deal with him, is steamed or braised, or cold, to see the raw materials.

as for how to confirm, we have also talked about the Moran index this thing, of course, accompanied by certain P Values and Z score God horse, interested classmates, please check the previous article.

So what happens when you get the data and make sure it's possible to assemble?

Let's continue to look at the following example:

Continue to toss coins:

Disposable Throw - a coin with a good number, as a result. I circled the results with a red circle, and it was easy to see that the gathering had occurred, and the result of the experiment was mainly the reverse.

So, after we find out the possibility of clustering, we can further analyze what kind of data is gathered, which determines what kind of values produce clustering, called "High / Low-value clustering "analysis.

The following entry into the history of popular science practice, this is used to determine high / the method of value clustering was first developed by the McDonough School of Business, University of Georgetown, USA (McDonough School of Business) of J. Keith Ord and Arthurgetis, of the geography department at San Diego State University, proposed that, therefore, this algorithm is usually referred to by the Getis-ord General G analysis. Is the following two dudes (I've always paid tribute to the people who study algorithms):

Unlike coins, the data can be divided into high and low values, such as:

In the previous measurement of spatial autocorrelation, the parameters used are Moran ' I (Moran Index), then in the measurement of low-value clustering, the use of an exponent, the index is called the General G Index.

General G The index, like the Moran Index, is a corollary statistic, that is, you get the data to the next step. For example, when you blind Date, the first time the sister paper photos to the time, the first thing to do is to see if it is in line with their own aesthetic, and then is to find out if there are traces of PS , Through small details to imagine a younger sister paper what kind of love character ah , such; the process of using limited data to estimate the characteristics of an overall situation is the inference statistic.

The results obtained from the analysis are interpreted in the context of 0 assumptions (in the context of a blind guess). In other words, your calculated value, just a comparison with the result of a blind guess, does not represent the actual result.

General G Statistically, there is no clustering for the null hypothesis (blind guessing). When you perform the general G method for calculation, you will get a bunch of values, as follows:

Z the points and P The value and the variance is what meaning does not explain, everybody looks back to the original article, emphatically explains the observation General G Indices and expectations General index is something.

first, it's important to see if the data is meaningful because P The value represents whether your data is random, as shown in:

P value determines whether your data has analytical value, and if we can get to the next step, then Z value becomes important. Unlike the z - values in spatial correlation, the positive and negative signs ofZ -values are meaningful in the general G - statistic calculation, as follows:

See, there's going to be people jumping out of here, your observations . General G Indices and expectations General G where did the index go? Now that Z -values have already marked you with a high / low value cluster, what's the use of this two index?

Don't worry, keep looking down.

we started talking, General G method is used to explore the high \ value Clustering, the two indices are also used to measure whether high-value clustering or low-value clustering is occurring.

A single index is meaningless, since he gives two indices, which means that you have to compare them. In the algorithm, as long as the z - score is positive, then generally the observation index will be larger than the expected index, and if the z -score is negative, then the expected index will be greater than the observation index, as follows:

Then combine the two graphs to get the following results:

Z the score is positive--observation General G index greater than expected Generalg index-data is clustered in high-value regions.

Z the score is negative--expectation General G index greater than observation Generalg index-data is clustered in low-value regions.

But, as everyone was young, the other bears have been the elder-"Do you like Baba or hemp?" "Children are often overwhelmed, and parents teach children how to deal with these elder bear elders," say ' all like ', and then everyone is happy. " What if a single piece of data shows clustering in both high and low values?

then it's easy to see Generalg Indices and expectations General G exponential equality, then it is officially said that "when high and low values are clustered together, they tend to cancel each other out." "such as:

when these high and low values are all clustered, you can basically discard the tool and use the spatial autocorrelation tool ( Globe Moran ' I ).

Therefore, it is obvious that this tool is mainly to look for high value or low value when one of the parties occurs clustering, in order to play his value.

(to be continued before the end)

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Vernacular spatial Statistics 14: Clustering of high/low values (upper)