Two-Way Imputation

Two-way imputation using the simple method of Sijtsma and van der Ark (2003) and the MCMC based imputation of van Ginkel, van der Ark, Sijtsma and Vermunt (2007).

tw.imputation(data, integer=FALSE)

tw.mcmc.imputation(data, iter=100, integer=FALSE)

Arguments

data	Matrix of item responses corresponding to a scale
integer	A logical indicating whether imputed values should be integers. The default is FALSE.
iter	Number of iterations

Details

For persons \(p\) and items \(i\), the two-way imputation is conducted by posing a linear model of tau-equivalent measurements: $$X_{pi}=\theta_p + b_i + \varepsilon_{ij} $$ If the score \(X_{pi}\) is missing then it is imputed by $$\hat{X}_{pi}=\tilde{X}_p + b_i $$ where \(\tilde{X}_p\) is the person mean of person \(p\) of the remaining items with observed responses.

The two-way imputation can also be seen as a scaling procedure to obtain a scale score which takes different item means into account.

Value

A matrix with original and imputed values

References

Sijtsma, K., & Van der Ark, L. A. (2003). Investigation and treatment of missing item scores in test and questionnaire data. Multivariate Behavioral Research, 38(4), 505-528. doi: 10.1207/s15327906mbr3804_4

Van Ginkel, J. R., Van der Ark, A., Sijtsma, K., & Vermunt, J. K. (2007). Two-way imputation: A Bayesian method for estimating missing scores in tests and questionnaires, and an accurate approximation. Computational Statistics & Data Analysis, 51(8), 4013-4027. doi: 10.1016/j.csda.2006.12.022

See also

The two-way imputation method is also implemented in the TestDataImputation::Twoway function of the TestDataImputation package.

Examples

if (FALSE) {
#############################################################################
# EXAMPLE 1: Two-way imputation data.internet
#############################################################################

data(data.internet)
data <- data.internet

#***
# Model 1: Two-way imputation method of Sijtsma and van der Ark (2003)
set.seed(765)
dat.imp <- miceadds::tw.imputation( data )
dat.imp[ 278:281,]
  ##       IN9     IN10    IN11     IN12
  ##   278   5 4.829006 5.00000 4.941611
  ##   279   5 4.000000 4.78979 4.000000
  ##   280   7 4.000000 7.00000 7.000000
  ##   281   4 3.000000 5.00000 5.000000

#***
# Model 2: Two-way imputation method using MCMC
dat.imp <- miceadds::tw.mcmc.imputation( data, iter=3)
dat.imp[ 278:281,]
  ##       IN9     IN10     IN11     IN12
  ##   278   5 6.089222 5.000000 3.017244
  ##   279   5 4.000000 5.063547 4.000000
  ##   280   7 4.000000 7.000000 7.000000
  ##   281   4 3.000000 5.000000 5.000000
}