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ACCEPTABLE MODEL-BASED MISSING DATA PROCEDURES Before embarking on a description of acceptable procedures, we should note that our description of acceptable procedures is neither highly technical nor exhaustive. For more technical and more general treatments on these topics, other publications are available (e.g., Little & Schenker, 1995; Schafer & Graham, in press). Model-based missing data procedures deal with the missing data at the same time that they deal with parameter estimation. That is, missing data and data analysis are handled in a single step. As we see below, most of these procedures have been built around latent variable procedures and are thus somewhat less accessible for the average data analyst than are the data-based procedures described next. Still, some of these procedures are extremely easy to use and, when used properly, can be enormously valuable as a general tool for dealing with missing data. Multiple Group Structural Equation Modeling At the outset of this chapter we mentioned this method as being one of the rst accessible approaches to analysis with missing data. We cannot go into great detail here in describing this procedure (greater detail about this procedure may be found in Allison, 1987; Duncan & Duncan, 1994; Graham et al., 1994). In brief, the procedure divides up the sample into groups containing cases with the same pattern of missing and nonmissing values. A system of equality constraints is then placed on the parameter estimates across groups, such that parameters are estimated based only on those cases having data that bear on that parameter estimate. This procedure has some serious limitations and has thus been supplanted by the other procedures to be described below. However, this procedure continues to be valuable for particular applications. The main limitation of this procedure is that it can be extremely unwieldy and error prone, especially when there are many distinct missing data patterns. Because the SEM code must be changed in subtle ways from group to group in the multiple group design, it is very easy to introduce errors into the code. In addition, one requirement of this procedure is that there must be more cases than variables for every group. With a typical longitudinal data set, this means that some data must be discarded in order to produce groups (of missing data patterns) with suf ciently large sample sizes. Beyond these limitations, however, this procedure can be quite good. The parameter estimates are good (i.e., unbiased

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