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

["Jun Xu" <mystata@hotmail.com>]

If I am right, it's titled "Adding Covariates to Loglinear Models for the 
Study of Social Mobility" in American Sociological Review, 55(5):757-773 and 
relevant discussion appears on the right column of p.761, I believe.

Jun Xu
Ph.D. Candidate
Department of Sociology
Indiana University at Bloomington


> From: rgates@stata.com (Richard Gates)
> Reply-To: statalist@hsphsun2.harvard.edu
> 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
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