‘MCMCvis’ package
Casey Youngflesh
Intro
MCMCvis is an R package used to visualize, manipulate, and summarize MCMC output. MCMC output may be derived from Bayesian model output fit with JAGS, Stan, or other MCMC samplers.
The package contains five functions:
MCMCsummary - summarize MCMC output for particular parameters of interestMCMCpstr - summarize MCMC output for particular parameters of interest while preserving parameter structureMCMCtrace - create trace and density plots of MCMC chains for particular parameters of interestMCMCchains - easily extract posterior chains from MCMC output for particular parameters of interestMCMCplot - create caterpillar plots from MCMC output for particular parameters of interest
MCMCvis was designed to perform key functions for MCMC analysis using minimal code, in order to free up time/brainpower for interpretation of analysis results. Functions support simple and straightforward subsetting of model parameters within the calls, and produce presentable and ‘publication-ready’ output.
MCMCsummary
MCMCsummary is used to output summary information from MCMC output. This function accepts stanfit objects (created with the rstan package), mcmc.list objects (created with the rjags or coda packages), R2jags output (created with the R2jags package), jagsUI output (created with the jagsUI package), and matrices of MCMC output (one chain per column). The function automatically detects the object type and proceeds accordingly. Two decimal places are reported by default. This can be changed using the digits argument.
library(MCMCvis)
data(MCMC_data)
MCMCsummary(MCMC_data)
## mean sd 2.5% 50% 97.5% Rhat
## alpha[1] -10.45 5.32 -20.82 -10.48 0.01 1
## alpha[2] -11.92 0.50 -12.91 -11.93 -10.94 1
## alpha[3] -10.36 5.06 -20.28 -10.40 -0.34 1
## alpha[4] -11.91 4.49 -20.77 -11.90 -3.16 1
## alpha[5] -12.78 7.43 -27.23 -12.81 1.85 1
## alpha[6] -11.65 6.42 -24.27 -11.61 0.81 1
## alpha[7] -11.31 7.03 -25.08 -11.29 2.43 1
## alpha[8] -9.18 4.95 -18.88 -9.16 0.64 1
## alpha[9] -11.29 1.72 -14.66 -11.28 -7.89 1
## alpha[10] -9.43 9.55 -28.15 -9.44 9.41 1
## beta[1] -13.83 5.53 -24.67 -13.78 -2.96 1
## beta[2] -5.60 0.14 -5.88 -5.60 -5.32 1
## beta[3] -16.82 1.71 -20.15 -16.82 -13.45 1
## beta[4] -19.55 2.61 -24.59 -19.55 -14.41 1
## beta[5] 8.68 5.26 -1.66 8.69 19.04 1
## beta[6] 2.86 7.68 -12.04 2.83 17.93 1
## beta[7] 2.06 7.78 -13.11 2.01 17.27 1
## beta[8] -15.95 3.62 -23.08 -15.93 -8.93 1
## beta[9] 8.44 4.64 -0.69 8.44 17.58 1
## beta[10] 16.69 4.36 8.24 16.66 25.40 1
## gamma[1] -5.18 3.22 -11.51 -5.15 0.99 1
## gamma[2] 7.48 6.13 -4.53 7.47 19.36 1
## gamma[3] -4.16 4.70 -13.45 -4.11 4.98 1
## gamma[4] 15.80 12.20 -8.37 15.81 39.44 1
## gamma[5] -1.98 6.90 -15.41 -1.99 11.60 1
## gamma[6] 19.94 2.02 16.00 19.93 23.92 1
## gamma[7] -5.81 0.23 -6.26 -5.81 -5.36 1
## gamma[8] -3.53 6.74 -16.75 -3.54 9.80 1
## gamma[9] -0.93 5.67 -12.06 -0.92 10.26 1
## gamma[10] 13.10 0.09 12.91 13.10 13.28 1
Specific parameters can be specified to subset summary information. Square brackets are ignored by default. For instance, all alpha parameters can be plotted using params = 'alpha'.
