Calculate "worst linear function of the parameters"

DESCRIPTION:

Calculates the sequence of the worst linear function of the parameter iterates produced by data augmentation. Plots can help assess convergence.

USAGE:

worstLinFun(da.missmod, wfrac, subset) 

REQUIRED ARGUMENTS:

da.missmod
class missmodel object produced by a data augmentation algorithm.
wfrac
output of the function worstFraction.

OPTIONAL ARGUMENTS:

subset
vector specifying which subset of the rows of the parameter iterates (in the paramIter component of the missmodel object) should be used to calculate the worst linear function. This can be a logical vector (which is replicated to have length equal to the number of rows), a numeric vector indicating the observation numbers to be included, or a character vector of the row names to be included. All observations are included by default.

VALUE:

the sequence of the worst linear function of the parameters is returned. The names attribute of the returned vector give the iteration numbers.

DETAILS:

In high-dimensional situations, it may not be practical to monitor convergence for every component of the parameter, or for every relevant function of the parameter. Instead, it may suffice to pay attention to components or functions for which convergence is slow. Finding a scalar function of the parameter whose marginal distribution converges most slowly would strengthen the evidence for global convergence.

Among linear functions, the "worst linear function of the parameters" has the highest asymptotic rate of missing information, as justified by the convergence behavior of EM. For an EM algorithm, convergence is approximately linear, with rate governed by the largest eigenvalue of the asymptotic rate matrix. The "worst linear function" is the inner product of the parameter with the eigenvector corresponding to this largest eigenvalue.

REFERENCES:

C. Fraley, "On Computing the Largest Fraction of Missing Information for the EM Algorithm and the Worst Linear Function for Data Augmentation", to appear in Computational Statistics and Data Analysis.

Schafer, J. L. (1997), Analysis of Incomplete Multivariate Data , Chapman & Hall, London.

SEE ALSO:

, , .

EXAMPLES:

worst.est <- worstFraction(crime.EM, method = "power") 
wlf <- worstLinFun(crime.DA, worst.est) 
# return the first 100 elements 
wlf <- worstLinFun(crime.DA, worst.est, subset =  1:100) 
# return iteration numbers labeled 50 to 150 
wlf <- worstLinFun(crime.DA, worst.est, subset =  paste(50:150)) 
# time series plot 
plot(as.numeric(names(wlf)), wlf, xlab = "Iteration Number", 
            ylab = "Worst Linear Function", main = "Crime Data") 
#ACF plot 
wlf.acf <- acf(wlf, lag.max = 100, plot = F) 
wlf.acf$series <- "Worst Linear Function" 
acf.plot(wlf.acf)