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log: C:\AAA Miker Files\newer web pages\soc_388_notes\soc_388_2007\class_eleven_log.log
log type: text
opened on: 30 Oct 2007, 11:04:47
. edit
(4 vars, 8 obs pasted into editor)
- preserve
. table defendant victim [fweight=count], contents (mean death_penalty freq) row col
-------------------------------------
| victim
defendant | black white Total
----------+--------------------------
black | .058252 .174603 .10241
| 103 63 166
|
white | 0 .125828 .11875
| 9 151 160
|
Total | .053571 .140187 .110429
| 112 214 326
-------------------------------------
. set linesize 79
. *first relevant issue: the crude pct who get the death penalty is a bit higher for white defendants than for black defendants. A bit surprising at first.
. *Secondly, people who kill whites are much more likely to get the death penalty, 14% to 5%
. *There is another interesting relationship here potentially, between race of victim and race of perpetrator, which not immediately obvious from the table.
. *How about crude odds ratio?
. display 103*151/(9*63)
27.430335
. display ln(103*151/(9*63))
3.3116495
. *So the log odds ratio of the interaction between perpetrator's race and victim's race is also high, 3.3
. *Let's look at a couple of loglinear models.
. desmat: poisson count defendant victim death_penalty
----------------------------------------------------------------------------------
Poisson regression
----------------------------------------------------------------------------------
Dependent variable count
Optimization: ml
Number of observations: 8
Initial log likelihood: -215.798
Log likelihood: -86.805
LR chi square: 257.986
Model degrees of freedom: 3
Pseudo R-squared: 0.598
Prob: 0.000
----------------------------------------------------------------------------------
nr Effect Coeff s.e.
----------------------------------------------------------------------------------
count
defendant
1 white -0.037 0.111
victim
2 white 0.647** 0.117
death_penalty
3 1 -2.086** 0.177
4 _cons 3.927** 0.111
----------------------------------------------------------------------------------
* p < .05
** p < .01
. poisgof
Goodness-of-fit chi2 = 137.9293
Prob > chi2(4) = 0.0000
. *Well, no surprise that the mutual independence model doesn't fit.
. desmat defendant*victim*death_penalty=dev(1)*dev(1)*dev(1)
Desmat generated the following design matrix:
nr Variables Term Parameterization
First Last
1 _x_1 defendant dev(1)
2 _x_2 victim dev(1)
3 _x_3 defendant.victim dev(1).dev(1)
4 _x_4 death_penalty dev(0)
5 _x_5 defendant.death_penalty dev(1).dev(0)
6 _x_6 victim.death_penalty dev(1).dev(0)
7 _x_7 defendant.victim.death_penaltydev(1).dev(1).dev(0)
. sw poisson count (_x_1 _x_2 _x_4) _x_3 _x_5 _x_6, forward pe(.001) pr(.05)
begin with empty model
p = 0.0000 < 0.0010 adding _x_1 _x_2 _x_4
p = 0.0000 < 0.0010 adding _x_3
Poisson regression Number of obs = 8
LR chi2(4) = 387.78
Prob > chi2 = 0.0000
Log likelihood = -21.906596 Pseudo R2 = 0.8985
------------------------------------------------------------------------------
count | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
_x_1 | -.3908398 .0946425 -4.13 0.000 -.5763358 -.2053438
_x_2 | .5821152 .0946425 6.15 0.000 .3966193 .7676112
_x_4 | -1.043181 .0883545 -11.81 0.000 -1.216353 -.8700094
_x_3 | .8279124 .0946425 8.75 0.000 .6424164 1.013408
_cons | 2.837895 .1170309 24.25 0.000 2.608518 3.067271
------------------------------------------------------------------------------
. desrep
----------------------------------------------------------------------------------
Poisson regression
----------------------------------------------------------------------------------
Dependent variable count
Optimization: ml
Number of observations: 8
Initial log likelihood: -215.798
Log likelihood: -21.907
LR chi square: 387.784
Model degrees of freedom: 4
Pseudo R-squared: 0.898
Prob: 0.000
----------------------------------------------------------------------------------
nr Effect Coeff s.e.
