# st: interpreting marginal effects of poisson

 From Scott Cunningham To statalist@hsphsun2.harvard.edu Subject st: interpreting marginal effects of poisson Date Tue, 18 Apr 2006 22:10:35 -0400

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
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?

*
* 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/