Power analysis for longitudinal binary data

Abstract

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. 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 change over time (trends). We want to evaluate the influence of the sampling size, frequency, repetition, etc... on the statistical power and the size of the confidence intervals. A first function generate the simulations, analyze the fake dataset and stores the model parameters. A grid of function parameters is generated to apply this first function with various combinations of options corresponding to various sampling protocols. A second function aggregate these for each combination of parameters and compute descriptive statistics like the power of the tests and the confidence intervals of the parameters The outputs are saved on the disc and are available for data visualization (produced in another script). The pdf report present a graphical exploration of the of these simulations. 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. 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. This approach of power analysis is described by Gelman & Hill (2007) : Gelman A, Hill J (2007) Data analysis using regression and multilevel/hierarchical models. Cambridge University Press