DOI: 10.5061/dryad.3bk3j9kv6
title: Data from: Accurately estimating correlations between demographic parameters: A comment on Deane et al. (2023)

description: Estimating correlations among demographic parameters is an important
 method in population ecology. A recent paper by Deane et al. (2023)
 attempted to explore the effects of different priors for covariance
 matrices on inference when using mark-recovery data. Unfortunately, Deane
 et al. (2023) made a mistake when parameterizing some of their models.
 Rather than exploring the effects of different priors, they examined the
 effects of the use of incorrect equations on inference. In this
 manuscript, we clearly describe the mistake in Deane et al. (2023). We
 then demonstrate the use of an alternative and appropriate method and
 reach different conclusions regarding the effects of priors on inference.
 Consistent with other recent literature, informative inverse Wishart
 priors can lead to flawed inference, while vague priors on covariance
 matrix components have little impact when sample sizes are adequate.
description: The data used in this manuscript were simulated, and the
 simulation and analysis code are stored in this repository.
description: # Data from: Accurately estimating correlations between demographic
 parameters: A comment on Deane et al. (2023)
 [https://doi.org/10.5061/dryad.3bk3j9kv6](https://doi.org/10.5061/dryad.3bk3j9kv6) ## Description of the data and file structure The manuscript uses simulated data. ### Files and variables There are two Stan model files (mGamma.STAN and mUniform.STAN) that analyze the data generated in the simulation_marr_Stan.R file. The figures.R file generates the figures published in the manuscript. Abbreviations used in simulation_marr_Stan.R: nS: the number of Simulations to run nR: the number of individuals to Release during each year nT: the number of years (i.e., Time-steps) of data to simulate Gres.rho: storing correlation estimates from each simulation from models using gamma priors Gres.s1 and Gres.s2: storing standard deviations estimates from each simulation from models using gamma priors Gres.m1 and Gres.m2: storing mean estimates from each simulation from models using gamma priors for Ures.rho: storing correlation estimates from each simulation from models using uniform priors Ures.s1 and Ures.s2: storing standard deviations estimates from each simulation from models using uniform priors Ures.m1 and Ures.m2: storing mean estimates from each simulation from models using uniform priors tru.____: the simulated values used to generate the data rho: the correlation between survival and band-recovery rates sigma: standard deviations of hunting and natural mortality hazard rate Sigma: covariance matrix epsilon: time-varying correlated random effects h: hunting mortality hazard rates (h[,1] is hunting, h[,2] is natural) S: Survival c: crippling loss rate r: band reporting rate f: band recovery probability pr: cell probabilities for the m-array marr: the simulated m-array stan_data: data fed to Stan for use in models using uniform and gamma priors ni: number of iterations nb: number of iterations to 'burn' nc: number of chains and cores to use for parallel processing nt: thinning rate (e.g., we saved every fifth iteration, this is unnecessary) m1: results from the model with gamma priors for the standard deviations m2: results from the model with uniform priors for the standard deviations Abbreviations used in figures.R: fail: identifying models that did not converge based on Vehtari's modified R-hat U: a data frame used to plot correlation estimates from the model with uniform priors for the standard deviations G: a data frame used to plot correlation estimates form the model with gamma priors for the standard deviations pU: a ggplot scatterplot regressing estimates from the Uniform model against the true values used to generate the data pG: a ggplot scatterplot regressing estimates from the Gamma model against the true values used to generate the data pRho: a scatterplot of the median estimates from each model.## Code/software We used R version 4.2.2 ('innocent and trusting') and the most recent version of Stan and package Rstan, as well as ggplot2.