----------------------------------------------------------------------------------
count
defendant
1 white -0.391** 0.095
victim
2 white 0.582** 0.095
death_penalty
3 1 -1.043** 0.088
defendant.victim
4 white.white 0.828** 0.095
5 _cons 2.838** 0.117
----------------------------------------------------------------------------------
* p < .05
** p < .01
. *What we see here is that, with a .001 entry criteria, the only 2-way that gets put into the model is interaction between defendant race and victim race.
. *Let me see if I can run the model with indicator dummies to get the value of the odds ratio we got by hand.
. desmat: poisson count defendant*victim death_penalty=dev(1)
----------------------------------------------------------------------------------
Poisson regression
----------------------------------------------------------------------------------
Dependent variable count
Optimization: ml
Number of observations: 8
Initial log likelihood: -215.798
Log likelihood: -21.907
LR chi square: 387.784
Model degrees of freedom: 4
Pseudo R-squared: 0.898
Prob: 0.000
----------------------------------------------------------------------------------
nr Effect Coeff s.e.
----------------------------------------------------------------------------------
count
defendant
1 white -2.438** 0.348
victim
2 white -0.492** 0.160
defendant.victim
3 white.white 3.312** 0.379
death_penalty
4 1 -1.043** 0.088
5 _cons 3.475** 0.120
----------------------------------------------------------------------------------
* p < .05
** p < .01
. *We get our 3.31 log odds ratio for the defendant-victim interaction.
. poisgof
Goodness-of-fit chi2 = 8.131552
Prob > chi2(3) = 0.0434
. *let's look at a couple of logistic regressions.
. desmat: logistic death_penalty victim [fweight=count]
----------------------------------------------------------------------------------
logistic
----------------------------------------------------------------------------------
Dependent variable death_penalty
Number of observations: 326
fweight: count
Initial log likelihood: -113.256
Log likelihood: -110.132
LR chi square: 6.250
Model degrees of freedom: 1
Pseudo R-squared: 0.028
Prob: 0.012
----------------------------------------------------------------------------------
nr Effect Coeff s.e.
----------------------------------------------------------------------------------
victim
1 white 1.058* 0.464
2 _cons -2.872** 0.420
----------------------------------------------------------------------------------
* p < .05
** p < .01
. lfit table
variable table not found
r(111);
. lfit, table
Logistic model for death_penalty, goodness-of-fit test
+--------------------------------------------------------+
| Group | Prob | Obs_1 | Exp_1 | Obs_0 | Exp_0 | Total |
|-------+--------+-------+-------+-------+-------+-------|
| 1 | 0.0536 | 6 | 6.0 | 106 | 106.0 | 112 |
| 2 | 0.1402 | 30 | 30.0 | 184 | 184.0 | 214 |
+--------------------------------------------------------+
+-----------------------+
| Group | Prob | _x_1 |
|-------+--------+------|
| 1 | 0.0536 | 0 |
| 2 | 0.1402 | 1 |
+-----------------------+
number of observations = 326
number of covariate patterns = 2
Pearson chi2(0) = 0.00
Prob > chi2 = .
. *What we get from the logistic regression, is a dataset that has 2 cells of victim's race by death_penalty, with the defendant's race dimension collapsed.
. *So, which loglinear model would be the equivalent to this logistic regression?
. desmat: poisson count victim*death_penalty
----------------------------------------------------------------------------------
Poisson regression
----------------------------------------------------------------------------------
Dependent variable count
Optimization: ml
Number of observations: 8
Initial log likelihood: -215.798
Log likelihood: -83.736
LR chi square: 264.125
Model degrees of freedom: 3
Pseudo R-squared: 0.612
Prob: 0.000
----------------------------------------------------------------------------------
nr Effect Coeff s.e.
