RESULTS AND DISCUSSION FOR ASSIGNMENT #3 See the command file for the details of the tests run. The initial points used were the same as for Assignment #2. Note that this assignment uses the parameterization with alpha rather than gamma. RESULTS ON THE FIRST DATA SET (WITH FULL M STEP) INITIAL VALUES LOGLIKE ESTIMATES COMMENTS Default -1079.4 0.3 -3.3 1.9 converged in about 140 iterations exp(-2) 0 0 -1079.4 0.3 -3.3 1.9 converged in about 130 iterations exp(-2) -2 2 -1079.4 0.3 -3.3 1.9 converges in about 75 iterations exp(-2) -1 1 -1079.4 0.3 -3.3 1.9 converges in about 115 iterations exp(-2) -0.5 0.5 -1079.4 0.3 -3.3 1.9 converges in about 130 iterations exp(-2) -3 2 -1079.4 0.3 -3.3 1.9 converges in about 95 iterations exp(-2) -1.5 1 -1079.4 0.3 -3.3 1.9 converges in about 125 iterations exp(-2) -0.75 0.5 -1079.4 0.3 -3.3 1.9 converges in about 130 iterations exp(-2) -4 2 -1079.4 0.3 -3.3 1.9 converges in about 110 iterations exp(-2) -2 1 -1079.4 0.3 -3.3 1.9 converges in about 130 iterations exp(-2) -1 0.5 -1079.4 0.3 -3.3 1.9 converges in about 135 iterations What appears to be the right answers was reliably found, though only after a hundred or so iterations. RESULTS ON THE SECOND DATA SET (WITH FULL M STEP) INITIAL VALUES LOGLIKE ESTIMATES COMMENTS Default -23.5 0.58 -44 19 terminated after 354 iterations exp(-1) -4 -1 -26.5 0.75 -138 -30 converged in about 15 iterations exp(-1) -4 1 -23.5 0.55 -81 35 converged in about 6 iterations exp(-1) -3 -1 -26.5 0.75 -136 -30 converged in about 11 iterations exp(-1) -3 1 -23.5 0.54 -161 72 terminated after 7 iterations exp(0) -4 -1 -26.5 0.75 -127 -28 converged in about 10 iterations exp(0) -4 1 -23.5 0.55 -160 72 converged in about 5 iterations exp(0) -3 -1 -26.5 0.75 -129 -28 converged in about 10 iterations exp(0) -3 1 -23.5 0.55 -160 72 converged in about 4 iterations One of the two solutions found in Assignment #2 was found in every run, though two runs terminated with an error message from nlm regarding a non-finite value. The betas are very large, as was the case in Assignment #2. Unlike Assignment #2, these large values are stable at the end of each run, perhaps because of limitations of nlm. As before, the ratio of the two betas, which determines where the logistic function changes sharply from 0 to 1, is estimated well, as -2.3 or 4.6 for the two solutions. Surprisingly, the default initial values from glm were the worst ones tested, for both data sets - drastically worse than the others for the second data set. I tried the second of the test runs for each data set again with the M step done with just one iteration of nlm. For the first data set, the number of iterations needed to get parameter estimates accurate to around three significant digits increased from about 130 to about 260. However, the compute time (measured on fisher.utstat, with printing in each iteration disabled) was 9.5 seconds for the 130 iterations with the full M step, but only 6.9 seconds for the 260 iterations with just one nlm iteration. For the second data set, however, even 500 iterations with only one iteration of nlm were not enough to get to an answer accurate to three significant digits, as compared to 15 iterations with a full M step.