Retrieve descriptive statistics from fitted objects to evaluate convergence

Description

The function is used to retrieve descriptive statistics from fitted objects on order to evaluate convergence of the data cloning algorithm. This is best done via visual display of the results, separately for each parameters of interest.

Usage

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dctable(x, ...)
## Default S3 method:
dctable(x, ...)
## S3 method for class 'dctable'
plot(x, which = 1:length(x), 
    type = c("all", "var", "log.var"),
    position = "topright", box.cex = 0.75, box.bg, ...)
extractdctable(x, ...)
## Default S3 method:
extractdctable(x, ...)

dcdiag(x, ...)
## Default S3 method:
dcdiag(x, ...)
## S3 method for class 'dcdiag'
plot(x, which = c("all", "lambda.max", 
    "ms.error", "r.squared", "log.lambda.max"), 
    position = "topright", ...)
extractdcdiag(x, ...)
## Default S3 method:
extractdcdiag(x, ...)

Arguments

x

An MCMC or a 'dctable' object.

...

Optionally more fitted model objects for function dctable.

which

What to plot. For dctable, character names or integer indices of the estimated parameters are accepted. for dcdiag it should be one of c("all", "lambda.max", "ms.error", "r.squared").

type

Type of plot to be drawn. See Details.

position

Position for the legend, as for legend.

box.cex

Scaling factor for the interquartile boxes.

box.bg

Background color for the interquartile boxes.

Details

dctable returns the "dctable" attribute of the MCMC object, or if it is NULL, calculates the dctable summaries. If more than one fitted objects are provided, summaries are calculated for all objects, and results are ordered by the number of clones.

The plot method for dctable helps in graphical representation of the descriptive statistics. type = "all" results in plotting means, standard deviations and quantiles against the number of clones as boxplot. type = "var" results in plotting the scaled variances against the number of clones. In this case variances are divided by the variance of the model with smallest number of clones, min(n.clones). type = "log.var" is the same as "var", but on the log scale. Along with the values, the min(n.clones) / n.clones line is plotted for reference.

Lele et al. (2010) introduced diagnostic measures for checking the convergence of the data cloning algorithm which are based on the joint posterior distribution and not only on single parameters. These include to calculate the largest eigenvalue of the posterior variance covariance matrix (lambda.max as returned by lambdamax.diag), or to calculate mean squared error (ms.error) and another correlation-like fit statistic (r.squared) based on a Chi-squared approximation (as returned by chisq.diag). The maximum eigenvalue reflects the degenerateness of the posterior distribution, while the two fit measures reflect if the Normal approximation is adequate. All three statistics should converge to zero as the number of clones increases. If this happens, different prior specifications are no longer influencing the results (Lele et al., 2007, 2010). These are conveniently collected by the dcdiag function.

IMPORTANT! Have you checked if different prior specifications lead to the same results?

Value

An object of class 'dctable'. It is a list, and contains as many data frames as the number of parameters in the fitted object. Each data frame contains descriptives as the function of the number of clones.

dcdiag returns a data frame with convergence diagnostics.

The plot methods produce graphs as side effect.

Author(s)

Peter Solymos, solymos@ualberta.ca, implementation is based on many discussions with Khurram Nadeem and Subhash Lele.

References

Lele, S.R., B. Dennis and F. Lutscher, 2007. Data cloning: easy maximum likelihood estimation for complex ecological models using Bayesian Markov chain Monte Carlo methods. Ecology Letters 10, 551–563.

Lele, S. R., K. Nadeem and B. Schmuland, 2010. Estimability and likelihood inference for generalized linear mixed models using data cloning. Journal of the American Statistical Association 105, 1617–1625.

Solymos, P., 2010. dclone: Data Cloning in R. The R Journal 2(2), 29–37. URL: http://journal.r-project.org/archive/2010-2/RJournal_2010-2_Solymos.pdf

See Also

Data cloning: dclone

Model fitting: jags.fit, bugs.fit, dc.fit

Examples

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## Not run: 
## simulation for Poisson GLMM
set.seed(1234)
n <- 20
beta <- c(2, -1)
sigma <- 0.1
alpha <- rnorm(n, 0, sigma)
x <- runif(n)
X <- model.matrix(~x)
linpred <- crossprod(t(X), beta) + alpha
Y <- rpois(n, exp(linpred))
## JAGS model as a function
jfun1 <- function() {
    for (i in 1:n) {
        Y[i] ~ dpois(lambda[i])
        log(lambda[i]) <- alpha[i] + inprod(X[i,], beta[1,])
        alpha[i] ~ dnorm(0, 1/sigma^2)
    }
    for (j in 1:np) {
        beta[1,j] ~ dnorm(0, 0.001)
    }
    sigma ~ dlnorm(0, 0.001)
}
## data
jdata <- list(n = n, Y = Y, X = X, np = NCOL(X))
## number of clones to be used, etc.
## iteartive fitting
jmod <- dc.fit(jdata, c("beta", "sigma"), jfun1, 
    n.clones = 1:5, multiply = "n", unchanged = "np")
## summary with DC SE and R hat
summary(jmod)
dct <- dctable(jmod)
plot(dct)
## How to use estimates to make priors more informative?
glmm.model.up <- function() {
    for (i in 1:n) {
        Y[i] ~ dpois(lambda[i])
        log(lambda[i]) <- alpha[i] + inprod(X[i,], beta[1,])
        alpha[i] ~ dnorm(0, 1/sigma^2)
    }
    for (j in 1:p) {
        beta[1,j] ~ dnorm(priors[j,1], priors[j,2])
    }
    sigma ~ dgamma(priors[(p+1),2], priors[(p+1),1])
}
## function for updating, x is an MCMC object
upfun <- function(x) {
    if (missing(x)) {
        p <- ncol(X)
        return(cbind(c(rep(0, p), 0.001), rep(0.001, p+1)))
    } else {
        par <- coef(x)
        return(cbind(par, rep(0.01, length(par))))
    }
}
updat <- list(n = n, Y = Y, X = X, p = ncol(X), priors = upfun())
dcmod <- dc.fit(updat, c("beta", "sigma"), glmm.model.up,
    n.clones = 1:5, multiply = "n", unchanged = "p",
    update = "priors", updatefun = upfun)
summary(dcmod)
dct <- dctable(dcmod)
plot(dct)
plot(dct, type = "var")

## End(Not run)

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