On Interaction Effects Involving Block Variables

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Abstract
The problem of estimating interaction effects involving unmeasured block variables determined by observed indicator variables is discussed. It is shown that interaction effects involving block variables can be estimated using currently available software. In the case in which a block variable interacts with an observed variable, the multiplicative identity for the unobserved interaction term reduces to a linear combination of cross-products of the measured variable and constituents of the block variable. In this case the model can be estimated via nonlinear regression, or via LISREL with equality restrictions. The former technique can also be used to estimate models in which two or more unobserved block variables interact with one another; in this case, nonlinear combinations of cross-products involving constituent variables constitute the unobserved interaction term. Numerical illustration of the proposed procedures is given, as applied to a problem involving the effects of socioeconomic variables on job satisfaction, conditional on the level of an unmeasured complexity-of-work block variable.