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Multilevel Modeling

14. Non-linear Multilevel Models

So far we have illustrated the methodological concepts by considering a continuous response variable that has a Normal distribution.

However, a large number of outcomes of interest in public health research are not continuous and do not have Gaussian (Normal) distributive properties.

While not discussed in detail here, multilevel models are capable of handling a wide range of responses and in this sense there exist ‘generalized multilevel models’ to deal with:

  • Binary outcomes;
  • Proportions (as logit, log-log, and probit models);
  • Multiple categories (as multinomial and ordered multinomial models); and
  • Counts (as poisson and negative binomial distribution models) (Leyland and Goldstein, 2001).

Indeed, all these outcomes can be modeled using any of the hierarchical and non-hierarchical structures previously discussed (Goldstein, 2003).

These models work, in effect, by assuming a specific, non-Normal distribution for the random part at level-1, while maintaining the Normality assumptions for random parts at higher levels. Consequently, much of the discussion presented in this chapter focusing at the neighborhood and region level (higher contextual levels) would continue to hold regardless of the nature of the response variable. It may, however, be noted that the computation of VPC, discussed earlier, is not as straightforward in complex non-linear models as it is in Normal models, and is an issue of applied methodological research (Goldstein, Browne et al., 2002; Subramanian, Jones et al., 2003).

We should also mention that there are research developments whereby multilevel a perspective has been extended to survival and event history models, meta-analysis, structural equation modeling, and factor analysis (Goldstein, 2003).
Leyland, A. H., Goldstein, H. (Eds.). (2001) Multilevel modelling of health statistics. Wiley Series in Probability and Statistics. Chichester: John Wiley & Sons Ltd.
Goldstein, H. (2003) Multilevel statistical models. London: Edward Arnold.
Subramanian, S., Jones, K., et al. (2003) Multilevel methods for public health research. In: I. Kawachi and L. Berkman (Eds.). Neighborhoods and Health. New York: Oxford Press. 65-111.
Goldstein, H., Browne, W. J., et al. (2002) Partitioning variation in multilevel models. Understanding Statistics 1: 223-232.