----------------------------------------------------------------------------------
count
victim
1 white 0.551** 0.122
death_penalty
2 1 -2.872** 0.420
victim.death_penalty
3 white.1 1.058* 0.464
4 _cons 3.970** 0.097
----------------------------------------------------------------------------------
* p < .05
** p < .01
. poisgof
Goodness-of-fit chi2 = 131.79
Prob > chi2(4) = 0.0000
. *The coefficient for the key interaction (and its standard error) is exactly the same in the loglinear and the logistic formats. The models are the same, but the fit statistics are different.
. desmat: logistic death_penalty defendant victim [fweight=count]
----------------------------------------------------------------------------------
logistic
----------------------------------------------------------------------------------
Dependent variable death_penalty
Number of observations: 326
fweight: count
Initial log likelihood: -113.256
Log likelihood: -109.541
LR chi square: 7.431
Model degrees of freedom: 2
Pseudo R-squared: 0.033
Prob: 0.024
----------------------------------------------------------------------------------
nr Effect Coeff s.e.
----------------------------------------------------------------------------------
defendant
1 white -0.440 0.401
victim
2 white 1.324* 0.519
3 _cons -2.842** 0.420
----------------------------------------------------------------------------------
* p < .05
** p < .01
. lfit, table
Logistic model for death_penalty, goodness-of-fit test
+--------------------------------------------------------+
| Group | Prob | Obs_1 | Exp_1 | Obs_0 | Exp_0 | Total |
|-------+--------+-------+-------+-------+-------+-------|
| 1 | 0.0362 | 0 | 0.3 | 9 | 8.7 | 9 |
| 2 | 0.0551 | 6 | 5.7 | 97 | 97.3 | 103 |
| 3 | 0.1237 | 19 | 18.7 | 132 | 132.3 | 151 |
| 4 | 0.1798 | 11 | 11.3 | 52 | 51.7 | 63 |
+--------------------------------------------------------+
+------------------------------+
| Group | Prob | _x_1 | _x_2 |
|-------+--------+------+------|
| 1 | 0.0362 | 1 | 0 |
| 2 | 0.0551 | 0 | 0 |
| 3 | 0.1237 | 1 | 1 |
| 4 | 0.1798 | 0 | 1 |
+------------------------------+
number of observations = 326
number of covariate patterns = 4
Pearson chi2(1) = 0.38
Prob > chi2 = 0.5400
. *That above logistic regression corresponds to the all-2-way loglinear model.
. desmat: poisson count defendant*victim defendant*death_penalty victim*death_penalty
----------------------------------------------------------------------------------
Poisson regression
----------------------------------------------------------------------------------
Dependent variable count
Optimization: ml
Number of observations: 8
Initial log likelihood: -215.798
Log likelihood: -18.191
LR chi square: 395.215
Model degrees of freedom: 6
Pseudo R-squared: 0.916
Prob: 0.000
----------------------------------------------------------------------------------
nr Effect Coeff s.e.
----------------------------------------------------------------------------------
count
defendant
1 white -2.418** 0.348
victim
2 white -0.633** 0.171
defendant.victim
3 white.white 3.358** 0.382
death_penalty
4 1 -2.842** 0.420
defendant.death_penalty
5 white.1 -0.440 0.401
victim.death_penalty
6 white.1 1.324* 0.519
7 _cons 4.578** 0.101
----------------------------------------------------------------------------------
* p < .05
** p < .01
. poisgof
Goodness-of-fit chi2 = .7006815
Prob > chi2(1) = 0.4026
. *This all 2-way model suggests that we could drop the defendant*death_penalty interaction, and have a nice model with good fit left, and of course it also seems to suggest, as our initial data analysis made us suspect, that race of defendant is not a significant factor in who gets the death penalty
. *The interactions with death penalty in the poisson model are the terms which are the direct effects of the independent variables in the logistic regression.
. *How can we see the interaction between victim's race and defendant's race in the logistic regressions?
.