MCMCsummary(MCMC_data,
params = 'alpha')
## mean sd 2.5% 50% 97.5% Rhat
## alpha[1] -10.45 5.32 -20.82 -10.48 0.01 1
## alpha[2] -11.92 0.50 -12.91 -11.93 -10.94 1
## alpha[3] -10.36 5.06 -20.28 -10.40 -0.34 1
## alpha[4] -11.91 4.49 -20.77 -11.90 -3.16 1
## alpha[5] -12.78 7.43 -27.23 -12.81 1.85 1
## alpha[6] -11.65 6.42 -24.27 -11.61 0.81 1
## alpha[7] -11.31 7.03 -25.08 -11.29 2.43 1
## alpha[8] -9.18 4.95 -18.88 -9.16 0.64 1
## alpha[9] -11.29 1.72 -14.66 -11.28 -7.89 1
## alpha[10] -9.43 9.55 -28.15 -9.44 9.41 1
Individual parameters can also be specified. For example, one alpha (of many) may be specified. In this case, the square brackets should not be ignored, so that only the alpha[1] parameter can be specified. Use the argument ISB = FALSE to specify particular parameters that contain brackets. ISB is short for ‘Ignore Square Brackets’. When ISB = FALSE, the params argument reads like a regular expression. Because of this, the square brackets must be escaped with \\. All other regular expression syntax is accepted, as typically applied in R. A useful cheatsheet for regular expressions in R can be found here. \\d can be used to specify any digits in a particular place.
MCMCsummary(MCMC_data,
params = 'alpha\\[1\\]',
ISB = FALSE)
## mean sd 2.5% 50% 97.5% Rhat
## alpha[1] -10.45 5.32 -20.82 -10.48 0.01 1
The excl argument can be used to exclude any parameters. This can be used in conjunction with the params argument. This is particularly useful when specifying ISB = FALSE. For instance, if all alpha parameters are desired except for alpha[1], params = 'alpha', excl = 'alpha\\[1\\]', ISB = FALSE can be used. Once again, since the params argument takes a regular expression, the square brackets must be escaped using \\. When ISB = TRUE, an exact match of the specified parameter is required (excluding the square brackets). When ISB = FALSE, partial names will be matched. Leaving the default (ISB = TRUE) is generally recommended for simplicity. These arguments can be used in any of the functions in the package.
MCMCsummary(MCMC_data,
params = 'alpha',
excl = 'alpha\\[1\\]',
ISB = FALSE)
## mean sd 2.5% 50% 97.5% Rhat
## alpha[2] -11.92 0.50 -12.91 -11.93 -10.94 1
## alpha[3] -10.36 5.06 -20.28 -10.40 -0.34 1
## alpha[4] -11.91 4.49 -20.77 -11.90 -3.16 1
## alpha[5] -12.78 7.43 -27.23 -12.81 1.85 1
## alpha[6] -11.65 6.42 -24.27 -11.61 0.81 1
## alpha[7] -11.31 7.03 -25.08 -11.29 2.43 1
## alpha[8] -9.18 4.95 -18.88 -9.16 0.64 1
## alpha[9] -11.29 1.72 -14.66 -11.28 -7.89 1
## alpha[10] -9.43 9.55 -28.15 -9.44 9.41 1
Setting the Rhat and n.eff arguments to FALSE can be used to avoid calculating the Rhat statistic and number of effective samples, respectively (default for Rhat and n.eff are TRUE and FALSE, respectively). Specifying FALSE can greatly increase function speed with very large mcmc.list objects. Values for Rhat near 1 suggest convergence (Brooks and Gelman 1998). Kruschke (2014) recommends n.eff > 10,000 for reasonably stable posterior estimates.
MCMCsummary(MCMC_data,
params = 'alpha',
Rhat = TRUE,
n.eff = TRUE)
## mean sd 2.5% 50% 97.5% Rhat n.eff
## alpha[1] -10.45 5.32 -20.82 -10.48 0.01 1 17745
## alpha[2] -11.92 0.50 -12.91 -11.93 -10.94 1 18000
## alpha[3] -10.36 5.06 -20.28 -10.40 -0.34 1 18358
## alpha[4] -11.91 4.49 -20.77 -11.90 -3.16 1 18638
## alpha[5] -12.78 7.43 -27.23 -12.81 1.85 1 18141
## alpha[6] -11.65 6.42 -24.27 -11.61 0.81 1 18000
## alpha[7] -11.31 7.03 -25.08 -11.29 2.43 1 17778
## alpha[8] -9.18 4.95 -18.88 -9.16 0.64 1 18000
## alpha[9] -11.29 1.72 -14.66 -11.28 -7.89 1 17996
## alpha[10] -9.43 9.55 -28.15 -9.44 9.41 1 17975
The func argument can be used to return metrics of interest not already returned by default for MCMCsummary. Input is a function to be performed on posteriors for each specified parameter. Values returned by function will be displayed as a column in the summary output (or multiple columns if the function returns more than one value). In this way, functions from other packages can be used to derive metrics of interest on posterior output. Column name(s) for function output can be specified with the func_name argument.
