STA429/1007 F 2004 Handout 12
Loglinear modelling (Fever and death penalty data)
/************* dengue.sas ************************
Dengue fever example: NWK data set C.3
**************************************************/
title 'Log-linear on Dengue fever data';
options linesize=79 pagesize=500 noovp formdlim='_';
proc format; /* value labels used in data step below */
value agefmt 1 = '12 and under' 2 = '13-29' 3 = '30+';
value sesfmt 1 = 'High' 2 = 'Middle' 3 = 'Low';
value ynfmt 0 = 'No' 1 = 'Yes';
data mexico;
infile 'fever.dat';
input id age ses sector gotfever savings;
label ses = 'Socioeconomic Status'
sector = 'Area of City'
savgings = 'Have Savings Account';
if 1 <= age <= 12 then agegrp=1;
else if 13 <= age <= 29 then agegrp=2;
else if age >= 30 then agegrp=3;
/* if savings=2 then err=id; */
format agegrp agefmt.;
format ses sesfmt.;
format gotfever savings ynfmt.;
proc freq;
title2 'Check to make sure there are no sampling zeros';
tables agegrp*ses*sector*gotfever / norow nocol nopercent;
proc freq;
title2 'First look, to see what we have';
tables agegrp * (ses sector gotfever)
ses * (sector gotfever)
sector*gotfever / nopercent chisq;
/* Here is a rough summary of the findings
agegrp ses sector gotfever
agegrp x . . youngLess
ses x 1=low .
sector x 2=yes
gotfever x
The first model we will try will have just these relationships -- see
if it fits okay. In bracket notation,
[agegrp gotfever] [ses sector] [sector gotfever]
Here are the proc catmod syntax rules for loglinear models:
model and all the vars, separated by *s = _response_;
loglin and all the subsets (items in same brackets) connected by |s;
*/
proc catmod;
title2 'Model with just selected 2-way relationships';
model agegrp*ses*sector*gotfever = _response_
/ nodesign noprofile noresponse noparm;
loglin agegrp|gotfever ses|sector sector|gotfever;
/* In practice, we never have to fit a saturated model in order to test
goodness of fit because SAS produces the LR test by default. It is being done
here just to verify that this is exactly the test for goodness of fit that SAS
produces. */
proc catmod;
title2 'Saturated model';
model agegrp*ses*sector*gotfever = _response_
/ nodesign noprofile noresponse noparm;
loglin agegrp|ses|sector|gotfever;
proc iml;
title2 'Reproduce Goodness of fit LR Chisquare = 10.18 with 24 df';
G = 1318.5055 - 1308.3252; pval = 1-probchi(G,24);
print "G = " G ", df = 24, p = " pval;
/* Now test each of the three 2-way relationships with LR tests. Just do the
first here. */
proc catmod;
title2 'Reduced model for testing agegrp by gotfever';
model agegrp*ses*sector*gotfever = _response_
/ nodesign noprofile noresponse noparm;
loglin agegrp ses|sector sector|gotfever;
proc iml;
title2 'LR Chisquare for agegrp by gotfever. Compare Wald chisq = 14.08';
G = 1336.9829 - 1318.5055; pval = 1-probchi(G,2);
print "G = " G ", df = 2, p = " pval;
_______________________________________________________________________________
Log-linear on Dengue fever data 1
Check to make sure there are no sampling zeros
11:00 Monday, November 22, 2004
The FREQ Procedure
Table 1 of sector by gotfever
Controlling for agegrp=12 and under ses=High
sector(Area of City)
gotfever
Frequency|No |Yes | Total
---------+--------+--------+
1 | 9 | 1 | 10
---------+--------+--------+
2 | 6 | 1 | 7
---------+--------+--------+
Total 15 2 17
Table 2 of sector by gotfever
Controlling for agegrp=12 and under ses=Middle
sector(Area of City)
gotfever
Frequency|No |Yes | Total
---------+--------+--------+
1 | 10 | 1 | 11
---------+--------+--------+
2 | 6 | 1 | 7
---------+--------+--------+
Total 16 2 18
Table 3 of sector by gotfever
Controlling for agegrp=12 and under ses=Low
sector(Area of City)
gotfever
Frequency|No |Yes | Total
---------+--------+--------+
1 | 18 | 1 | 19
---------+--------+--------+
2 | 5 | 1 | 6
