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Information Consistency-Based Measures for Spatial Association

1. The principle of the information consistency-based measures

IN(d,s)=I(d,s)I(d)=I(d)I(ds)I(d)=1siSxVdp(si,x)logp(xsi)xVdp(x)logp(x)

where p(x) is the probability of observing x in U, p(si,x) is the probability of observing si and x in U, and p(xsi) is the probability of observing x given that the stratum is si.

2. Example

install.packages("itmsa", dep = TRUE)
install.packages("gdverse", dep = TRUE)
library(itmsa)
ntds = gdverse::NTDs
ntds$incidence = sdsfun::discretize_vector(ntds$incidence, 5)
itm(incidence ~ watershed + elevation + soiltype,
    data = ntds, method = "icm")
## # A tibble: 3 × 3
##   Variable     Iv    Pv
##   <chr>     <dbl> <dbl>
## 1 watershed 0.445     0
## 2 elevation 0.390     0
## 3 soiltype  0.210     0