Thursday, April 30, 2015

Changes and their causes

Here are two specifications of change scores, as latent variables however, that can be used in subsequent analyses of changes. Note that the causal assumptions behind them differs slightly, and I prefer the causal logic of the 1st: the final values depend on initial values and on some mechanism of change, i.e. the causal mechanism 'precedes' the final observed values, not the other way around.



One can defend the view that 'changes are a result of both initial and final values', but with less grounding I'd say. This is supposed to help with the posting SEMNET: (does it?)

This 2-wave simplified example of course would not be enough to model a pattern like the one below, which, however, LCS can fit pretty well with attention to nuance and detail... J.J. McArdle's work has lots of dynamic applications like this. Some issues are: what window of time to model, and how to 'initialize' the process.

Tuesday, April 7, 2015

mixtures

Here are some examples taken from Jeff Harring's 3 day (!!!) workshop "INTRODUCTION TO FINITE MIXTURE MODELS; he pointed me to the 1st mixture modeling idea, published in 1894 (!)
Pearson, K. (1894). Contributions to the mathematical theory of evolution. Philosophical Transactions of the Royal Society of London. A, 185, 71-110.
* Here are also other ways of gauging if one has more than 1 population in their data: 

or by looking at the random slopes and intercepts: