class eleven

log type: text

opened on: 31 Oct 2005, 10:58:47

. *So a not entirely useful but practical introduction to stepwise modeling

. table husb wife, contents (sum count) row col

-----------------------------------------------------------------------------------

| wife

husb | black Mexican Oth Hisp All Others white Total

-----------+-----------------------------------------------------------------------

black | 4074 63 32 42 215 4426

Mexican | 25 3947 143 95 1009 5219

Oth Hisp | 16 132 239 18 304 709

All Others | 19 78 18 1022 360 1497

white | 103 1156 373 492 28453 30577

Total | 4237 5376 805 1669 30341 42428

-----------------------------------------------------------------------------------

. *the familiar HW 2 dataset

. *Let me show you some of the sets of interaction terms

. table husb wife, contents (mean endog)

-----------------------------------------------------------------------

| wife

husb | black Mexican Oth Hisp All Others white

-----------+-----------------------------------------------------------

black | 1 0 0 0 0

Mexican | 0 2 0 0 0

Oth Hisp | 0 0 3 0 0

All Others | 0 0 0 4 0

white | 0 0 0 0 5

-----------------------------------------------------------------------

. table husb wife, contents (mean QS)

-----------------------------------------------------------------------

| wife

husb | black Mexican Oth Hisp All Others white

-----------+-----------------------------------------------------------

black | 0 21 31 41 51

Mexican | 21 0 32 42 52

Oth Hisp | 31 32 0 43 53

All Others | 41 42 43 0 54

white | 51 52 53 54 0

-----------------------------------------------------------------------

. *QS is the quasi symmetry terms, symmetric off diagonal associations

. table husb wife, contents (mean QS2)

-----------------------------------------------------------------------

| wife

husb | black Mexican Oth Hisp All Others white

-----------+-----------------------------------------------------------

black | 1 21 0 41 51

Mexican | 21 2 32 0 0

Oth Hisp | 0 32 3 0 0

All Others | 41 0 0 4 45

white | 51 0 0 45 5

-----------------------------------------------------------------------

. *Another version of the quasi symmetry terms

. table husb wife, contents (mean Asym)

-----------------------------------------------------------------------

| wife

husb | black Mexican Oth Hisp All Others white

-----------+-----------------------------------------------------------

black | 0 0 0 0 0

Mexican | 21 0 0 0 0

Oth Hisp | 31 32 0 0 0

All Others | 41 42 43 0 0

white | 51 52 53 54 0

-----------------------------------------------------------------------

. set linesize 79

. desmat wife husb QS

Desmat generated the following design matrix:

nr Variables Term Parameterization

First Last

1 _x_1 _x_4 wife ind(1)

2 _x_5 _x_8 husb ind(1)

3 _x_9 _x_18 QS ind(0)

. sw poisson count (_x_1-_x_8) _x_9-_x_18, forward pe(.001) pr(.05)

begin with empty model

p = 0.0000 < 0.0010 adding _x_1 _x_2 _x_3 _x_4 _x_5 _x_6 _x_7 _x_8

p = 0.0000 < 0.0010 adding _x_15

p = 0.0000 < 0.0010 adding _x_16

p = 0.0000 < 0.0010 adding _x_9

p = 0.0000 < 0.0010 adding _x_18

p = 0.0000 < 0.0010 adding _x_13

p = 0.0000 < 0.0010 adding _x_12

p = 0.0000 < 0.0010 adding _x_10

p = 0.0000 < 0.0010 adding _x_17

p = 0.0000 < 0.0010 adding _x_11

p = 0.0000 < 0.0010 adding _x_14

Poisson regression Number of obs = 25

LR chi2(18) = 160097.82

Prob > chi2 = 0.0000

Log likelihood = -89.595854 Pseudo R2 = 0.9989

------------------------------------------------------------------------------

count | Coef. Std. Err. z P>|z| [95% Conf. Interval]

