STA2201s06 Assignment 5

Please consider the model of Figure 1.1 on Page 5 of the text; this leads to the covariance matrix (1.4) on Page 3.

1. Prove that the model is identified.
2. Using the data in assign5.dat, estimate the model parameters using R. Your goal is the MLE of gamma. Please circle it on your printout. My answer is 1.196442. Take whatever code you like from the overheads. In particular, the function LLMVN is something you will want to use directly. If you copy-paste any of the code, do it from the Word document. PDF files contain invisible characters that can cause trouble.

   Just for fun, try it once with a set of starting values that you  choose, but do not be surprised if the result is a disaster. Don't worry about it; just try Gamma = 1, Phi = 2, Psi = 3, V(delta1) = 4, V(delta2) = 5.

   When you copy/paste Assign5.dat, you will probably have to strip off the first line (with the variable names).

3. Please read pages 80-88 in Chapter 4. The idea of a recursive  model is important. The derivation of Sigma is something that we did in class, and you should be able to do it too.
4. Please read pages 88-104, on model identification. The author's choice of the terms "known" and "unknown" paramters on page 88 is very unfortunate, but we will live with it.
   • The t-rule is what I have been calling a parameter count. It's useful and very easy to apply.
   • The Null B rule says there is no beta. This one is easy to apply too, but when it holds, the models are much less interesting.
   • The Recursive rule is great and easy to apply, but the proof is difficult to follow, because of the funny notation. Forget about the proof. It operates by identifying the parameters one section at a time, using all the preceding information.
   • I find those rank and order conditions very hard to apply. I would say skim this part.