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The variety of datasets allowed the procedures to be investigated for different proportions of missing data and for different missing data patterns.
However, this approach is only appropriate for small proportions of missing data.
Proportions of missing data for both background variables X1 and X2: m(X1) = {.25,.4} and m X2) = {.25,.4}.
Higher proportions of missing data for background variable X1 caused a bias in the estimation of β2.
Figure 3 shows the proportions of missing values for the variables under consideration in our analysis of the RAD data.
The practical usefulness of the proposed methodology is illustrated with real data examples and a simulation study with varying proportions of missing values.
Finally, as noted earlier, there is substantial missing data on income in all countries and the range of the proportions of missing data, 15 42%, is considerable.
Rutkowski ([2011]) pointed out that the estimation of subgroup differences can be problematic if the proportions of missing values on the background variables differ between groups.
Among the teachers who responded to the TEDDICS and CSE scales, low proportions of missing values at the item level occurred (less than 1%%).
Figures 4 and 5 illustrate the extent to which Ireland may be considered idiosyncratic in this respect by displaying the results of time-series correlations that represent changes in average proportions of missing and not reached items, respectively.
The differences between the two imputation methods, however, were apparent only for substantial proportions of missing data of about 40%, which may occur empirically for some sensitive variables such as SES (Stanat et al. [2012]).
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com