-------------+----------------------------------------------------------------

_x_1 | .3989251 .0513505 7.77 0.000 .2982799 .4995703

_x_2 | -.9695073 .0646542 -15.00 0.000 -1.096227 -.8427874

_x_3 | -.193238 .0573864 -3.37 0.001 -.3057133 -.0807627

_x_4 | 1.318979 .048543 27.17 0.000 1.223836 1.414121

_x_5 | -.4305946 .0513505 -8.39 0.000 -.5312398 -.3299495

_x_6 | -1.86641 .0646542 -28.87 0.000 -1.99313 -1.73969

_x_7 | -1.189626 .0573864 -20.73 0.000 -1.302101 -1.077151

_x_8 | .6246497 .048543 12.87 0.000 .5295072 .7197922

_x_15 | -4.274379 .0589036 -72.57 0.000 -4.389828 -4.15893

_x_16 | -2.283614 .0231474 -98.66 0.000 -2.328983 -2.238246

_x_9 | -4.596011 .1089742 -42.18 0.000 -4.809596 -4.382425

_x_18 | -2.549685 .0380546 -67.00 0.000 -2.624271 -2.4751

_x_13 | -3.148446 .0780804 -40.32 0.000 -3.301481 -2.995411

_x_12 | -4.322503 .1316565 -32.83 0.000 -4.580545 -4.064461

_x_10 | -3.813722 .1499479 -25.43 0.000 -4.107615 -3.51983

_x_17 | -2.046833 .050421 -40.59 0.000 -2.145656 -1.94801

_x_11 | -1.955531 .068899 -28.38 0.000 -2.09057 -1.820491

_x_14 | -3.313855 .170508 -19.44 0.000 -3.648045 -2.979666

_cons | 8.312381 .0156671 530.56 0.000 8.281674 8.343088

------------------------------------------------------------------------------

. desrep

-------------------------------------------------------------------------------

Poisson regression

-------------------------------------------------------------------------------

Dependent variable count

Optimization: ml

Number of observations: 25

Initial log likelihood: -80138.505

Log likelihood: -89.596

LR chi square: 160097.818

Model degrees of freedom: 18

Pseudo R-squared: 0.999

Prob: 0.000

-------------------------------------------------------------------------------

nr Effect Coeff s.e.

-------------------------------------------------------------------------------

count

wife

1 Mexican 0.399** 0.051

2 Oth Hisp -0.970** 0.065

3 All Others -0.193** 0.057

4 white 1.319** 0.049

husb

5 Mexican -0.431** 0.051

6 Oth Hisp -1.866** 0.065

7 All Others -1.190** 0.057

8 white 0.625** 0.049

9 51 -4.274** 0.059

10 52 -2.284** 0.023

11 21 -4.596** 0.109

12 54 -2.550** 0.038

13 42 -3.148** 0.078

14 41 -4.323** 0.132

15 31 -3.814** 0.150

16 53 -2.047** 0.050

17 32 -1.956** 0.069

18 43 -3.314** 0.171

19 _cons 8.312** 0.016

-------------------------------------------------------------------------------

* p < .05

** p < .01

. poisgof

Goodness-of-fit chi2 = 1.379208

Prob > chi2(6) = 0.9671

. desmat wife husb QS2

Desmat generated the following design matrix:

nr Variables Term Parameterization

First Last

1 _x_1 _x_4 wife ind(1)

2 _x_5 _x_8 husb ind(1)

3 _x_9 _x_17 QS2 ind(0)

. sw poisson count (_x_1-_x_8) _x_9-_x_17, forward pe(.001) pr(.05)

begin with empty model

p = 0.0000 < 0.0010 adding _x_1 _x_2 _x_3 _x_4 _x_5 _x_6 _x_7 _x_8

p = 0.0000 < 0.0010 adding _x_9

p = 0.0000 < 0.0010 adding _x_10

p = 0.0000 < 0.0010 adding _x_12

p = 0.0000 < 0.0010 adding _x_16

p = 0.0000 < 0.0010 adding _x_11

p = 0.0000 < 0.0010 adding _x_14

p = 0.0000 < 0.0010 adding _x_13

p = 0.0000 < 0.0010 adding _x_17

p = 0.0000 < 0.0010 adding _x_15

Poisson regression Number of obs = 25

LR chi2(17) = 160092.91

Prob > chi2 = 0.0000

Log likelihood = -92.0512 Pseudo R2 = 0.9989

------------------------------------------------------------------------------

count | Coef. Std. Err. z P>|z| [95% Conf. Interval]

