Replicate analysis from: Measuring complexity for hierarchical models using effective degrees of freedom

Hierarchical models can express ecological dynamics using a combination of fixed and random effects, and measurement of their complexity (effective degrees of freedom, EDF) requires estimating how much random effects are shrunk towards a shared mean.  Estimating EDF is helpful to (1) penalize complexity during model selection and (2) to improve understanding of model behavior.  I apply the conditional Akaike Information Criterion (cAIC) to estimate EDF from the finite-difference approximation to the gradient of model predictions with respect to each datum.  I confirm that this has similar behavior to widely used Bayesian criteria, and I illustrate ecological applications using three case studies.  The first compares model parsimony with or without time-varying parameters when predicting density-dependent survival, where cAIC favors time-varying demographic parameters more than conventional AIC.  The second estimates EDF in a phylogenetic structural equation model, and identifies a large..., See README for details., , # Replicate analysis from: Measuring complexity for hierarchical models using effective degrees of freedom

https://doi.org/10.5061/dryad.tmpg4f54z

This Open Science archive contains data and scripts to replicate one simulation and three case-study explorations of a generic approach to estimate effective degrees of freedom for widely-used ecological models.

## Description of the data and file structure:

This includes four R scripts that can each be run separately. It also includes three directories:

\* R for shared R-functions;

\* TMB for TMB scripts that specify hierarchical models,

\* Data for data used in case-study demonstrations.

## Sharing/Access information:

\* The case study involving fish life-history is includes two files:

\* fish_traits.csv is extracted from Mlifehist_ver1.0.csv, which is from the Then et al. (2015) natural mortality database and copied from https://www.vims.edu/research/departments/fisheries/programs/mort_db/, but replaced blank cells are replace...

分层模型（hierarchical models）可结合固定效应与随机效应刻画生态动态，而其复杂度的量化（有效自由度（effective degrees of freedom, EDF））需要评估随机效应向共享均值收缩的程度。
估算有效自由度有助于（1）在模型选择阶段对模型复杂度进行惩罚，（2）加深对模型行为特性的理解。
本研究采用条件赤池信息准则（conditional Akaike Information Criterion, cAIC），通过对模型预测关于各数据点的梯度进行有限差分近似，来估算有效自由度。本研究证实该方法与广泛使用的贝叶斯准则具有相近的性能，并通过3个案例研究展示其生态学应用场景。
第一个案例对比了在预测密度依赖存活时，含时变参数与不含时变参数的模型简约性，结果显示条件赤池信息准则较常规AIC更倾向于选择时变人口统计学参数模型。第二个案例在系统发育结构方程模型中估算有效自由度，并识别出较大的……详见README文件。

# 复现分析源自：《基于有效自由度的分层模型复杂度量化》
https://doi.org/10.5061/dryad.tmpg4f54z

本开放科学存档包含复现一项模拟实验与3个案例研究探索所需的数据和代码，该通用方法可用于估算广泛应用的生态模型的有效自由度。

## 数据与文件结构说明：
本存档包含4个可独立运行的R脚本，同时包含3个目录：
* R：存放共用R函数；
* TMB：存放指定分层模型的TMB脚本；
* Data：存放案例研究演示所用的数据集。

## 共享与获取说明：
* 涉及鱼类生活史的案例研究包含2个文件：
* fish_traits.csv 提取自Mlifehist_ver1.0.csv，该数据集源自Then等人2015年的自然死亡率数据库，从https://www.vims.edu/research/departments/fisheries/programs/mort_db/ 复制而来，其中空白单元格已被替换……