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Abstract:
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Regression modeling is a technique often used in survey data. Standard application of regression analysis in surveys typically violates two important assumptions. The first is that in regression analysis the variables are assumed to have no measurement error. The second is that standard estimation methods assume simple random sampling (SRS), while survey data collection generally use complex sampling designs, e.g. a cluster designs. The consequences of these violations are known in principle: the presence of measurement error tends to attenuate relationships, and using SRS-based estimation methods in complex samples results in biased standard errors, usually (but not always) too small.
One standard approach to including measurement errors in the analysis is to use structural equation modeling including an explicit measurement model. Two different techniques can be used in this respect. The first is including multiple indicators for each variable of interests, which allows estimation of the measurement error within the structural model itself. The second is using an external estimate for the measurement error, to be used as a plug-in estimate for the measurement error in the regression model.
Until recently, estimation methods in structural modeling have assumed simple random sampling. However, multilevel models are effective tools to estimate parameters in many complex survey designs. In addition, structural equation modeling software has appeared that includes multilevel extensions of the classical structural equation model.
This paper will examine the two approaches to measurement error indicated above, and the multilevel extension needed to estimate the model in complex surveys. It will be shown that, provided the interest is only in incorporating measurement errors in clustered samples, any modern structural equation software will do (e.g., any recent version of Amos, Eqs, Lisrel). If the survey design is more complicated, e.g. incorporating weights, 'second generation' modeling software such as Mplus is needed.
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