-------------+----------------------------------------------------------------

_x_1 | -2.02435 .2156884 -9.39 0.000 -2.447092 -1.601609

_x_2 | -3.178646 .2263842 -14.04 0.000 -3.622351 -2.734941

_x_3 | .6088636 .1785219 3.41 0.001 .2589672 .95876

_x_4 | 3.0674 .1639647 18.71 0.000 2.746035 3.388765

_x_5 | -2.85263 .2063502 -13.82 0.000 -3.257069 -2.448191

_x_6 | -4.078832 .2154986 -18.93 0.000 -4.501201 -3.656462

_x_7 | -.3880939 .1689121 -2.30 0.022 -.7191556 -.0570321

_x_8 | 2.3733 .1522354 15.59 0.000 2.074924 2.671676

_x_9 | 1.603634 .3317839 4.83 0.000 .953349 2.253918

_x_10 | 6.448944 .1442074 44.72 0.000 6.166303 6.731586

_x_12 | -1.893438 .1469865 -12.88 0.000 -2.181526 -1.60535

_x_16 | -3.496464 .085671 -40.81 0.000 -3.664376 -3.328552

_x_11 | 6.025194 .1692812 35.59 0.000 5.693409 6.356979

_x_14 | 4.28146 .1558883 27.46 0.000 3.975924 4.586995

_x_13 | -.5694784 .18482 -3.08 0.002 -.9317189 -.2072378

_x_17 | -4.419243 .2138822 -20.66 0.000 -4.838445 -4.000042

_x_15 | -3.520818 .2108343 -16.70 0.000 -3.934045 -3.10759

_cons | 6.708747 .3314138 20.24 0.000 6.059188 7.358306

------------------------------------------------------------------------------

. poisgof

Goodness-of-fit chi2 = 6.289901

Prob > chi2(7) = 0.5063

. desrep

-------------------------------------------------------------------------------

Poisson regression

-------------------------------------------------------------------------------

Dependent variable count

Optimization: ml

Number of observations: 25

Initial log likelihood: -80138.505

Log likelihood: -92.051

LR chi square: 160092.907

Model degrees of freedom: 17

Pseudo R-squared: 0.999

Prob: 0.000

-------------------------------------------------------------------------------

nr Effect Coeff s.e.

-------------------------------------------------------------------------------

count

wife

1 Mexican -2.024** 0.216

2 Oth Hisp -3.179** 0.226

3 All Others 0.609** 0.179

4 white 3.067** 0.164

husb

5 Mexican -2.853** 0.206

6 Oth Hisp -4.079** 0.215

7 All Others -0.388* 0.169

8 white 2.373** 0.152

QS2

9 1 1.604** 0.332

10 2 6.449** 0.144

11 5 -1.893** 0.147

12 45 -3.496** 0.086

13 3 6.025** 0.169

14 32 4.281** 0.156

15 21 -0.569** 0.185

16 51 -4.419** 0.214

17 41 -3.521** 0.211

18 _cons 6.709** 0.331

-------------------------------------------------------------------------------

* p < .05

** p < .01

. desmat wife husb QS2 Asym

Desmat generated the following design matrix:

nr Variables Term Parameterization

First Last

1 _x_1 _x_4 wife ind(1)

2 _x_5 _x_8 husb ind(1)

3 _x_9 _x_16 QS2 ind(0)

4 _x_17 _x_23 Asym ind(0)

. sw poisson count (_x_1-_x_8) _x_9-_x_23, forward pe(.001) pr(.05)

begin with empty model

p = 0.0000 < 0.0010 adding _x_1 _x_2 _x_3 _x_4 _x_5 _x_6 _x_7 _x_8

p = 0.0000 < 0.0010 adding _x_9

p = 0.0000 < 0.0010 adding _x_10

p = 0.0000 < 0.0010 adding _x_11

p = 0.0000 < 0.0010 adding _x_16

p = 0.0000 < 0.0010 adding _x_15

p = 0.0000 < 0.0010 adding _x_13

p = 0.0000 < 0.0010 adding _x_14

p = 0.0000 < 0.0010 adding _x_12

Poisson regression Number of obs = 25

LR chi2(16) = 160066.21

Prob > chi2 = 0.0000

Log likelihood = -105.39899 Pseudo R2 = 0.9987

------------------------------------------------------------------------------

count | Coef. Std. Err. z P>|z| [95% Conf. Interval]

