simmr_mcmc: Run a `simmr_input` object through the main simmr Markov chain Monte Carlo (MCMC) function

Description

This is the main function of simmr. It takes a simmr_input object created via simmr_load, runs an MCMC to determine the dietary proportions, and then outputs a simmr_output object for further analysis and plotting via summary.simmr_output and plot.simmr_output.

Usage

simmr_mcmc(simmr_in, 
prior.control=list(means=rep(0,simmr_in$n_sources), sd=rep(1,simmr_in$n_sources)), 
mcmc.control=list(iter=10000,burn=1000,thin=10,n.chain=4))

Arguments

simmr_in

An object created via the function simmr_load

prior.control

A list of values including arguments named means and sd which represent the prior means and standard deviations of the dietary proportions in centralised log-ratio space. These can usually be left at their default values unless y

mcmc.control

A list of values including arguments named iter (number of iterations), burn (size of burn-in), thin (amount of thinning), and n.chain (number of MCMC chains).

Value

An object of class simmr_output with two named top-level components:
inputThe simmr_input object given to the simmr_mcmc function
outputA set of MCMC chains of class mcmc.list from the coda package. These can be analysed using the summary.simmr_output and plot.simmr_output functions.

Details

If, after running simmr_mcmc the convergence diagnostics in summary.simmr_output are not satisfactory, the values of iter, burn and thin in mcmc.control should be increased by a factor of 10.

References

Andrew C. Parnell, Donald L. Phillips, Stuart Bearhop, Brice X. Semmens, Eric J. Ward, Jonathan W. Moore, Andrew L. Jackson, Jonathan Grey, David J. Kelly, and Richard Inger. Bayesian stable isotope mixing models. Environmetrics, 24(6):387–399, 2013.

Andrew C Parnell, Richard Inger, Stuart Bearhop, and Andrew L Jackson. Source partitioning using stable isotopes: coping with too much variation. PLoS ONE, 5(3):5, 2010.

Examples

Run this code

## See the package vignette for a detailed run through of these 4 examples

# Data set 1: 10 obs on 2 isos, 4 sources, with tefs and concdep

# The data
mix = matrix(c(-10.13, -10.72, -11.39, -11.18, -10.81, -10.7, -10.54, 
-10.48, -9.93, -9.37, 11.59, 11.01, 10.59, 10.97, 11.52, 11.89, 
11.73, 10.89, 11.05, 12.3), ncol=2, nrow=10)
colnames(mix) = c('d13C','d15N')
s_names=c('Source A','Source B','Source C','Source D')
s_means = matrix(c(-14, -15.1, -11.03, -14.44, 3.06, 7.05, 13.72, 5.96), ncol=2, nrow=4)
s_sds = matrix(c(0.48, 0.38, 0.48, 0.43, 0.46, 0.39, 0.42, 0.48), ncol=2, nrow=4)
c_means = matrix(c(2.63, 1.59, 3.41, 3.04, 3.28, 2.34, 2.14, 2.36), ncol=2, nrow=4)
c_sds = matrix(c(0.41, 0.44, 0.34, 0.46, 0.46, 0.48, 0.46, 0.66), ncol=2, nrow=4)
conc = matrix(c(0.02, 0.1, 0.12, 0.04, 0.02, 0.1, 0.09, 0.05), ncol=2, nrow=4)

# Load into simmr
simmr_1 = simmr_load(mixtures=mix,
                     source_names=s_names,
                     source_means=s_means,
                     source_sds=s_sds,
                     correction_means=c_means,
                     correction_sds=c_sds,
                     concentration_means = conc)

# Plot
plot(simmr_1)

# Print
simmr_1

# MCMC run
simmr_1_out = simmr_mcmc(simmr_1)

# Print it
print(simmr_1_out)

# Summary
summary(simmr_1_out)
summary(simmr_1_out,type='diagnostics')
summary(simmr_1_out,type='correlations')
summary(simmr_1_out,type='statistics')
ans = summary(simmr_1_out,type=c('quantiles','statistics'))

# Plot
plot(simmr_1_out)
plot(simmr_1_out,type='boxplot')
plot(simmr_1_out,type='histogram')
plot(simmr_1_out,type='density')
plot(simmr_1_out,type='matrix')

#####################################################################################

# A version with just one observation
simmr_2 = simmr_load(mixtures=mix[1,,drop=FALSE], # drop required to keep the mixtures as a matrix 
                     source_names=s_names,
                     source_means=s_means,
                     source_sds=s_sds,
                     correction_means=c_means,
                     correction_sds=c_sds,
                     concentration_means = conc)

# Plot
plot(simmr_2)

# MCMC run - automatically detects the single observation
simmr_2_out = simmr_mcmc(simmr_2)

# Print it
print(simmr_2_out)

# Summary
summary(simmr_2_out)
summary(simmr_2_out,type='diagnostics')
ans = summary(simmr_2_out,type=c('quantiles'))

# Plot
plot(simmr_2_out)
plot(simmr_2_out,type='boxplot')
plot(simmr_2_out,type='histogram')
plot(simmr_2_out,type='density')
plot(simmr_2_out,type='matrix')

#####################################################################################

