I haven't been using LJ for a while, so not sure how active this community is anymore. Either way I thought I'd throw this out here.
I'm working on plotting out my dissertation -- analyzing ecological momentary assessment. I don't fully understand the capabilities of what types of questions can be asked/answered with dynamic systems modeling. I have a pretty 'interesting' variability scheme. Looking at negative affect, which understandably on intervals of 30-40 minutes will have lots of 0's. Further, increases in negative affect are (not surprisingly) usually followed by decreases a bit later. I also know that if you simply lag observations, higher NA at T-1 are associated with higher NA at T-2 (again not surprising). Given the ebb and flow nature of the phenomena, I have a hard time picturing that a linear association would best capture the nature of the construct.
In my mind, I picture the function as a type of sinusoidal oscillation, with perturbations associated with exogenous events (in my case, child misbehaviors). The literature seems pretty complex, and I don't want to spend too much time chasing a dead end (advancement deadline fast approaches).
To synthesize, here's my question: Can dynamic systems models be done using advanced non-linear, non-quadratic equations (again, in my instance, oscillations I picture like sinusoidal parameterization). And beyond that, can you use time-varying child misbehavior observations to predict fluctuations in this model? I see child misbehavior as one of many different things that could cause a perturbation to the system, but it's pretty much the big one that this dataset has.
Thanks for all your help in advance!