Power analysis for longitudinal binary data

The aim of this work is to generate simulations of various sampling protocols of a longitudinal study of binary data. The conservation status of a site is evaluated as good or bad. This evaluation is repeated on several sites and repeated over time.<br><br>The main interest is to evaluate the proportion of sites in good or bad conservation state during the first year (initial situation) and then to evaluate how the situation<br>change over time (trends).<br><br>We want to evaluate the influence of the sampling size, frequency, repetition, etc... on the statistical power and the size of the confidence intervals.<br><br>A first function generate the simulations, analyze the fake dataset and stores the model parameters.<br>A grid of function parameters is generated to apply this first function with various combinations of options corresponding to various sampling protocols.<br>A second function aggregate these results for each combination of parameters and compute descriptive statistics like the power of the tests and the confidence<br>intervals of the parameters<br>The outputs are saved on the disc and are available for data visualization (produced in another script).<br><br>The pdf report present a graphical exploration of the results of these simulations.<br><br>The "results" directory contains the ouput of the raw simulations : output_simulations_initial.csv are simulation for one year only to estimate the initial proportion of sites in bad conservation state. output_simulations_trends.csv contains simulations of dataset over several years to explore the statistical power of the slopes/trends over time. there are 50 simulations for each combination of parameters.<br><br>The 2 other files are aggregated versions of these files. The 50 simulations for each combination of parameters are grouped to compute the statistical power and confidence intervals. <br><br>This approach of power analysis is described by Gelman &amp; Hill (2007) : Gelman A, Hill J (2007) Data analysis using regression and multilevel/hierarchical models. Cambridge University Press