Nonloglinear Marginal Models
Despite the great flexibility of loglinear models, loglinear marginal models are not always the most appropriate way of analyzing marginal categorical data. Investigators might prefer or need to compare averages, dispersion measures, association coefficients, etc. rather than (specifically) odds and odds ratios. Many of these statistics cannot be formulated within the loglinear framework. Therefore, in this chapter, nonloglinear marginal modeling will be discussed. It will be shown how to extend themaximum likelihood inference procedures and algorithms of the previous chapter to include nonloglinear models. A few concrete examples of the appropriate matrix manipulations for defining these nonloglinear indices will be presented to give the reader a clear picture of howto implement these nonloglinear procedures. Sometimes these matrix manipulations may become rather complicated. However, we have developed R and Mathematica procedures (found on the book’s website) that do many of these manipulations automatically. In this way, the examples on the book’s website can be adapted in an easy and flexible way for the researcher’s specific purposes. But first, as in the previous chapter, several motivating empirical examples will be introduced. The same data from the previous chapter will be used, answering similar research questions but by means of different coefficients. The interested reader may want to compare more closely the results obtained in this chapter with the results from the previous loglinear analyses.
KeywordsBody Satisfaction Loglinear Model Previous Chapter Marginal Model Cell Probability
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