-------------+----------------------------------------------------------------

_x_1 | -3.037627 .0802013 -37.88 0.000 -3.194818 -2.880435

_x_2 | -4.251087 .0810706 -52.44 0.000 -4.409983 -4.092192

_x_3 | -.2085674 .0560674 -3.72 0.000 -.3184575 -.0986773

_x_4 | 2.432403 .0843156 28.85 0.000 2.267147 2.597658

_x_5 | -3.803611 .0853107 -44.59 0.000 -3.970817 -3.636405

_x_6 | -5.070484 .0907108 -55.90 0.000 -5.248274 -4.892694

_x_7 | -1.15285 .0557006 -20.70 0.000 -1.262021 -1.043679

_x_8 | 1.797491 .0783424 22.94 0.000 1.643943 1.951039

_x_9 | 6.813906 .1344068 50.70 0.000 6.550474 7.077339

_x_10 | 6.489992 .1496864 43.36 0.000 6.196612 6.783372

_x_11 | -2.281927 .1344963 -16.97 0.000 -2.545535 -2.01832

_x_16 | -5.40365 .0900035 -60.04 0.000 -5.580054 -5.227247

_x_15 | -3.699758 .079329 -46.64 0.000 -3.855239 -3.544276

_x_13 | 4.696629 .1408534 33.34 0.000 4.420561 4.972697

_x_14 | -4.317155 .1313244 -32.87 0.000 -4.574547 -4.059764

_x_12 | -1.17485 .1264584 -9.29 0.000 -1.422704 -.9269958

_cons | 8.308043 .0156765 529.97 0.000 8.277317 8.338768

------------------------------------------------------------------------------

. desrep

-------------------------------------------------------------------------------

Poisson regression

-------------------------------------------------------------------------------

Dependent variable count

Optimization: ml

Number of observations: 25

Initial log likelihood: -80138.505

Log likelihood: -105.399

LR chi square: 160066.212

Model degrees of freedom: 16

Pseudo R-squared: 0.999

Prob: 0.000

-------------------------------------------------------------------------------

nr Effect Coeff s.e.

-------------------------------------------------------------------------------

count

wife

1 Mexican -3.038** 0.080

2 Oth Hisp -4.251** 0.081

3 All Others -0.209** 0.056

4 white 2.432** 0.084

husb

5 Mexican -3.804** 0.085

6 Oth Hisp -5.070** 0.091

7 All Others -1.153** 0.056

8 white 1.797** 0.078

QS2

9 2 6.814** 0.134

10 3 6.490** 0.150

11 5 -2.282** 0.134

12 51 -5.404** 0.090

13 45 -3.700** 0.079

14 32 4.697** 0.141

15 41 -4.317** 0.131

16 21 -1.175** 0.126

17 _cons 8.308** 0.016

-------------------------------------------------------------------------------

* p < .05

** p < .01

. sw poisson count (_x_1-_x_8) _x_9-_x_23, pe(.001) pr(.05)

begin with full model

p = 0.4095 >= 0.0500 removing _x_23

p = 0.0640 >= 0.0500 removing _x_12

Poisson regression Number of obs = 25

LR chi2(21) = 160091.88

Prob > chi2 = 0.0000

Log likelihood = -92.562575 Pseudo R2 = 0.9988

------------------------------------------------------------------------------

count | Coef. Std. Err. z P>|z| [95% Conf. Interval]