MCMCsummary(MCMC_data,
params = 'alpha',
Rhat = TRUE,
n.eff = TRUE,
func = function(x) quantile(x, probs = c(0.01, 0.99)),
func_name = c('1%', '99%'))
## mean sd 2.5% 50% 97.5% Rhat n.eff 1% 99%
## alpha[1] -10.45 5.32 -20.82 -10.48 0.01 1 17745 -22.89 1.73
## alpha[2] -11.92 0.50 -12.91 -11.93 -10.94 1 18000 -13.09 -10.75
## alpha[3] -10.36 5.06 -20.28 -10.40 -0.34 1 18358 -21.99 1.49
## alpha[4] -11.91 4.49 -20.77 -11.90 -3.16 1 18638 -22.56 -1.48
## alpha[5] -12.78 7.43 -27.23 -12.81 1.85 1 18141 -29.98 4.91
## alpha[6] -11.65 6.42 -24.27 -11.61 0.81 1 18000 -26.74 2.98
## alpha[7] -11.31 7.03 -25.08 -11.29 2.43 1 17778 -27.61 5.14
## alpha[8] -9.18 4.95 -18.88 -9.16 0.64 1 18000 -20.67 2.48
## alpha[9] -11.29 1.72 -14.66 -11.28 -7.89 1 17996 -15.25 -7.28
## alpha[10] -9.43 9.55 -28.15 -9.44 9.41 1 17975 -31.83 12.89
MCMCpstr
MCMCpstr is used to output summary information from MCMCoutput while preserving the original structure of the specified parameters (i.e., scalar, vector, matrix, array). Function outputs a list with calculated values for each specified parameter, similar to output obtained when fitting models with the jags.samples function (as opposed to coda.samples) from the rjags package. Preserving the original strucutre can be helpful when plotting or summarizing parameters with multidimensional structure. Particular parameters of interest can be specified as with other functions with the params argument.
The function calculates summary information only for the specified function. The function to be used is specified using the func argument.
MCMCpstr(MCMC_data,
params = 'alpha',
func = mean)
## $alpha
## [1] -10.446737 -11.923542 -10.357373 -11.914417 -12.775968 -11.648787
## [7] -11.312254 -9.175784 -11.291176 -9.432991
Custom functions can be specified as well.
MCMCpstr(MCMC_data,
func = function(x) quantile(x, probs = 0.01))
## $alpha
## [1] -22.89336 -13.09206 -21.99133 -22.55954 -29.98487 -26.74312 -27.60646
## [8] -20.66593 -15.25340 -31.82656
##
## $beta
## [1] -26.819905 -5.929502 -20.805661 -25.542002 -3.651755 -14.755597
## [7] -15.989007 -24.246330 -2.334725 6.467677
##
## $gamma
## [1] -12.618568 -6.987008 -15.107793 -12.400142 -17.854705 15.247380
## [7] -6.333839 -19.218067 -14.205980 12.879043
MCMCtrace
MCMCtrace is used to create trace and density plots for MCMC output. This is useful for diagnostic purposes. Particular parameters can also be specified, as with MCMCsummary. Output is written to PDF by default to enable more efficient review of posteriors - this also reduces computation time. PDF output is particularly recommended for large numbers of parameters. pdf = FALSE can be used to prevent output to PDF.
MCMCtrace(MCMC_data,
params = c('beta\\[1\\]', 'beta\\[2\\]', 'beta\\[3\\]'),
ISB = FALSE,
pdf = FALSE)
Just trace plot can be plotted with type = 'trace'. Just density plots can be plotted with type = 'density'. Default is type = 'both' which outputs both trace and density plots. Individual chains for the density plot can be output using the ind argument.
MCMCtrace(MCMC_data,
params = 'beta',
type = 'density',
ind = TRUE,
pdf = FALSE)
PDF document will be output to the current working directory by default, but another directory can be specified.
MCMCtrace(MCMC_data,
pdf = TRUE,
filename = 'MYpdf',
wd = 'DIRECTORY_HERE')
iter denotes how many iterations should be plotted for the chain the trace and density plots. The default is 5000, meaning that the last 5000 iterations of each chain are plotted. Remember, this is the final posterior chain, not including the specified burn-in (specified when the model was run). If less than 5000 iterations are run, the full number of iterations will be plotted.
MCMCtrace(MCMC_data,
params = c('beta\\[1\\]', 'beta\\[2\\]', 'beta\\[3\\]'),
ISB = FALSE,
iter = 1800,
ind = TRUE,
pdf = FALSE)
Overlap between the priors and posteriors can also be calculated by specifying the priors associated with each parameter using the priors argument. Ths is particularly useful when investigating how large the effect of the prior is on the posterior distribution - this can be informative when trying to determine how identifiable a particular parameter is in a model.
