How can I simulate census microdata for small areas using a 1% microdata sample at a large scale and aggregate statistics at the small area scale? I would like to perform an individual-level multivariate analysis at small levels of geographic aggregation (Australian census collection districts).  Clearly, the census isn't available at these small levels of aggregation for privacy reasons so I am investigating other alternatives.  Almost all the variables of interest are categorical.  I have two datasets at my disposal:


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*The 1% census sample is available at a much greater level of spatial aggregation (an area with a population of ~190,000 and vast spatial segregation of demographics). 

*Frequency tables for the variables I am interested in at the small area level (500 small areas, mean pop = 385, sd = 319, median = 355).
How can I use these two datasets to simulate a population distribution at the small area level that is as close as possible to the actual population of the small area?
I appreciate that there may well be routine methods for doing this; if so a pointer to a textbook or relevant journal articles would be vastly appreciated.
 A: Dasymetric mapping is mainly focused on interpolating population estimates to smaller areas than available in currently disseminated data (see this question for a host of useful references on the topic). Frequently this was done by simply identifying areas (based on land characteristics) in which obviously no population exists, and then re-estimating population densities (ommitting those areas). An example might be if there is a body of water in a city, another might be if you identify industrial land parcels which can not have any residential population. More recent approaches to dasymetric mapping incorporate other ancillary data in a probabilistic framework to allocate population estimates (Kyriakidis, 2004; Liu et al., 2008; Lin et al., 2011; Zhang & Qiu, 2011).
Now it is easy to see the relation to your question at hand. You want the population estimates of the small areas. But, it should also be clear how it may fall short of your goals. You not only want the population data, but characteristics of those populations as well. One of the terms used to describe this situation is the change of support problem (Cressie, 1996; Gotway & Young, 2002). Borrowing from the geostatistical literature in which one tries to make predictions of a certain characteristic over a wide area from point samples, recent work has attempted to interpolate areal data to different target zones. Much of the work of Pierre Goovaerts focuses on such area-to-point kriging methods, a recent article in the journal Geographical Analysis has several examples of the method applied different subject materials (Haining et al., 2010), and one of my favorite applications of it is in this article (Young et al., 2009).
What I cite should hardly be viewed as a panacea to the problem though. Ultimately many of the same issues with ecological inference and aggregation bias apply to the goals of areal interpolation as well. It is likley many of the relationships between the micro level data are simply lost in the aggregation process, and such interpolation techiques will not be able to recover them. Also the process through which the data is empirically interpolated (through estimating variograms from the aggregate level data) is often quite full of ad-hoc steps which should make the process questionable (Goovaerts, 2008).
Unfortunately, I post this in a separate answer as the ecological inference literature and the literature on dasymetric mapping and area-to-point kriging are non-overlapping. Although the literature on ecological inference has many implications for these techniques. Not only are the interpolation techniques subject to aggregation bias, but the intelligent dasymetric techniques (which use the aggregate data to fit models to predict the smaller areas) are likely suspect to aggregation bias. Knowledge of the situations in which aggregation bias occurs should be enlightening as to the situations in which areal interpolation and dasymetric mapping will largely fail (especially in regards to identifying correlations between different variables at the disaggregated level).

Citations

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*Cressie N. (1996). Change of support and the modifiable areal unit problem. Geographical Systems 3: 159-180.

*Gotway C.A. & L. J. Young (2002). Combining incompatible spatial data. Journal of the American Statistical Association 97(458): 632-648. (PDF here)

*Goovaerts P. (2008). Kriging and semivariogram deconvolution in the presence of irregualar geographical units. Mathematical Geosciences 40(1): 101-128 (PDF here)

*Haining, R.P., R. Kerry & M.A. Oliver (2010). Geography, spatial data analysis, and geostatistics: An overview. Geographical Analysis 42(1): 7-31.

*Kyriakidis P.C. (2004). A geostatistical framework for area-to-point spatial interpolation. Geographical Analysis 36(3): 259-289. (PDF here)

*Liu X.H., P.C. Kyriakidis & M.F. Goodchild (2008). Population-density estimation using regression and area-to-point residual kriging. International Journal of Geographical Information Science 22(4): 431-447.

*Lin J., R. Cromley & C. Zhang (2011). Using geographically weighted regression to solve the areal interpolation problem. Annals of GIS 17(1): 1-14.

*Young, L.J., C.A. Gotway, J. Yang, G. Kearney & C. DuClos (2009). Linking health and environmental data in geographical analysis: It's so much more than centroids. Spatial and Spatio-temporal Epidemiology 1(1): 73-84.

*Zhang C. & F. Qiu (2011). A point-based intelligent approach to areal interpolation. The Professional Geographer 63(2): 262-276. (PDF here)

A: I am not sure a well-defined answer exists in the literature for this, given that Google search gives basically three usable references on multivariate small area estimation. Pfeffermann (2002) discusses discrete response variables in section 4 of the paper, but these will be univariate models. Of course, with hierarchical Bayesian methods (Rao 2003, Ch. 10), you can do any sort of wonders, but if in the end you find yourself just replicating your priors (because you have so little data), this would be a terrible outcome of your simulation exercise. Besides, Rao only treats continuous variables.
I guess the biggest challenge will be the decomposition of the covariance matrix into the between- and within-small-area components. With 1% sample, you will only have 3 observations from your SAE, so it might be hard to get a stable estimate of the within-component.
If I were in your shoes, I would try a multivariate extension of Pfeffermann's model with a multivariate random effect of the small area. You may indeed end up with a hierarchical Bayesian model for this, if nothing design-based works.
UPDATE (to address Andy's comment to this answer): the bootstrap methods for small area estimation (Lahiri 2003) specifically recreate a plausible population from the study. While the focus of the bootstrap exercise is to estimate the variances of the small area estimates, the procedures should be of interest and relevance to the posted problem.