# Data set 2: 3 isotopes (d13C, d15N and d34S), 30 observations, 4 sources

# The data
mix = matrix(c(-11.67, -12.55, -13.18, -12.6, -11.77, -11.21, -11.45, 
               -12.73, -12.49, -10.6, -12.26, -12.48, -13.07, -12.67, -12.26, 
               -13.12, -10.83, -13.2, -12.24, -12.85, -11.65, -11.84, -13.26, 
               -12.56, -12.97, -12.18, -12.76, -11.53, -12.87, -12.49, 7.79, 
               7.85, 8.25, 9.06, 9.13, 8.56, 8.03, 7.74, 8.16, 8.43, 7.9, 8.32, 
               7.85, 8.14, 8.74, 9.17, 7.33, 8.06, 8.06, 8.03, 8.16, 7.24, 7.24, 
               8, 8.57, 7.98, 7.2, 8.13, 7.78, 8.21, 11.31, 10.92, 11.3, 11, 
               12.21, 11.52, 11.05, 11.05, 11.56, 11.78, 12.3, 10.87, 10.35, 
               11.66, 11.46, 11.55, 11.41, 12.01, 11.97, 11.5, 11.18, 11.49, 
               11.8, 11.63, 10.99, 12, 10.63, 11.27, 11.81, 12.25), ncol=3, nrow=30)
colnames(mix) = c('d13C','d15N','d34S')
s_names = c('Source A', 'Source B', 'Source C', 'Source D') 
s_means = matrix(c(-14, -15.1, -11.03, -14.44, 3.06, 7.05, 13.72, 5.96, 
                   10.35, 7.51, 10.31, 9), ncol=3, nrow=4)
s_sds = matrix(c(0.46, 0.39, 0.42, 0.48, 0.44, 0.37, 0.49, 0.47, 0.49, 
                 0.42, 0.41, 0.42), ncol=3, nrow=4)
c_means = matrix(c(1.3, 1.58, 0.81, 1.7, 1.73, 1.83, 1.69, 3.2, 0.67, 
                   2.99, 3.38, 1.31), ncol=3, nrow=4)
c_sds = matrix(c(0.32, 0.64, 0.58, 0.46, 0.61, 0.55, 0.47, 0.45, 0.34, 
                 0.45, 0.37, 0.49), ncol=3, nrow=4)
conc = matrix(c(0.05, 0.1, 0.06, 0.07, 0.07, 0.03, 0.07, 0.05, 0.1, 
                0.05, 0.12, 0.11), ncol=3, nrow=4)

# Load into simmr
simmr_3 = simmr_load(mixtures=mix,
                     source_names=s_names,
                     source_means=s_means,
                     source_sds=s_sds,
                     correction_means=c_means,
                     correction_sds=c_sds,
                     concentration_means = conc)

# Get summary
print(simmr_3)

# Plot 3 times
plot(simmr_3)
plot(simmr_3,tracers=c(2,3))
plot(simmr_3,tracers=c(1,3))
# See vignette('simmr') for fancier axis labels

# MCMC run
simmr_3_out = simmr_mcmc(simmr_3)

# Print it
print(simmr_3_out)

# Summary
summary(simmr_3_out)
summary(simmr_3_out,type='diagnostics')
summary(simmr_3_out,type='quantiles')
summary(simmr_3_out,type='correlations')

# Plot
plot(simmr_3_out)
plot(simmr_3_out,type='boxplot')
plot(simmr_3_out,type='histogram')
plot(simmr_3_out,type='density')
plot(simmr_3_out,type='matrix')

#####################################################################################

# Data set 4 - identified by Fry (2014) as a failing of SIMMs
# See the vignette for more interpreation of these data and the output

# The data
mix = matrix(c(-14.65, -16.39, -14.5, -15.33, -15.76, -15.15, -15.73, 
               -15.52, -15.44, -16.19, 8.45, 8.08, 7.39, 8.68, 8.23, 7.84, 8.48, 
               8.47, 8.44, 8.37), ncol=2, nrow=10)
s_names = c('Source A', 'Source B', 'Source C', 'Source D') 
s_means = matrix(c(-25, -25, -5, -5, 4, 12, 12, 4), ncol=2, nrow=4)
s_sds = matrix(c(1, 1, 1, 1, 1, 1, 1, 1), ncol=2, nrow=4)

# Load into simmr - note no corrections or concentrations
simmr_4 = simmr_load(mixtures=mix,
                     source_names=s_names,
                     source_means=s_means,
                     source_sds=s_sds)

# Get summary
print(simmr_4)

# Plot 
plot(simmr_4)

# MCMC run - needs slightly longer
simmr_4_out = simmr_mcmc(simmr_4,
mcmc.control=list(iter=100000,burn=10000,thin=100,n.chain=4))

# Print it
print(simmr_4_out)

# Summary
summary(simmr_4_out)
summary(simmr_4_out,type='diagnostics')
ans = summary(simmr_4_out,type=c('quantiles','statistics'))

# Plot
plot(simmr_4_out)
plot(simmr_4_out,type='boxplot')
plot(simmr_4_out,type='histogram')
plot(simmr_4_out,type='density') # Look at the massive correlations here
plot(simmr_4_out,type='matrix')

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