CC with heterogeneity example-misinterpretation or typo

[jlaufenb]

In the newest version of the Gentle Intro, the mixture model example described on page 14.21 states the parameter values for the generating model were pi=0.40, p(piA)=0.70 and p(piB)=0.50. I constructed the DM shown on page 14.25 and examined the output. The real parameter estimates were as follows: pi-hat=0.582, p(piA)-hat=0.656 and p(piB)-hat=0.460. Obviously, it appears that the pi-hat estimate reported reflects (1-pi). Why is this? Am I correct to conclude that the first half of p-hat estimates (6 in this case) always corresponds to mixture A? Does how you code the mixture identifier column consisting of 6 1's, 6 0's, 6 1's and 6 0's that follows the common intercept column for p and c make a difference in interpreting p-hat estimates (i.e., changing the order from top to bottom to 6 0's, 6 1's, etc) ? I don't see how it would, but maybe I'm missing some subtle detail, or worse, a blatantly obvious mistake. Could this possibly be a typo in the new intro?

Thanks
Jared

[egc]

In the newest version of the Gentle Intro, the mixture model example described on page 14.21 states the parameter values for the generating model were pi=0.40, p(piA)=0.70 and p(piB)=0.50. I constructed the DM shown on page 14.25 and examined the output. The real parameter estimates were as follows: pi-hat=0.582, p(piA)-hat=0.656 and p(piB)-hat=0.460. Obviously, it appears that the pi-hat estimate reported reflects (1-pi). Why is this? Am I correct to conclude that the first half of p-hat estimates (6 in this case) always corresponds to mixture A? Does how you code the mixture identifier column consisting of 6 1's, 6 0's, 6 1's and 6 0's that follows the common intercept column for p and c make a difference in interpreting p-hat estimates (i.e., changing the order from top to bottom to 6 0's, 6 1's, etc) ? I don't see how it would, but maybe I'm missing some subtle detail, or worse, a blatantly obvious mistake. Could this possibly be a typo in the new intro?

Thanks
Jared

I'll check, but you need to keep one thing in mind - pi is not interpretable biologically. It is an 'artificial' parameter that is fit to account for heterogeneity. It parametrizes a finite mixture, which is almost inevitably biologically unrealistic. In other words, the value of pi that MARK reports is not of any real importance.

[egc]

In the newest version of the Gentle Intro, the mixture model example described on page 14.21 states the parameter values for the generating model were pi=0.40, p(piA)=0.70 and p(piB)=0.50. I constructed the DM shown on page 14.25 and examined the output. The real parameter estimates were as follows: pi-hat=0.582, p(piA)-hat=0.656 and p(piB)-hat=0.460. Obviously, it appears that the pi-hat estimate reported reflects (1-pi). Why is this? Am I correct to conclude that the first half of p-hat estimates (6 in this case) always corresponds to mixture A? Does how you code the mixture identifier column consisting of 6 1's, 6 0's, 6 1's and 6 0's that follows the common intercept column for p and c make a difference in interpreting p-hat estimates (i.e., changing the order from top to bottom to 6 0's, 6 1's, etc) ? I don't see how it would, but maybe I'm missing some subtle detail, or worse, a blatantly obvious mistake. Could this possibly be a typo in the new intro?

Thanks
Jared

I had a look at the example - while the example (and accompanying text) were essentially correct, I've decided it wasn't a particularly good example, so I've worked up a better one. I'll post a revised Chapter 14 in the next few days.

[cooch]

I had a look at the example - while the example (and accompanying text) were essentially correct, I've decided it wasn't a particularly good example, so I've worked up a better one. I'll post a revised Chapter 14 in the next few days.

Done - just uploaded revised Chapter 14, and a new 'example' .inp file for the finite mixture heterogeneity example (as presented in section 14.6).

Made a number of other tweaks as well, most reflecting changes in the expression used to generate unconditional variances for model-averaged parameters.