The One Cup-L Project

For our reading group, Systems n Coffee (SYNC) we spent the year using a variety of computational modeling approaches consistent with Dynamical Systems Theory to examine the same data.  The idea was that we would be able to determine different analytic properties and see techniques similarities and differences.  The data was taken from a study by Brian Baucom and is a very small subset of the study as to not overlap with his future publications based on the study.  Specifically we examine heart rate data from one couple on one day over a 16 hour period.  The data was scaled to the minute epoch level giving us over 900 minutes of data on the couple.  Furthermore, we utilized GPS data to determine when during the day the couple was together or apart.  To simplify this, we used a threshold of being within 250 ft of one another to distinguish these.  For cleaning purposes, heart rate values equal to zero and over 130 were treated as missing data for all analyses.  It is noteworthy, that this was considered a distressed couple according to established indicators on the health of the couple's relationship.

Exploratory Approaches Taken
These approaches make minimal assumptions about the nature of the relationship other than being consistent with a systems approach.  Some can be thought of as diagnostic tools for helping to identify others.

Recurrence Quantification Analysis and Cross-recurrence Quantification Analysis

First Order Approaches Taken
These approaches assume that the key dynamic features of the system are captured in terms of the first derivative or first discrete differences.  In each case we are building two simultaneous equations, one for husband and one for wife.  These models are able to show relatively simple attractor dynamics including attractors, repellers, saddles, limit cycles and combinations of these (e.g. spiral attractors).  

Cross-lagged APIM Autoregressive Model
Smoothed 1st order APIM Continuous Change Model in SEM (Growth Models on Toeplitz Data structures)

Ones on our list to try but did not get to
Oud's True Change Model
Molenaar's Gimme Model

Second Order Approaches Taken
These approaches assume that the key dynamic features of the system are captured in terms of the second derivative or second discrete differences.  These models begin with the assumption of oscillatory properties (limit cycles) and examine how two oscillatory outcomes combine together to make different torus behaviors (think donuts).  These can actually be interpreted similarly to the first order models (e.g. attractors, repellers, etc.) but inherently imply a higher dimensional system and are actually combining vector based math and complex numbers.  That is, a fixed point attractor in the second order model is equivalent to the limit cycle of a pair of first order models.

Second order APIM in SEM
Linear and Nonlinear Coupled Oscillator Model

Ones on our list to try but did not get to
Butler's Bayesian Generative Coupled Oscillator Model
Discrete Second Order Latent Change Score Model