. desmat: logistic death_penalty victim*defendant [fweight=count]
----------------------------------------------------------------------------------
logistic
----------------------------------------------------------------------------------
Dependent variable death_penalty
Number of observations: 326
fweight: count
Initial log likelihood: -113.256
Log likelihood: -109.191
LR chi square: 8.132
Model degrees of freedom: 3
Pseudo R-squared: 0.036
Prob: 0.043
----------------------------------------------------------------------------------
nr Effect Coeff s.e.
----------------------------------------------------------------------------------
victim
1 white 1.230* 0.536
defendant
2 white -15.490** 0.413
victim.defendant
3 white.white 15.105 .
4 _cons -2.783** 0.421
----------------------------------------------------------------------------------
* p < .05
** p < .01
. *Something weird starts to happen. Which is, the coefficients start to get too big, and unreliable. Why?
.
. *Because this logistic regression corresponds to the saturated model, and the data have a zero.
. desmat: poisson count defendant*victim*death_penalty
----------------------------------------------------------------------------------
Poisson regression
----------------------------------------------------------------------------------
Dependent variable count
Optimization: ml
Number of observations: 8
Initial log likelihood: -215.798
Log likelihood: -17.841
LR chi square: 395.915
Model degrees of freedom: 7
Pseudo R-squared: 0.917
Prob: 0.000
----------------------------------------------------------------------------------
nr Effect Coeff s.e.
----------------------------------------------------------------------------------
count
defendant
1 white -2.377** 0.348
victim
2 white -0.623** 0.172
defendant.victim
3 white.white 3.309** 0.385
death_penalty
4 1 -2.783** 0.421
defendant.death_penalty
5 white.1 -14.711 2096.899
victim.death_penalty
6 white.1 1.230* 0.536
defendant.victim.death_penalty
7 white.white.1 14.326 2096.899
8 _cons 4.575** 0.102
----------------------------------------------------------------------------------
* p < .05
** p < .01
. *Here you see the crazy SEs...
. *because we have a zero.
. *What to do?
. *Answer, from Leo Goodman: add something to every cell.
. *It might seem kind of sacriligeous to add something to the data, but in some sense if we want to see the saturated model, we have no choice.
. gen count_plus1=count+1
. desmat: poisson count_plus1 defendant*victim*death_penalty
----------------------------------------------------------------------------------
Poisson regression
----------------------------------------------------------------------------------
Dependent variable count_plus1
Optimization: ml
Number of observations: 8
Initial log likelihood: -209.216
Log likelihood: -19.054
LR chi square: 380.324
Model degrees of freedom: 7
Pseudo R-squared: 0.909
Prob: 0.000
----------------------------------------------------------------------------------
nr Effect Coeff s.e.
----------------------------------------------------------------------------------
count_plus1
defendant
1 white -2.282** 0.332
victim
2 white -0.615** 0.171
defendant.victim
3 white.white 3.202** 0.370
death_penalty
4 1 -2.639** 0.391
defendant.death_penalty
5 white.1 0.336 1.119
victim.death_penalty
6 white.1 1.154* 0.505
defendant.victim.death_penalty
7 white.white.1 -0.746 1.189
8 _cons 4.585** 0.101
----------------------------------------------------------------------------------
* p < .05
** p < .01
. *What do we see? First of all, the defendant*death penalty is still insignificant. The 3-way is completely insignificant.
. poisgof
Goodness-of-fit chi2 = .0000109
Prob > chi2(0) = .
. desmat: logistic death_penalty defendant*victim
----------------------------------------------------------------------------------
logistic
----------------------------------------------------------------------------------
Dependent variable death_penalty
Number of observations: 8
Initial log likelihood: -5.545
Log likelihood: -5.545
LR chi square: 0.000
Model degrees of freedom: 3
Pseudo R-squared: 0.000
Prob: 1.000
----------------------------------------------------------------------------------
nr Effect Coeff s.e.