The priors argument takes a matrix as input, with each column representing a prior for a different parameter and each row representing a random draw from that prior distribution. These draws can be generated using R functions such as rnorm, rgamma, runif, etc. Parameters are plotted alphabetically - priors should be sorted accordingly. If the priors argument contains only one prior and more than one parameter is specified for the params argument, this prior will be used for all parameters. The number of draws for each prior should equal the number of iterations specified by (or total draws if less than ) times the number of chains, though the function will automatically adjust if more or fewer iterations are specified. It is important to note that some discrepencies between MCMC samplers and R may exist regarding the parameterization of distributions - one example of this is the use of precision in JAGS but standard deviation in R for the ‘second parameter’ of the normal distribution.
#same prior used for all parameters
PR <- rnorm(15000, 0, 32) #equivalent to dnorm(0, 0.001) in JAGS
MCMCtrace(MCMC_data,
params = c('beta\\[1\\]', 'beta\\[2\\]', 'beta\\[3\\]'),
ISB = FALSE,
priors = PR,
pdf = FALSE)
## Warning in MCMCtrace(MCMC_data, params = c("beta\\[1\\]", "beta\\[2\\]", :
## Only one prior specified for > 1 parameter. Using a single prior for all
## parameters.
MCMCchains
MCMCchains is used to extract MCMC chains from MCMC objects. Chains can then be manipulated directly. Particular parameters can be specified as with other functions.
ex <- MCMCchains(MCMC_data,
params = 'beta')
#extract mean values for each parameter
apply(ex, 2, mean)
## beta[1] beta[2] beta[3] beta[4] beta[5] beta[6]
## -13.826007 -5.601035 -16.820354 -19.545768 8.678547 2.856033
## beta[7] beta[8] beta[9] beta[10]
## 2.055310 -15.953090 8.439410 16.685924
Using the mcmc.list argument, MCMCchains can return an mcmc.list object, instead of a matrix, for the specified parameters. This can be useful when saving posterior information for only a subset of parameters is desired.
ex2 <- MCMCchains(MCMC_data,
params = 'beta',
mcmc.list = TRUE)
MCMCplot
MCMCplot is used to create caterpillar plots from MCMC output. Points represent posterior medians. For parameters where 50% credible intervals overlap 0 are indicated by ‘open’ circles. For parameters where 50 percent credible intervals DO NOT overlap 0 AND 95 percent credible intervals DO overlap 0 are indicated by ‘closed’ grey circles. For parameters where 95 percent credible intervals DO NOT overlap 0 are indicated by ‘closed’ black circles. Thick lines represent 50 percent credible intervals while thin lines represent 95 percent credible intervals.
As with the other functions in the package, particular parameters of interest can be specified.
MCMCplot(MCMC_data,
params = 'beta')
ref_ovl = FALSE can be used to disable this feature. All median dots will be represented as ‘closed’ black circles. A vertical reference at 0 is plotted by default. The position of this reference line can be modified with the ref argument. ref = NULL removes the reference line altogether.
MCMCplot(MCMC_data,
params = 'beta',
ref_ovl = FALSE,
ref = NULL)
Parameters can be ranked by posterior median estimates using the rank argument. xlab can be used to create an alternative label for the x-axis.
MCMCplot(MCMC_data,
params = 'beta',
rank = TRUE,
xlab = 'ESTIMATE')
The orientation of the plot can also be change using the horiz argument. ylab is then used to specify an alternative label on the ‘estimate axis’.
MCMCplot(MCMC_data,
params = 'beta',
rank = TRUE,
horiz = FALSE,
ylab = 'ESTIMATE')
Graphical parameters for x and y-axis limitation, row labels, title, median dot size, CI line thickness, axis and tick thickness, text size, and margins can be specified.
MCMCplot(MCMC_data,
params = 'beta',
xlim = c(-60, 40),
xlab = 'My x-axis label',
main = 'MCMCvis plot',
labels = c('First param', 'Second param', 'Third param',
'Fourth param', 'Fifth param', 'Sixth param',
'Seventh param', 'Eighth param', 'Nineth param',
'Tenth param'),
labels_sz = 1.5,
med_sz = 2,
thick_sz = 7,
thin_sz = 3,
ax_sz = 4,
main_text_sz = 2)
References
Brooks, S. P., and A. Gelman. 1998. General methods for monitoring convergence of iterative simulations. Journal of Computational and Graphical Statistics 7:434.
Kruschke, J. 2014. Doing Bayesian data analysis: A tutorial with R, JAGS, and Stan. Academic Press.
For more information see ?MCMCvis