single.MA_demo.Rmd

Meta-analysis: Example of Single.MA
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Individual Meta-analysis

Individual meta-analysis for a specific trait and PFT is run by the function
single.MA. This will allow power analysis  to run repeated MA outside of the
full loop over traits and PFTs. 

The first step is to convert the R distribution to JAGS distribution. The prior transformed is then stored in jagsprior and the parameters are renamed as "distn", "a", "b" and "n".
The input used here is a simple example with 4 observations.
r2bugs.distributions function is to convert R parameterizations to BUGS paramaterizations or to convert from BUGS to R. It can work on the distributions including normal, weibull, gamma, chsq, binormial, negative binormial. 
The input of this function are information of the prior distribution, including the name of the distribution and 2 parameters. It will convert the parameterization format from R to BUGS or from BUGS to R automaticaly. 

jagify is to convert queried data to format required by JAGS meta-analysis model. 

In the single.MA function, when input the trait data and prior, it will transfer the prior from R parameterization into BUGS parameterization by using the function r2bugs.distributions. 
Using the jags.model function, the Bayesian graphical model is generated based on the initials. The posterior samples in mcmc.list format are then created as the output of the function. 

```{r message=FALSE}
require(knitr)
opts_chunk$set(echo = FALSE, message = FALSE, results='hide', cache=TRUE, 
               eval = FALSE ## just to allow .md to be compiled
               )
require(PEcAn.MA)
##initializing
data <- data.frame(t(data.frame(array(c(5.3,1.0976426,4,1,1,1,3.4,2.1821789,4,1,1,1,5.9,0.9622504,4,1,1,1,6.6,1.3245324,4,1,1,1),dim=c(6,4)),row.names=c("Y","obs.prec","n","ghs","trt","site"))))
j.chains <- 4
j.iter <- 1000
jag.model.file <- "tesst.bug"
tauA <- 0.001
tauB <- 0.001
prior <- data.frame(distn = "norm", parama = 0, paramb = 2, n = NA)
##running single.MA
output <- single.MA(data, j.chains, j.iter, tauA, tauB, prior,jag.model.file, overdispersed=TRUE)
```


```{r fig.width=7, fig.height=6}
plot(output, trace = FALSE, density = TRUE)
plot(output,density = FALSE)
autocorr.plot(output, ask = FALSE)
```

The meta-analysis outputs are summarized by the pecan.ma.summary function. It will create several log files for all the traits to record the R output of the convergency diagnosis, and several PDF file for all the traits to store the diagnosis plot of convergency. 
G-R diagnostics is used to test convergence. The diagnose result is output into the log file. If the JAGS model failed to converge, a warning will also be generated.