----------------------------------------------------------------------------------
defendant
1 white 0.000 2.000
victim
2 white 0.000 2.000
defendant.victim
3 white.white 0.000 2.828
4 _cons 0.000 1.414
----------------------------------------------------------------------------------
* p < .05
** p < .01
. desmat: logistic death_penalty defendant*victim [fweight=count]
----------------------------------------------------------------------------------
logistic
----------------------------------------------------------------------------------
Dependent variable death_penalty
Number of observations: 326
fweight: count
Initial log likelihood: -113.256
Log likelihood: -109.191
LR chi square: 8.132
Model degrees of freedom: 3
Pseudo R-squared: 0.036
Prob: 0.043
----------------------------------------------------------------------------------
nr Effect Coeff s.e.
----------------------------------------------------------------------------------
defendant
1 white -15.490** 0.413
victim
2 white 1.230* 0.536
defendant.victim
3 white.white 15.105 .
4 _cons -2.783** 0.421
----------------------------------------------------------------------------------
* p < .05
** p < .01
. desmat: logistic death_penalty defendant*victim [fweight= count_plus1]
----------------------------------------------------------------------------------
logistic
----------------------------------------------------------------------------------
Dependent variable death_penalty
Number of observations: 334
fweight: count_plus1
Initial log likelihood: -122.393
Log likelihood: -119.485
LR chi square: 5.816
Model degrees of freedom: 3
Pseudo R-squared: 0.024
Prob: 0.121
----------------------------------------------------------------------------------
nr Effect Coeff s.e.
----------------------------------------------------------------------------------
defendant
1 white 0.336 1.119
victim
2 white 1.154* 0.505
defendant.victim
3 white.white -0.746 1.189
4 _cons -2.639** 0.391
----------------------------------------------------------------------------------
* p < .05
** p < .01
. *these estimates are pretty much the same as with count, but here we get more stability
. *What would our best loglinear model look like?
. desmat: poisson count victim*defendant victim*death_penalty
----------------------------------------------------------------------------------
Poisson regression
----------------------------------------------------------------------------------
Dependent variable count
Optimization: ml
Number of observations: 8
Initial log likelihood: -215.798
Log likelihood: -18.782
LR chi square: 394.033
Model degrees of freedom: 5
Pseudo R-squared: 0.913
Prob: 0.000
----------------------------------------------------------------------------------
nr Effect Coeff s.e.
----------------------------------------------------------------------------------
count
victim
1 white -0.588** 0.164
defendant
2 white -2.438** 0.348
victim.defendant
3 white.white 3.312** 0.379
death_penalty
4 1 -2.872** 0.420
victim.death_penalty
5 white.1 1.058* 0.464
6 _cons 4.580** 0.101
----------------------------------------------------------------------------------
* p < .05
** p < .01
. poisgof
Goodness-of-fit chi2 = 1.881837
Prob > chi2(2) = 0.3903
. *This fits well by the LRT, this v*d, v*p model
. *let's look at that same best model with countplus
. desmat: poisson count_plus1 victim*defendant victim*death_penalty
----------------------------------------------------------------------------------
Poisson regression
----------------------------------------------------------------------------------
Dependent variable count_plus1
Optimization: ml
Number of observations: 8
Initial log likelihood: -209.216
Log likelihood: -19.607
LR chi square: 379.218
Model degrees of freedom: 5
Pseudo R-squared: 0.906
Prob: 0.000
----------------------------------------------------------------------------------
nr Effect Coeff s.e.
----------------------------------------------------------------------------------
count_plus1
victim
1 white -0.567** 0.162
defendant
2 white -2.256** 0.317
victim.defendant
3 white.white 3.112** 0.350
death_penalty
4 1 -2.603** 0.366
victim.death_penalty
5 white.1 0.843* 0.413
6 _cons 4.583** 0.101
----------------------------------------------------------------------------------
* p < .05
** p < .01
. poisgof
Goodness-of-fit chi2 = 1.105725
Prob > chi2(2) = 0.5753
. *The significance level and direction of the key interactions is the same, but the values are a little different....
. *The one zero only became a problem when were doing the saturated model. Otherwise, the zero was hidden by combination with other things.
. exit, clear