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

as regression, that quantify the relationship between a given covariate and the
response variable, in the presence of other covariates. Thus, the response variable
itself is indirectly used to determine donors.
• Problem of sparse neighborhoods is considerably reduced, making it easier to
implement restrictions on the donor set. Because the distance function is defined as
a continuous function of the predicted mean, it is possible to find donors arbitrarily
close to the recipient. Thus, it is less likely to have the problem of sparse
neighborhoods for hot decking. Moreover, having sufficient donors in the
neighborhood allows for imposing extra constraints on the donor set, which would be
difficult to incorporate directly in the model.
• Sampling weights are easily incorporated in the models. The weighted hot deck
can be viewed as a special case of PMN.
• Correlations across response variables are justified by making the imputation
multivariate.
• Choice of donor can be made random by choosing delta large enough such that
the neighborhood is of a size greater than 1. Under the assumption that the
recipient and the candidate donors in the neighborhood have approximately equal
means, the random selection allows the case where the error distribution with mean
zero can be mimicked. This helps to avoid bias in estimating means and totals,
variances of which can be estimated in two-phase sampling or by suitable resampling
methods.
In comparison with other model-based methods, discrete and continuous variables can be
handled jointly and relatively easily in MPMN by using the idea of univariate (conditional)
modeling in a hierarchical manner. In MPMN, differential weights can be objectively assigned to
different elements of the predictive mean vector depending on the variability of predicted means
in the dataset via the Mahalanobis squared distance.
As noted earlier, the PMN method has some similarity with the predictive mean matching
method of Rubin (1986) except that, for the donor records, the observed variable value and not
the predicted mean, is used for computing the distance function. Also, the well-known method of
nearest neighbor imputation is similar to PMN, except that the distance function is in terms of
the original predictor variables and would often require arbitrary scaling of discrete variables.
Moreover, for this method, it is generally hard to make objective decisions about the relative
weights for different predictor variables.
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