Abstract
Often quantitative data analysis begins with an inspection of attribute variable histograms. Ratio scale demographic variables, such as population density (which has a natural, meaningful absolute 0 value), are expected to conform, at least approximately, to a normal probability distribution. Frequently this conformity requires that these variables be subjected to a symmetricizing, variance stabilizing transformation, such as the Box-Cox class of power functions or the Manley exponential function. Counts (i.e., aggregated nominal measurement scale) data used to construct ratios, such as the crude fertility rate (i.e., number of births per number of women in the child bearing age cohort), are expected to conform to a Poisson probability distribution. And, counts data that constitute some subset of a total, such as the percentage of people at least 100 years of age or the percentage of a population that is the women in the child bearing age cohort, are expected to conform to a binomial probability distribution.
Keywords
- Markov Chain Monte Carlo
- Spatial Autocorrelation
- Markov Chain Monte Carlo Simulation
- Poisson Random Variable
- Positive Spatial Autocorrelation
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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- 1.
The correlations between the simulated random normal variate and the sum of two eigenvectors representing global map, two representing regional, and two representing local map patterns used to construct Table 2 respectively are 0.031, 0.018 and –0.004—essentially 0.
- 2.
Auto- models have values of the response variable, Y, on both sides of the equation. The right-hand side, which relates to a probability model, contains a linear combination of values of Y for other than the observation in question.
- 3.
More work has been done on the Bernoulli, vis-à-vis the autologistic model, than on the general binomial RV.
- 4.
This is not the case for binary 0–1 Bernoulli RVs, which by their very nature cannot exhibit extra variation. The concept of extra variation in a logistic regression has to be teased out of data by, for example, grouping values in order to have an N > 1.
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Acknowledgment
This research was completed while the author was a visiting scientist at the Max Planck Institute for Demographic Research, Rostock, Germany, 2005.
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Griffith, D.A., Paelinck, J.H. (2011). Frequency Distributions for Simulated Spatially Autocorrelated Random Variables. In: Non-standard Spatial Statistics and Spatial Econometrics. Advances in Geographic Information Science, vol 1. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-16043-1_4
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