[sledghammer]

I'm not sure how much statistics you know so maybe someone else can answer this for me.

I feel like this is analogous to the difference between a logistic regression model and a loglinear model. In a logistic regression, there are defined dependent variable and independent variables, whereas the loglinear model variables are not treated as independent or dependent, but as a whole 'system' that simply exists.

I wish I had some of my stat books with me so I could actually look at the equations. I'll try and dig something up online. I also have a vague feeling there might be similar things in time series. I think when you said 'covariate' it triggered something in my brain.