| mi.inference {cat} | R Documentation |
Multiple imputation inference
Description
Combines estimates and standard errors from m complete-data analyses performed on m imputed datasets to produce a single inference. Uses the technique described by Rubin (1987) for multiple imputation inference for a scalar estimand.
Usage
mi.inference(est, std.err, confidence=0.95)
Arguments
est |
a list of $m$ (at least 2) vectors representing estimates (e.g., vectors of estimated regression coefficients) from complete-data analyses performed on $m$ imputed datasets. |
std.err |
a list of $m$ vectors containing standard errors from the
complete-data analyses corresponding to the estimates in |
confidence |
desired coverage of interval estimates. |
Value
a list with the following components, each of which is a vector of the
same length as the components of est and std.err:
est |
the average of the complete-data estimates. |
std.err |
standard errors incorporating both the between and the within-imputation uncertainty (the square root of the "total variance"). |
df |
degrees of freedom associated with the t reference distribution used for interval estimates. |
signif |
P-values for the two-tailed hypothesis tests that the estimated quantities are equal to zero. |
lower |
lower limits of the (100*confidence)% interval estimates. |
upper |
upper limits of the (100*confidence)% interval estimates. |
r |
estimated relative increases in variance due to nonresponse. |
fminf |
estimated fractions of missing information. |
METHOD
Uses the method described on pp. 76-77 of Rubin (1987) for combining the complete-data estimates from $m$ imputed datasets for a scalar estimand. Significance levels and interval estimates are approximately valid for each one-dimensional estimand, not for all of them jointly.
References
Fienberg, S.E. (1981) The Analysis of Cross-Classified Categorical Data, MIT Press, Cambridge.
Rubin (1987) Multiple Imputation for Nonresponse in Surveys, Wiley, New York,
Schafer (1996) Analysis of Incomplete Multivariate Data. Chapman & Hall, Chapter 8.
See Also
Examples
#
# Example 1 Based on Schafer's p. 329 and ss. This is a toy version,
# using a much shorter length of chain than required. To
# generate results comparable with those in the book, edit
# the \dontrun{ } line below and comment the previous one.
#
data(belt)
attach(belt.frame)
oddsr <- function(x) { # Odds ratio of 2 x 2 table.
o <- (x[1,1]*x[2,2])/
(x[1,2]*x[2,1])
o.sd <- sqrt(1/x[1,1] + # large sample S.D. (Fienberg,
1/x[1,2] + # p. 18)
1/x[2,1] +
1/x[2,2])
return(list(o=o,sd=o.sd))
}
colns <- colnames(belt.frame)
a <- xtabs(Freq ~ D + S + B2 + I2 + B1 + I1,
data=belt.frame)
m <- list(c(1,2,5,6),c(1,2,3,4),c(3,4,5,6),
c(1,3,5),c(1,4,6),c(2,4,6))
b <- loglin(a,margin=m) # fits (DSB1I1)(DSB2I2)(B2I2B1I1)(DB1B2)
# (DI1I2)(SI1I2) in Schafer's p. 329
s <- prelim.cat(x=belt[,-7],counts=belt[,7])
m <- c(1,2,5,6,0,1,2,3,4,0,3,4,5,6,0,1,3,5,0,1,4,6,0,2,4,6)
theta <- ecm.cat(s,margins=m, # excruciantingly slow; needs 2558
maxits=5000) # iterations.
rngseed(1234)
#
# Now ten multiple imputations of the missing variables B2, I2 are
# generated, by running a chain and taking every 2500th observation.
# Prior hyperparameter is set at 0.5 as in Schafer's p. 329
#
est <- std.error <- vector("list",10)
for (i in 1:10) {
cat("Doing imputation ",i,"\n")
theta <- dabipf(s,m,theta,prior=0.5, # toy chain; for comparison with
steps=25) # results in Schafer's book the next
# statement should be run,
# rather than this one.
## Not run: theta <- dabipf(s,m,theta,prior=0.5,steps=2500)
imp<- imp.cat(s,theta)
imp.frame <- cbind(imp$x,imp$counts)
colnames(imp.frame) <- colns
a <- xtabs(Freq ~ B2 + I2, # 2 x 2 table relating belt use
data=imp.frame) # and injury
print(a)
odds <- oddsr(a) # odds ratio and std.dev.
est[[i]] <- odds$o - 1 # check deviations from 1 of
std.error[[i]] <- odds$sd # odds ratio
}
odds <- mi.inference(est,std.error)
print(odds)
detach(belt.frame)