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From |
Steven Samuels <[email protected]> |

To |
[email protected] |

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

Date |
Tue, 25 Jan 2011 10:16:47 -0500 |

-- Quang-

Steve [email protected] On Jan 24, 2011, at 10:11 AM, Nick Cox wrote: I understand the words, but not what they imply for your analyses.

Nick [email protected] Quang Nguyen The model is kinda comlicated to present in detail here. The main point is that both x1 and x2 (the threshold levels) are derived from other exgogenous parameters of the model. An example of such model is women's childbearing decision in which x1=10 and x2=50. On Mon, Jan 24, 2011 at 3:20 AM, Nick Cox <[email protected]> wrote:

Consider graphs like . twoway function invlogit(5+ (x - 2) - 5*(x-2)^2), ra(-3 5)These to me suggest that if this model is realistic it can beapproximated using a quadratic in the predictor and a logit link.Models like this are common in ecology whenever there is someoptimum for organisms (e.g. in moisture or temperature) andabundance is expected to be highest at that optimum.In other words, the model is equivalent to one symmetric around (x1+ x2)/2.There is no hint here why the theory suggests sharp thresholds at x1and x2. In practice I'd expect those to be fuzzy, so I wouldn't feelguilty about not taking the model very literally.

On Behalf Of Maarten buis

--- 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.

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**Follow-Ups**:**Re: st: Can we use the standard binary choice model?***From:*Steven Samuels <[email protected]>

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

**Re: st: Can we use the standard binary choice model?***From:*Maarten buis <[email protected]>

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

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

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

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