This function computes updated parameter and standard error estimates using multiple imputation methodology. Given a set of parameter estimates and their associated standard errors the function returns the weighted average of the overall between and within variability due to the multiple imputations according to Rubin's (1987) methodology.
averageMI(par, SEpar, as.data.frame = TRUE)a list containing parameter estimates which were computed the imputed datasets
a list containing standard errors associated with par
logical; return a data.frame instead of a list? Default is TRUE
returns a list or data.frame containing the updated averaged parameter estimates, standard errors, and t-values with the associated degrees of freedom and two tailed p-values
Chalmers, R., P. (2012). mirt: A Multidimensional Item Response Theory Package for the R Environment. Journal of Statistical Software, 48(6), 1-29. doi:10.18637/jss.v048.i06
Rubin, D.B. (1987) Multiple Imputation for Nonresponse in Surveys. Wiley & Sons, New York.
# \donttest{
# simulate data
set.seed(1234)
N <- 1000
# covariates
X1 <- rnorm(N); X2 <- rnorm(N)
covdata <- data.frame(X1, X2)
Theta <- matrix(0.5 * X1 + -1 * X2 + rnorm(N, sd = 0.5))
# items and response data
a <- matrix(1, 20); d <- matrix(rnorm(20))
dat <- simdata(a, d, 1000, itemtype = '2PL', Theta=Theta)
mod1 <- mirt(dat, 1, 'Rasch', covdata=covdata, formula = ~ X1 + X2)
coef(mod1, simplify=TRUE)
#> $items
#> a1 d g u
#> Item_1 1 -0.409 0 1
#> Item_2 1 0.491 0 1
#> Item_3 1 0.313 0 1
#> Item_4 1 1.965 0 1
#> Item_5 1 1.753 0 1
#> Item_6 1 -0.246 0 1
#> Item_7 1 -1.077 0 1
#> Item_8 1 0.533 0 1
#> Item_9 1 -1.232 0 1
#> Item_10 1 0.603 0 1
#> Item_11 1 -0.404 0 1
#> Item_12 1 1.238 0 1
#> Item_13 1 1.033 0 1
#> Item_14 1 1.524 0 1
#> Item_15 1 -0.548 0 1
#> Item_16 1 2.075 0 1
#> Item_17 1 -0.695 0 1
#> Item_18 1 -1.200 0 1
#> Item_19 1 0.121 0 1
#> Item_20 1 0.523 0 1
#>
#> $means
#> F1
#> 0
#>
#> $cov
#> F1
#> F1 0.215
#>
#> $lr.betas
#> F1
#> (Intercept) 0.000
#> X1 0.527
#> X2 -1.036
#>
# draw plausible values for secondary analyses
pv <- fscores(mod1, plausible.draws = 10)
pvmods <- lapply(pv, function(x, covdata) lm(x ~ covdata$X1 + covdata$X2),
covdata=covdata)
# compute Rubin's multiple imputation average
so <- lapply(pvmods, summary)
par <- lapply(so, function(x) x$coefficients[, 'Estimate'])
SEpar <- lapply(so, function(x) x$coefficients[, 'Std. Error'])
averageMI(par, SEpar)
#> par SEpar t df p
#> (Intercept) 0.003 0.016 0.209 198.555 0.209
#> covdata$X1 0.528 0.018 28.554 63.384 0
#> covdata$X2 -1.037 0.021 -49.312 35.706 0
# }