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From |
rgates@stata.com (Richard Gates) |

To |
statalist@hsphsun2.harvard.edu |

Subject |
Re: RE: st: Constraining alpha and theta in slogit |

Date |
Tue, 15 Nov 2005 08:43:01 -0600 |

Jun Xu <mystata@hotmail.com> responded to Michael Hout's <mikehout@berkeley.edu> inquiry about setting constraints in -slogit-. He suggested constraining the sum of the phi's to zero. > For setting the first constraint, it's like > > constrain def 1 > [phi1_1]_cons+[phi1_2]_cons+[phi1_3]_cons+...+[phi1_j]_cons=0 > > and it should work well, but I do find problems with your magnitude > constraints. I only have limited working knowledge with slogit, so others or > Stata staff might have some suggestions. But I guess one possibility why > this does not work is probably slogit in Stata has used the first strategy > (impose the first phi to be 1 and last to be zero) that DiPrete's paper > mentioned just above the discussion on Goodman's strategy (P.761), and that > might cause Goodman's strategy hard to implement? > The phi associated with the base category is always zero. For a dependent variable that is an ordered factor we set the last cateogory to be the base and constrain phi1_1 associated with the first category to be one. If the categories are truly ordered then the phi's will be monotonically decreasing from 1 to zero. Here I am assuming that the model is of dimension 1. Constraining the phi's to sum to zero is an interesting approach, if you would be kind enough to give me details of the Goodman and DiPrete references I would like to read them. Meanwhile, we still can constrain the sum of the phi's to zero (excluding the one associated with the base category). We have to turn off the corner constraints constraining the phi1_1 to 1 and use initialize(random) or initialize(svd) Below is a demonstation using the auto2yr data. . constraint 1 [phi1_1]_cons+[phi1_2]_cons+[phi1_3]_cons+[phi1_4]_cons = 0 . slogit repair foreign mpg price gratio, constraint(1) nocorner init(random) Iteration 0: log likelihood = -199.21095 (not concave) Iteration 1: log likelihood = -190.87692 (not concave) Iteration 2: log likelihood = -185.76278 (not concave) Iteration 3: log likelihood = -181.58171 (not concave) Iteration 4: log likelihood = -180.35418 (not concave) Iteration 5: log likelihood = -179.47387 (not concave) Iteration 6: log likelihood = -179.04793 (not concave) Iteration 7: log likelihood = -178.81528 Iteration 8: log likelihood = -178.54224 (not concave) Iteration 9: log likelihood = -178.42258 (not concave) Iteration 10: log likelihood = -178.41219 Iteration 11: log likelihood = -178.40734 Iteration 12: log likelihood = -178.40732 Iteration 13: log likelihood = -178.40732 (not concave) Iteration 14: log likelihood = -178.40732 Stereotype logistic regression Number of obs = 135 Wald chi2(4) = 0.00 Log likelihood = -178.40732 Prob > chi2 = 1.0000 ( 1) [phi1_1]_cons + [phi1_2]_cons + [phi1_3]_cons + [phi1_4]_cons = 0 ------------------------------------------------------------------------------ repair | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- foreign | -3.919207 2346.913 -0.00 0.999 -4603.784 4595.946 mpg | -.0670937 40.1774 -0.00 0.999 -78.81336 78.67917 price | .000244 .1460856 0.00 0.999 -.2860786 .2865665 gratio | 2.752465 1648.241 0.00 0.999 -3227.74 3233.245 -------------+---------------------------------------------------------------- /phi1_1 | .668205 400.1371 0.00 0.999 -783.586 784.9224 /phi1_2 | -.2599337 155.6544 -0.00 0.999 -305.337 304.8172 /phi1_3 | -.4009208 240.0809 -0.00 0.999 -470.9508 470.149 /phi1_4 | -.0073505 4.407548 -0.00 0.999 -8.645986 8.631285 /phi1_5 | 0 (base outcome) -------------+---------------------------------------------------------------- /theta1 | 2.96203 5.387697 0.55 0.582 -7.597662 13.52172 /theta2 | -1.658354 1.559043 -1.06 0.287 -4.714022 1.397314 /theta3 | -1.59848 3.312416 -0.48 0.629 -8.090697 4.893737 /theta4 | .8148797 1.604376 0.51 0.612 -2.32964 3.959399 /theta5 | 0 (base outcome) ------------------------------------------------------------------------------ (repair=Excellent is the base outcome) It does not seem to fit the data very well. Note that the default, initialize(const), does not work here since the phi's wind up constrained to zero. (I need to chew my cud on that.) If there is a need for other constraint options we would certainly consider adding the functionality to -slogit-. --Rich rgates@stata.com * * For searches and help try: * http://www.stata.com/support/faqs/res/findit.html * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

**Follow-Ups**:**Re: RE: st: Constraining alpha and theta in slogit***From:*"Jun Xu" <mystata@hotmail.com>

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