Questionnaire Dwelling Unit-Level and Person Pair-Level Sampling ...

The PMM method is only applicable to continuous outcome variables. With this method,
a distance function is used to determine distances between the predicted mean for the recipient,
obtained under a model, and the response variable outcomes for candidate donors. The
respondent with the smallest distance is chosen as the donor. Unlike the NNHD, the donor is not
randomly selected from a neighborhood. The advantages of PMM include the following:
• Model bias in the predicted mean can be minimized by using suitable covariates.
• The PMM method is not a pure model-based method, because the predicted mean is
only used to assist in finding a donor. Hence, like NNHD, it has the flexibility of
imposing certain constraints on the set of donors.
However, the choice of donor is nonrandom. This nonrandomness leads to bias in the estimators
of means and totals. It also tends to make the distribution of outcome values skewed to the
center. Furthermore, as mentioned earlier, the PMM method is not applicable to discrete
variables, because the distance function between the recipient's predicted mean (which takes
continuous values) and the donor's outcome value (which takes discrete values) is not well
defined.
N.2.2 Univariate and Multivariate Applications of the Predictive Mean Neighborhood
Method
The PMN method is easily applicable to problems of both univariate and multivariate
imputations. The need for univariate imputation arises when the value of a single variable, which
cannot be easily grouped together with other variables, is missing for the respondent. On the
other hand, the need for multivariate imputation arises when values of two or more related
variables are missing for a single respondent. The case of a single polytomous variable with
missing values also can be viewed as a multivariate imputation problem. An example of this in
pair applications is a missing pair relationship for a pair where both respondents are in the 21- to
25-year-old range. In this instance, the possible outcomes are spouse-spouse without children,
spouse-spouse with children, and all other pair relationships.
The standard approach to multivariate modeling, with a given set of outcome variables
(including both discrete and continuous), is likely to be tedious in practice because of the
computational problems due to the volume of model parameters and the difficulty in specifying a
suitable covariance structure. Following Little and Rubin's (1987) proposal of a joint model for
discrete and continuous variables, and its implementation by Schafer (1997), it is possible to fit a
pure multivariate model for multivariate imputation, but it would require making distributional
assumptions. Moreover, because of the obvious problem of specifying the probability
distribution underlying survey data, none of the existing solutions take the survey design into
account. However, since the 1999 survey, in the application of the multivariate predictive mean
neighborhood (MPMN) method to the imputation procedures, a multivariate model has been
fitted by a series of univariate parametric models (including the polytomous case), such that
variables modeled earlier in the hierarchy have a chance to be included in the covariate set for
subsequent models in the hierarchy. In the multivariate modeling with MPMN, the innovative
idea is to express the likelihood in the superpopulation model as a product of marginal and
N-4