Assesses the overall degree of heterogeneity in a collection of data sets at the sampling-unit scale.

power_law(data, log_base = exp(1), ...)

## Arguments

data A list of intensity objects (count or incidence objects). Logarithm base to be used. Additional arguments to be passed to other methods.

## Value

A power_law object.

## Details

The power law describes the relationship between the observed variance of individuals within a data set (s^2) and the corresponding variance under the assumption of no aggregation (s\'^2). It can be expressed under its logarithmic form as: log(s^2) = log(a) + b log(Y), with:

• Y = p in the case of count data (Taylor's power law).

• Y = p(1 - p) in the case of incidence data (binary power law).

p corresponds to the mean proportion of recorded individuals in case of incidence data, and the absolute value in case of count data.

## References

Taylor LR. 1961. Aggregation, variance and the mean. Nature 189: 732–35.

Hughes G, Madden LV. 1992. Aggregation and incidence of disease. Plant Pathology 41 (6): 657–660. doi:10.1111/j.1365-3059.1992.tb02549.x

Madden LV, Hughes G, van den Bosch F. 2007. Spatial aspects of epidemics - III: Patterns of plant disease. In: The study of plant disease epidemics, 235–278. American Phytopathological Society, St Paul, MN.

## Examples

require(magrittr)
my_data <- do.call(c, lapply(citrus_ctv, function(citrus_field) {
incidence(citrus_field) %>%
clump(unit_size = c(x = 3, y = 3)) %>%
split(by = "t")
}))#> Warning: To get even clumps of individuals, a total of 380 source sampling units were dropped.# my_data is a list of incidence object, each one corresponding to a given
# time at a given location.
my_power_law <- power_law(my_data)#> Warning: Missing cases were dropped.#> Warning: Missing cases were dropped.#> Warning: Missing cases were dropped.#> Warning: Missing cases were dropped.my_power_law#> Binary Power Law:
#> Power law analysis for 'incidence' data.
#>
#> Coefficients:
#> (Intercept)      log(x)
#>    3.653887    1.935628
#> summary(my_power_law)#>
#> Call:
#> power_law(data = my_data)
#>
#> Residuals:
#>      Min       1Q   Median       3Q      Max
#> -0.56432 -0.15156  0.00996  0.16278  0.57520
#>
#> Coefficients:
#>                           Estimate Std. Error t value Pr(>|t|)
#> (Intercept): log_base(Ar)   3.6539     2.1491   1.700  0.11993
#> log(x): b                   1.9356     0.5701   3.395  0.00683 **
#> Ai                         38.6245    83.0079   0.465  0.65168
#> ai                          0.5493     0.4940   1.112  0.29216
#> AI                          0.6327     0.2344   2.700  0.02233 *
#> aI                         44.4927    40.0118   1.112  0.29216
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#>
#> Residual standard error: 0.3255 on 10 degrees of freedom
#> Multiple R-squared:  0.5355,	Adjusted R-squared:  0.489
#> F-statistic: 11.53 on 1 and 10 DF,  p-value: 0.006827
#> plot(my_power_law) # Same as: plot(my_power_law, scale = "log")plot(my_power_law, scale = "lin")