1) In the Example 9.30, are you assuming that your outcome has a linear slope (y). I want to look at y on w (where w is a binary covariate: treatment group vs. control group) but I don't want to impose linearity in case the slope is quadratic or cubic, etc.
2) Colleagues have recommended that I use Generalized Linear Mixed Models for my analysis of a continuous outcome and a binary predictor with AR(1). Which model would be an analogue to this method?
1) It sounds like you have repeated measures y and a time-invariant predictor w. Using the two-level approach of DSEM, this means that w is a between-level covariate. The fact that it is binary doesn't matter. And you cannot formulate a quadratic or cubic regression with a binary predictor - it needs to be continuous.
2) Generalized LMM usually refers to a non-continuous (e.g. binary, count) dependent variable but you say your outcome is continuous so I don't see how GLMM can be relevant.