Plausible Value Imputation Using a Known Measurement Error Variance (Based on Classical Test Theory)
This function provides unidimensional plausible value imputation with a known measurement error variance or classical test theory (Mislevy, 1991). The reliability of the scale is estimated by Cronbach's Alpha or can be provided by the user.
draw.pv.ctt(y, dat.scale=NULL, x=NULL, samp.pars=TRUE,
alpha=NULL, sig.e=NULL, var.e=NULL, true.var=NULL)y |
Vector of scale scores if |
dat.scale |
Matrix of item responses |
x |
Matrix of covariates |
samp.pars |
An optional logical indicating whether scale parameters (reliability or measurement error standard deviation) should be sampled |
alpha |
Reliability estimate of the scale. The default of
|
sig.e |
Optional vector of the standard deviation of the error. Note that it is not the error variance. |
var.e |
Optional vector of the variance of the error. |
true.var |
True score variance |
The linear model is assumed for drawing plausible values of a variable Y contaminated by measurement error. Assuming Y=θ + e and a linear regression model for θ
θ=\bold{X} β + ε
(plausible value) imputations from the posterior distribution P( θ | Y, \bold{X} ) are drawn. See Mislevy (1991) for details.
A vector with plausible values
Plausible value imputation is also labeled as multiple overimputation (Blackwell, Honaker & King, 2011).
Blackwell, M., Honaker, J., & King, G. (2011). Multiple overimputation: A unified approach to measurement error and missing data. Technical Report.
Mislevy, R. J. (1991). Randomization-based inference about latent variables from complex samples. Psychometrika, 56(2), 177-196. doi: 10.1007/BF02294457
See also
sirt::plausible.value.imputation.raschtype
for plausible value imputation.
Plausible value imputations can be conducted in mice using the
imputation method mice.impute.plausible.values.
Plausible values can be drawn in Amelia by specifying observation-level
priors, see Amelia::moPrep and
Amelia::amelia.
#############################################################################
# SIMULATED EXAMPLE 1: Scale scores
#############################################################################
set.seed(899)
n <- 5000 # number of students
x <- round( stats::runif( n, 0,1 ) )
y <- stats::rnorm(n)
# simulate true score theta
theta <- .6 + .4*x + .5 * y + stats::rnorm(n)
# simulate observed score by adding measurement error
sig.e <- rep( sqrt(.40), n )
theta_obs <- theta + stats::rnorm( n, sd=sig.e)
# calculate alpha
( alpha <- stats::var( theta ) / stats::var( theta_obs ) )
# [1] 0.7424108
#=> Ordinarily, sig.e or alpha will be known, assumed or estimated by using items,
# replications or an appropriate measurement model.
# create matrix of predictors
X <- as.matrix( cbind(x, y ) )
# plausible value imputation with scale score
imp1 <- miceadds::draw.pv.ctt( y=theta_obs, x=X, sig.e=sig.e )
# check results
stats::lm( imp1 ~ x + y )
# imputation with alpha as an input
imp2 <- miceadds::draw.pv.ctt( y=theta_obs, x=X, alpha=.74 )
stats::lm( imp2 ~ x + y )
## Not run:
#--- plausible value imputation in Amelia package
library(Amelia)
# define data frame
dat <- data.frame( "x"=x, "y"=y, "theta"=theta_obs )
# generate observation-level priors for theta
priors <- cbind( 1:n, 3, theta_obs, sig.e )
# 3 indicates column index for theta
overimp <- priors[,1:2]
# run Amelia
imp <- Amelia::amelia( dat, priors=priors, overimp=overimp, m=10)
# create object of class datlist and evaluate results
datlist <- miceadds::datlist_create( imp$imputations )
withPool_MI( with( datlist, stats::var(theta) ) )
stats::var(theta) # compare with true variance
mod <- with( datlist, stats::lm( theta ~ x + y ) )
mitools::MIcombine(mod)
## End(Not run)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.