-------------+----------------------------------------------------------------

_x_1 | -4.06539 .1083477 -37.52 0.000 -4.277747 -3.853032

_x_2 | -5.089304 .1351684 -37.65 0.000 -5.354229 -4.824379

_x_3 | -.1919224 .0645821 -2.97 0.003 -.318501 -.0653437

_x_4 | 2.26076 .1173969 19.26 0.000 2.030666 2.490853

_x_5 | -3.655269 .1149749 -31.79 0.000 -3.880615 -3.429922

_x_6 | -4.859961 .1234203 -39.38 0.000 -5.101861 -4.618062

_x_7 | -1.190941 .0645821 -18.44 0.000 -1.31752 -1.064363

_x_8 | 1.561703 .1201971 12.99 0.000 1.326121 1.797285

_x_9 | 7.688989 .1591377 48.32 0.000 7.377085 8.000893

_x_10 | 7.113348 .2019181 35.23 0.000 6.717596 7.5091

_x_11 | -1.878834 .2098434 -8.95 0.000 -2.29012 -1.467549

_x_22 | 1.136799 .1874922 6.06 0.000 .769321 1.504277

_x_13 | 5.442126 .1698054 32.05 0.000 5.109313 5.774938

_x_14 | -4.32311 .132376 -32.66 0.000 -4.582562 -4.063658

_x_15 | -3.488946 .1152098 -30.28 0.000 -3.714753 -3.263139

_x_16 | -5.214588 .1201611 -43.40 0.000 -5.450099 -4.979077

_x_17 | -1.438236 .2306929 -6.23 0.000 -1.890386 -.9860864

_x_18 | -.6798307 .2788056 -2.44 0.015 -1.22628 -.1333817

_x_19 | 1.30066 .1687754 7.71 0.000 .9698659 1.631453

_x_20 | .8582368 .2788395 3.08 0.002 .3117215 1.404752

_x_21 | 1.244027 .1637258 7.60 0.000 .9231305 1.564924

_cons | 8.312381 .0156671 530.56 0.000 8.281674 8.343088

------------------------------------------------------------------------------

. poisgof

Goodness-of-fit chi2 = 7.31265

Prob > chi2(3) = 0.0626

. desrep

-------------------------------------------------------------------------------

Poisson regression

-------------------------------------------------------------------------------

Dependent variable count

Optimization: ml

Number of observations: 25

Initial log likelihood: -80138.505

Log likelihood: -92.563

LR chi square: 160091.885

Model degrees of freedom: 21

Pseudo R-squared: 0.999

Prob: 0.000

-------------------------------------------------------------------------------

nr Effect Coeff s.e.

-------------------------------------------------------------------------------

count

wife

1 Mexican -4.065** 0.108

2 Oth Hisp -5.089** 0.135

3 All Others -0.192** 0.065

4 white 2.261** 0.117

husb

5 Mexican -3.655** 0.115

6 Oth Hisp -4.860** 0.123

7 All Others -1.191** 0.065

8 white 1.562** 0.120

QS2

9 2 7.689** 0.159

10 3 7.113** 0.202

11 5 -1.879** 0.210

Asym

12 53 1.137** 0.187

QS2

13 32 5.442** 0.170

14 41 -4.323** 0.132

15 45 -3.489** 0.115

16 51 -5.215** 0.120

Asym

17 21 -1.438** 0.231

18 31 -0.680* 0.279

19 42 1.301** 0.169

20 43 0.858** 0.279

21 52 1.244** 0.164

22 _cons 8.312** 0.016

-------------------------------------------------------------------------------

* p < .05

** p < .01

. *It is worth noting here, that the forward and backward stepwise regressions, with the same criteria for inclusion and exclusion, gave quite different answers. The forward stepwise didn't have any of the asymmetric terms in its final answer.

. *Another tool that is worth knowing about.

. clear all

. *And for something rather different

. edit

(3 vars, 16 obs pasted into editor)

- preserve

. *The educational intermarriage dataset that we looked at earlier in the quarter

. table hed wed, contents (sum count) row col

--------------------------------------------------

| wed

hed | 1 2 3 4 Total

----------+---------------------------------------

1 | 32016 33374 8407 988 74785

2 | 28370 137876 43783 8446 218475

3 | 7051 48766 61633 18195 135645

4 | 984 13794 28635 51224 94637

Total | 68421 233810 142458 78853 523542

--------------------------------------------------

. desmat: poisson count hed wed

-------------------------------------------------------------------------------

Poisson regression

-------------------------------------------------------------------------------

Dependent variable count

Optimization: ml

Number of observations: 16

Initial log likelihood: -221501.223

Log likelihood: -113882.425

LR chi square: 215237.595

Model degrees of freedom: 6

Pseudo R-squared: 0.486

Prob: 0.000

-------------------------------------------------------------------------------

nr Effect Coeff s.e.

