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The Australian Bureau of Statistics is always under pressure from its clients to improve the accuracy of its estimates about the Australian population. In response to this pressure, the ABS has long exploited the potential to combine its surveys in various ways. This has typically been achieved within a design based framework but requires the assumption that the value of a common data item, collected from the surveys which are to be combined, does not depend upon the survey in which it is collected. This assumption is somewhat relaxed in this paper by assuming a measurement error model that relates data items from the different surveys. Inference is then over the sample design and measurement model. This paper uses diagnostics to test the validity of the measurement model which is used to combine the surveys. We describe an application of combining the Labour Force Survey and the National Aboriginal and Torres Strait Islander Health Survey to estimate employment characteristics about the Indigenous population. The findings suggest that combining these surveys is beneficial.
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