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Nonlinear Mixed Models
You can perform nonlinear mixed models analysis using the NLMIXED procedure. Nonlinear mixed models, in which both fixed and random effects enter nonlinearly, have a wide variety of applications, two of the most common being pharmacokinetics and overdispersed binomial data. PROC NLMIXED enables you to specify a conditional distribution for your data (given the random effects) having either a standard form (normal, binomial, Poisson) or a general distribution that you code using SAS programming statements.
PROC NLMIXED fits nonlinear mixed models by maximizing an approximation to the likelihood integrated over the random effects. Different integral approximations are available, the principal ones being adaptive Gaussian quadrature and a first-order Taylor series approximation for Gaussian data. The maximization is carried out using any number of alternative optimization techniques; the default is a dual quasi-Newton algorithm.
Successful convergence of the optimization problem results in parameter estimates along with their approximate standard errors based on the second derivative matrix of the likelihood function. PROC NLMIXED enables you to use the estimated model to construct predictions of arbitrary functions using empirical Bayes estimates of the random effects. You can also estimate arbitrary functions of the nonrandom parameters, with PROC NLMIXED computing approximate standard errors using the delta method.
Documentation
For more detail, refer to the chapter "The NLMIXED Procedure" in the SAS/STAT User's Guide. In addition, see Fitting Nonlinear Mixed Models with the New NLMIXED Procedure by Russ Wolfinger.
