Description
Optimal Stratification of Univariate Populations.
Description
The stratification of univariate populations under stratified sampling designs is implemented according to Khan et al. (2002) <doi:10.1177/0008068320020518> and Khan et al. (2015) <doi:10.1080/02664763.2015.1018674> in this library. It determines the Optimum Strata Boundaries (OSB) and Optimum Sample Sizes (OSS) for the study variable, y, using the best-fit frequency distribution of a survey variable (if data is available) or a hypothetical distribution (if data is not available). The method formulates the problem of determining the OSB as mathematical programming problem which is solved by using a dynamic programming technique. If a dataset of the population is available to the surveyor, the method estimates its best-fit distribution and determines the OSB and OSS under Neyman allocation directly. When the dataset is not available, stratification is made based on the assumption that the values of the study variable, y, are available as hypothetical realizations of proxy values of y from recent surveys. Thus, it requires certain distributional assumptions about the study variable. At present, it handles stratification for the populations where the study variable follows a continuous distribution, namely, Pareto, Triangular, Right-triangular, Weibull, Gamma, Exponential, Uniform, Normal, Log-normal and Cauchy distributions.
README.md
stratifyR 1.0-3
The goal of stratifyR is to construct stratification boundaries using either the continuous variable in your data or a hypothetical distribution for your variable.
Installation
You can install stratifyR using:
install.packages("stratifyR")
Example
This is a basic example which shows you how to solve a common stratification problem:
library(stratifyR)
#> Loading required package: fitdistrplus
#> Loading required package: MASS
#> Loading required package: survival
#> Loading required package: zipfR
#> Loading required package: actuar
#>
#> Attaching package: 'actuar'
#> The following objects are masked from 'package:stats':
#>
#> sd, var
#> The following object is masked from 'package:grDevices':
#>
#> cm
#> Loading required package: triangle
#> Loading required package: mc2d
#> Loading required package: mvtnorm
#>
#> Attaching package: 'mc2d'
#> The following objects are masked from 'package:base':
#>
#> pmax, pmin
## basic example code using data
data(sugarcane)
Production <- sugarcane$Production
hist(Production)
res <- strata.data(Production, h = 2, n=1000)
#> The program is running, it'll take some time!
summary(res)
#> _____________________________________________
#> Optimum Strata Boundaries for h = 2
#> Data Range: [0.42, 1570.38] with d = 1569.96
#> Best-fit Frequency Distribution: gamma
#> Parameter estimate(s):
#> shape rate
#> 1.520409984 0.009226811
#> ____________________________________________________
#> Strata OSB Wh Vh WhSh nh Nh fh
#> 1 195.18 0.68 2832.16 36.219 458 9456 0.05
#> 2 1570.38 0.32 18071.08 42.939 542 4438 0.12
#> Total 1.00 20903.24 79.158 1000 13894 0.07
#> ____________________________________________________
## basic example code using distribution
res <- strata.distr(h=2, initval=0.65, dist=68, distr = "gamma",
params = c(shape=3.8, rate=0.55), n=500, N=10000)
#> The program is running, it'll take some time!
summary(res)
#> _____________________________________________
#> Optimum Strata Boundaries for h = 2
#> Data Range: [0.65, 68.65] with d = 68
#> Best-fit Frequency Distribution: gamma
#> Parameter estimate(s):
#> shape rate
#> 3.80 0.55
#> ____________________________________________________
#> Strata OSB Wh Vh WhSh nh Nh fh
#> 1 7.47 0.63 2.61 1.014 247 6279 0.04
#> 2 68.65 0.37 7.83 1.041 253 3721 0.07
#> Total 1.00 10.44 2.055 500 10000 0.05
#> ____________________________________________________
The functions can be dynamically used to visualize the the strata boundaries, for 2 strata, over the density (or observations) of the “mag” variable from the quakes data (with purrr and ggplot2 packages loaded).
library(stratifyR)
library(ggplot2)
res <- strata.distr(h=2, initval=4, dist=2.4, distr = "lnorm",
params = c(meanlog=1.52681032, sdlog=0.08503554), n=300, N=1000)
#> The program is running, it'll take some time!
ggplot(data=quakes, aes(x = mag)) +
geom_density(fill = "blue", colour = "black", alpha = 0.3) +
geom_vline(xintercept = res$OSB, linetype = "dotted", color = "red")
Read the stratifyR vignette for a complete documentation and many more examples using 10 different distributions.