-------------------------------------------------------------------------------

count

hed

1 2 1.072** 0.004

2 3 0.595** 0.005

3 4 0.235** 0.005

wed

4 2 1.229** 0.004

5 3 0.733** 0.005

6 4 0.142** 0.005

7 _cons 9.187** 0.005

-------------------------------------------------------------------------------

* p < .05

** p < .01

. poisgof

Goodness-of-fit chi2 = 227578.9

Prob > chi2(9) = 0.0000

. predict P_independent

(option n assumed; predicted number of events)

. table hed wed, contents (sum P_independent)

--------------------------------------------------

| wed

hed | 1 2 3 4

----------+---------------------------------------

1 | 9773.551 33398.43 20349.32 11263.7

2 | 28552.2 97569.33 59447.98 32905.5

3 | 17727.26 60578.06 36909.58 20430.1

4 | 12367.98 42264.19 25751.13 14253.7

--------------------------------------------------

. *the local table odds ratios from predicted values of the independence model have to be=1

. display (60578*25751)/(36909.6*42264)

.99999791

. gen score=hed*wed

. table hed wed, contents (mean score)

----------------------------------

| wed

hed | 1 2 3 4

----------+-----------------------

1 | 1 2 3 4

2 | 2 4 6 8

3 | 3 6 9 12

4 | 4 8 12 16

----------------------------------

. desmat: poisson count hed wed @score

-------------------------------------------------------------------------------

Poisson regression

-------------------------------------------------------------------------------

Dependent variable count

Optimization: ml

Number of observations: 16

Initial log likelihood: -221501.223

Log likelihood: -6373.659

LR chi square: 430255.129

Model degrees of freedom: 7

Pseudo R-squared: 0.971

Prob: 0.000

-------------------------------------------------------------------------------

nr Effect Coeff s.e.

-------------------------------------------------------------------------------

count

hed

1 2 -0.836** 0.006

2 3 -3.731** 0.012

3 4 -7.128** 0.021

wed

4 2 -0.671** 0.006

5 3 -3.656** 0.012

6 4 -7.418** 0.022

7 score 1.000** 0.003

8 _cons 9.270** 0.005

-------------------------------------------------------------------------------

* p < .05

** p < .01

. display exp (1.00)

exp not found

r(111);

. display exp(1.00)

2.7182818

. predict P_modelrplusc

(option n assumed; predicted number of events)

. *The r plus c model is one of the log multiplicative models that you can generate with loglinear models, because it can be arrived at through maximum likelihood estimation.

. table hed wed, contents (sum P_modelrplusc)

--------------------------------------------------

| wed

hed | 1 2 3 4

----------+---------------------------------------

1 | 28854.76 40075.84 5506.446 347.9548

2 | 33991.05 128324.8 47927 8232.138

3 | 5110.256 52440.83 53237.8 24856.12

4 | 464.9252 12968.53 35786.75 45416.79

--------------------------------------------------

. display (52440.8*35786.8)/(53237.8*12968.5)

2.7182058

. poisgof

Goodness-of-fit chi2 = 12561.32

Prob > chi2(8) = 0.0000

. *For one degree of freedom, the r plus c model, which enforces constant local table odds ratio on the predicted values, actually doesn't do too badly.

. *If we add the endogamy diagonal to this, we improve it of course.

. gen endog=0

. replace endog=hed if hed==wed

(4 real changes made)

. desmat: poisson count hed wed endog @score

-------------------------------------------------------------------------------

Poisson regression

-------------------------------------------------------------------------------

Dependent variable count

Optimization: ml

Number of observations: 16

Initial log likelihood: -221501.223

Log likelihood: -152.338

LR chi square: 442697.771

Model degrees of freedom: 11

Pseudo R-squared: 0.999

Prob: 0.000

-------------------------------------------------------------------------------

nr Effect Coeff s.e.

-------------------------------------------------------------------------------

count

hed

1 2 -0.433** 0.010

2 3 -2.465** 0.017

3 4 -5.109** 0.027

wed

4 2 -0.243** 0.010

5 3 -2.359** 0.017

6 4 -5.431** 0.027

endog

7 1 0.409** 0.011

8 2 0.430** 0.008

9 3 0.249** 0.008

10 4 0.845** 0.011

11 score 0.705** 0.004

12 _cons 9.260** 0.009

-------------------------------------------------------------------------------

* p < .05

** p < .01

. poisgof

Goodness-of-fit chi2 = 118.6754

Prob > chi2(4) = 0.0000

. *It's not a panacea, but it is one useful way to take advantage of the ordinal nature of the data.

. * The r+c model is one way to take advantage of the ordinal nature of the data. See Clogg and Shihadeh's book for a good summary of this.

. exit, clear