st: interpreting marginal effects of poisson

[Scott Cunningham <scunning@gmail.com>]

Description of Data:
Individual-level survey data from waves 1998, 2000 and 2002.  It is a  
balanced panel dataset, and I am focusing currently just on Black  
American males aged 12-17 in 1998 (and thus age over the course of  
the survey).  The relevant variables are:

rp:  "recent sex partners"
sr:  "sex ratio"
age2:  age-squared
hgc:  "highest grade completed"
hhd1:  "household dummy variable for bio. parents still married"

Description of Model:
I am estimating a model in which the number of recent sex partners  
men have is a function of their age, age-squared, the relative  
availability of men and women in the mating market, their education  
attainment, whether their biological parents are married, and  
controls for individual, year and state fixed effects.  I'm modeling  
this as a Poisson distribution.  I'm having trouble taking the  
coefficients and creating marginal effects.  (FYI, I have downloaded - 
sposta- utilities, and have used -prchange- but at this point, am  
trying to manually create the marginal effects and decipher them).

Output:

. xi:poisson rp sr age2 hgc hhd1 i.year, robust
i.year            _Iyear_1998-2002    (naturally coded; _Iyear_1998  
omitted)

Iteration 0:   log pseudolikelihood = -10504.806
Iteration 1:   log pseudolikelihood = -10504.805

Poisson regression                                Number of obs    
=       2277
                                                  Wald chi2(6)     
=      60.92
                                                  Prob > chi2      
=     0.0000
Log pseudolikelihood = -10504.805                 Pseudo R2        
=     0.0347

------------------------------------------------------------------------ 
------
             |               Robust
          rp |      Coef.   Std. Err.      z    P>|z|     [95% Conf.  
Interval]
------------- 
+----------------------------------------------------------------
          sr |  -.6870002   .3183816    -2.16   0.031    -1.311017    
-.0629838
        age2 |   .0045666   .0012833     3.56   0.000     . 
0020515    .0070818
         hgc |    .000394   .0365008     0.01   0.991    -. 
0711463    .0719343
        hhd1 |   -.300639    .117171    -2.57   0.010    -.5302899    
-.0709881
_Iyear_2000 |    .065989   .1566268     0.42   0.674     -. 
240994     .372972
_Iyear_2002 |  -.3705945   .1926353    -1.92   0.054    -.7481528    . 
0069637
       _cons |   .5387156   .4899692     1.10   0.272    -. 
4216065    1.499038
------------------------------------------------------------------------ 
------





Question:  The coefficient on sr is -.6870002, and it is the variable  
of interest.  Am I correct in the following interpretations:

Q1.  The constant (_cons) represents the log of the mean number of  
sex partners for the reference cell, which in this case is Black men  
living in homes where parents are not married (hhd1=1 if biological  
parents are married).  Since exp{.5387156)=1.7138, we see that on the  
average these men have 1.7 sex partners at this point in their  
lives.  Is this the correct interpretation?

Q2.  The hhd1 variable reflects the state of the family in which the  
Black male lives.  As we move from hhd1=0 to hhd1=1, the log of the  
mean decreases by .7, which means that the number of sex partners  
gets multiplied by exp{-0.300639)=0.740345.  This means that Black  
males with married biological parents have 25% fewer sex partners  
than their counterparts whose parents are not married.  Is this the  
correct interpretation?

Q3.  The sr variable is continuous.  It is the ratio of eligible  
Black males (of a certain age range) to eligible Black females (of  
like age range) at the state level, and will take on a value from as  
low as 0.3 to 2.5.  I am unsure of how to interpret the marginal  
effect of a change in the sex ratio ("sr") on sex partners.  Am I  
correct that a one unit increase in the sex ratio causes recent sex  
partners for Black males to fall by 50%?  If so, what is a "one unit"  
when we are talking about a continuous random variable?  Is it a one  
unit increase in the standard deviation?  I've been unable to find  
this information from my reference books, and do not currently own  
the Stata book on categorical variables.  But if anyone can provide  
basic help here, I'd appreciate it.

Q4:  I am able to estimate a model with state, year and individual  
fixed effects using OLS with FE (-xtreg-), but not Poisson (- 
xtpoisson- nor -poisson-).  Specifically, I can estimate the Poisson  
model with year and individual effects, but not with year, state and  
individual fixed effects.  When I include the state effects, the  
likelihood iteratations hang up, even after letting it go for  
thousands of iterations.  It has hung up on a single likelihood, for  
that matter, and does not appear to be moving closer towards  
convergence.  What could be causing this?

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