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This Tutorial 3 was originally designed in part for NIMBioS Tutorial, "Computing in the Cloud" on April 6-8, 2014. The idea was suggested by and discussed with Dr. Russell Zaretzki at University of Tennessee, Knoxville. I reserved codes for parallel statistical applications focusing on intensive computation algorithms. The application can be found in a book ``Mixed Effects Models and Extensions in Ecology with R'' (2009) Zuur, Ieno, Walker, Saveliev and Smith. Springer. (ZIWSS)

Suppose the model is

$Y_{ij} \sim B(1, p_{ij})$

$ logit(p_{ij}) = \beta_0 + \beta_1 (Length)_{ij} + \beta_2 (Sex)_{ij} + \beta_3 (Length)_{ij} (Sex)_{ij} + a_i $

$a_i \sim N(0, \sigma^2_a)$

where $Y_{ij}$ is independent bernoulli distribution, is 1 if dear $j$ in farm $i$ has E. cervi L1 and 0 otherwise, $p_{ij}$ is the observing probability, Length and Sex are explanatory variables via logit link function, and $a_i$ is the independent random intercept for farm $i$. The main task is to fit generalized linear model (GLM) and generalized linear mixed-effect model (GLMM) to a Deer dataset via penalized quasi-likelihood (glmmPQL) and MCMC algorithm to find fixed/random effects and variance parameters of random effects.

The details are described in the Chapter 13 of the ZIWSS book, and the source of Deer dataset can be found from the ZIWSS book's website at ``www.highstat.com/book2.htm''. All files next are given in tutorial3.tar.gz or tutorial3.zip. The detais of R codes, data and relative information are:

File Name Purpose
00-readme.txt A read me first file that describe the models, data set, and rest of files.
DeerEcervi.txt Original Deer data set from the ZIWSS book.
01-max_pql.r Maximize penalized quasi-likelihood for GLMM.
11-npbs_for.r
  • Bootstrap confidence interval for standard deviation of random effects.
  • Using the for() loop.
12-npbs_lapply.r
  • Bootstrap confidence interval for standard deviation of random effects.
  • Using the lapply() function.
13-npbs_mclapply.r
  • Bootstrap confidence interval for standard deviation of random effects.
  • Using the mclapply() function from the parallel package.
  • Parallelization is done in the level of multiple independent bootstrap samples.
14-npbs_pbdR.r
  • Bootstrap confidence interval for standard deviation of random effects.
  • Using the task.pull() functions from the pbdMPI package.
  • Parallelization is done in the level of multiple independent bootstrap samples.
21-mcmc_glm.r
  • MCMC approach for GLM (no random effects).
  • Using the lapply() function.
22-mcmc_glm_mclapply.r
  • MCMC approach for GLM (no random effects).
  • Using the mclapply() function from the parallel package.
  • Parallelization is done in the level of multiple independent chains.
23-mcmc_glm_pbdR.r
  • MCMC approach for GLM (no random effects).
  • Using the task.pull() functions from the pbdMPI package.
  • Parallelization is done in the level of multiple independent chains.
31-mcmc_glmm.r MCMC approach for GLMM (random intercepts).
41-mcmc_glmm_mclapply.r
  • MCMC approach for GLMM (random intercepts).
  • Using the mclapply() function from the parallel package.
  • Parallelization is done within the iterations of MCMC.
  • See u4-mcmc_glmm_mclapply.r for details.
42-mcmc_glmm_pbdR.r
  • MCMC approach for GLMM (random intercepts).
  • Using the task.pull() functions from the pbdMPI package.
  • Parallelization is done within the iterations of MCMC.
  • See u4-mcmc_glmm_pbdR.r for details.
u0-deer.r Utility.
u1-npbs.r Utility.
u2-mcmc_glm.r Utility.
u3-mcmc_glmm.r Utility.
u4-mcmc_glmm_mclapply.r Utility.
u4-mcmc_glmm_pbdR.r Utility.