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From |
"Schaffer, Mark E" <M.E.Schaffer@hw.ac.uk> |

To |
<statalist@hsphsun2.harvard.edu> |

Subject |
st: Test of ordered probit vs ordinary probits |

Date |
Wed, 31 Oct 2007 19:07:46 -0000 |

Hi everybody. I have a question about ordered probits that follows on from the FAQ by Bill Gould about the role of the constant/cutoffs: http://www.stata.com/support/faqs/stat/constant.html At the end of the FAQ, Bill sets out a 3-outcome example: Pr(outcome==1) = Pr( X*b + u <= /cut1) Pr(outcome==2) = Pr(/cut1 < X*b + u <= /cut2) (1) Pr(outcome==3) = Pr(/cut2 < X*b + u) and then shows how these relate to two 2-outcome (basic probit) equations: Pr(outcome==3) = Pr(/cut2 < X*b + u) = Pr( 0 < X*b + (−/cut2) + u) = Pr( X*b + (−/cut2) + u > 0) (1.3) Pr(outcome>=2) = Pr(/cut1 < X*b + u) = Pr( 0 < X*b + (−/cut1) + u) = Pr( X*b + (−/cut1) + u > 0) (1.2) Bill writes, "Ordered probit amounts to estimating (1.3) and (1.2) simultaneously, and with the constraint, that b in (1.3) equals b in (1.2). Ergo, ordered probit amounts to estimating the standard binary probit models Pr(outcome==3) = Pr( X*b + (−/cut2) + u > 0) (1.3) and Pr(outcome>=2) = Pr( X*b + (−/cut1) + u > 0) (1.2) with the constraint that the cofficients, but not the INTERCEPTS, are equal." My question: Say we estimate two probits as above and test the constraint that the coefficients are equal. Can we interpret this test as a test of probit vs. ordered probit? That is, if the test fails to reject the null that the coefficients are different, would estimated an ordered probit be a logical next step? I suspect the answer is "not quite", because the ordered probit also has embodied in it the constraint that the intercepts (cutoffs) are ordered, but maybe I'm wrong. A specific example, using suest: sysuse auto, clear drop if rep78==. gen rep78_12=rep78>1 gen rep78_23=rep78>2 gen rep78_34=rep78>3 gen rep78_45=rep78>4 qui probit rep78_12 turn est store probit12 qui probit rep78_23 turn est store probit23 qui probit rep78_34 turn est store probit34 qui probit rep78_45 turn est store probit45 suest probit12 probit23 probit34 probit45 test [probit12]turn=[probit23]turn test [probit23]turn=[probit34]turn, accum test [probit34]turn=[probit45]turn, accum oprobit rep78 turn, robust Cheers, Mark Prof. Mark E. Schaffer Director Centre for Economic Reform and Transformation Department of Economics School of Management & Languages Heriot-Watt University Edinburgh EH14 4AS UK 44-131-451-3494 direct 44-131-451-3296 fax http://www.sml.hw.ac.uk/cert * * 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: st: Test of ordered probit vs ordinary probits***From:*Partha Deb <partha.deb@hunter.cuny.edu>

**Re: st: Test of ordered probit vs ordinary probits***From:*Richard Williams <Richard.A.Williams.5@ND.edu>

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