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From |
Maarten buis <[email protected]> |

To |
[email protected] |

Subject |
Re: st: Can we use the standard binary choice model? |

Date |
Mon, 24 Jan 2011 13:08:06 +0000 (GMT) |

--- On Mon, 24/1/11, Quang Nguyen wrote: > We have a theoretical model predicing the relationship between > a binary variable "y" and a continous variable in the following > pattern: y=1 if y is in the range of [x1,x2] and y=0 if y is > smaller than x1 or greater than x2. Where x1 and x2 are some > threshold determined by the theoretical model's parameters. > > Can you suggest an empirical model to verify the above > model's prediction? Let me fix some terminology and notation: y* is a latent continuous dependent/explained variable. y is the observed binary dependent/explained variable. xb is the linear predictor: b0 + b1 x1 + b2 x2 + b3 x3, the xs are independent/explanatory variables not your theshholds. a1 and a2 are your thresholds, (x1 x2 in your notation). Your problem would be: y* = xb y = 1 if a1 <= y* <= a2 y = 0 if y* < a1 | y* > a2 This would be relatively easy to solve if a1 = - a2: y*^2 = xb^2 y = 1 if y*^2 <= a2^2 y = 0 if y*^2 > a2^2 y = 1 if y*^2 - a2^2 <= 0 y = 0 if y*^2 - a2^2 > 0 So now it is just a regular binary choice model whith a lot of extra variables (squares and products of variables), and a hard to interpret constant. Hope this helps, Maarten -------------------------- Maarten L. Buis Institut fuer Soziologie Universitaet Tuebingen Wilhelmstrasse 36 72074 Tuebingen Germany http://www.maartenbuis.nl -------------------------- * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

**Follow-Ups**:**RE: st: Can we use the standard binary choice model?***From:*Nick Cox <[email protected]>

**References**:**st: Can we use the standard binary choice model?***From:*Quang Nguyen <[email protected]>

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