---------+--------+--------+
Total 23 2 25
Table 4 of sector by gotfever
Controlling for agegrp=13-29 ses=High
sector(Area of City)
gotfever
Frequency|No |Yes | Total
---------+--------+--------+
1 | 13 | 3 | 16
---------+--------+--------+
2 | 8 | 7 | 15
---------+--------+--------+
Total 21 10 31
Table 5 of sector by gotfever
Controlling for agegrp=13-29 ses=Middle
sector(Area of City)
gotfever
Frequency|No |Yes | Total
---------+--------+--------+
1 | 7 | 2 | 9
---------+--------+--------+
2 | 2 | 3 | 5
---------+--------+--------+
Total 9 5 14
Table 6 of sector by gotfever
Controlling for agegrp=13-29 ses=Low
sector(Area of City)
gotfever
Frequency|No |Yes | Total
---------+--------+--------+
1 | 12 | 6 | 18
---------+--------+--------+
2 | 3 | 3 | 6
---------+--------+--------+
Total 15 9 24
Table 7 of sector by gotfever
Controlling for agegrp=30+ ses=High
sector(Area of City)
gotfever
Frequency|No |Yes | Total
---------+--------+--------+
1 | 9 | 3 | 12
---------+--------+--------+
2 | 8 | 9 | 17
---------+--------+--------+
Total 17 12 29
Table 8 of sector by gotfever
Controlling for agegrp=30+ ses=Middle
sector(Area of City)
gotfever
Frequency|No |Yes | Total
---------+--------+--------+
1 | 6 | 1 | 7
---------+--------+--------+
2 | 4 | 7 | 11
---------+--------+--------+
Total 10 8 18
Table 9 of sector by gotfever
Controlling for agegrp=30+ ses=Low
sector(Area of City)
gotfever
Frequency|No |Yes | Total
---------+--------+--------+
1 | 11 | 5 | 16
---------+--------+--------+
2 | 2 | 3 | 5
---------+--------+--------+
Total 13 8 21
_______________________________________________________________________________
Log-linear on Dengue fever data 2
First look, to see what we have
11:00 Monday, November 22, 2004
The FREQ Procedure
Table of agegrp by ses
agegrp ses(Socioeconomic Status)
Frequency |
Row Pct |
Col Pct |High |Middle |Low | Total
-------------+--------+--------+--------+
12 and under | 17 | 18 | 25 | 60
| 28.33 | 30.00 | 41.67 |
| 22.08 | 36.00 | 35.71 |
-------------+--------+--------+--------+
13-29 | 31 | 14 | 24 | 69
| 44.93 | 20.29 | 34.78 |
| 40.26 | 28.00 | 34.29 |
-------------+--------+--------+--------+
30+ | 29 | 18 | 21 | 68
| 42.65 | 26.47 | 30.88 |
| 37.66 | 36.00 | 30.00 |
-------------+--------+--------+--------+
Total 77 50 70 197
Statistics for Table of agegrp by ses
Statistic DF Value Prob
------------------------------------------------------
Chi-Square 4 4.8988 0.2978
Likelihood Ratio Chi-Square 4 5.0638 0.2808
Mantel-Haenszel Chi-Square 1 2.5837 0.1080
Phi Coefficient 0.1577
Contingency Coefficient 0.1558
Cramer's V 0.1115
Sample Size = 197
Table of agegrp by sector
agegrp sector(Area of City)
Frequency |
Row Pct |
Col Pct | 1| 2| Total
-------------+--------+--------+
12 and under | 40 | 20 | 60
| 66.67 | 33.33 |
| 33.90 | 25.32 |
-------------+--------+--------+
13-29 | 43 | 26 | 69
| 62.32 | 37.68 |
| 36.44 | 32.91 |
-------------+--------+--------+
30+ | 35 | 33 | 68
| 51.47 | 48.53 |
| 29.66 | 41.77 |
-------------+--------+--------+
Total 118 79 197
Statistics for Table of agegrp by sector
Statistic DF Value Prob
------------------------------------------------------
Chi-Square 2 3.3233 0.1898
Likelihood Ratio Chi-Square 2 3.3146 0.1907
Mantel-Haenszel Chi-Square 1 3.1106 0.0778
Phi Coefficient 0.1299
Contingency Coefficient 0.1288
Cramer's V 0.1299
Sample Size = 197
Table of agegrp by gotfever
agegrp gotfever
Frequency |
Row Pct |
Col Pct |No |Yes | Total
-------------+--------+--------+
12 and under | 54 | 6 | 60
| 90.00 | 10.00 |
| 38.85 | 10.34 |
-------------+--------+--------+
13-29 | 45 | 24 | 69
| 65.22 | 34.78 |
| 32.37 | 41.38 |
-------------+--------+--------+
30+ | 40 | 28 | 68
| 58.82 | 41.18 |
| 28.78 | 48.28 |
-------------+--------+--------+
Total 139 58 197
Statistics for Table of agegrp by gotfever
Statistic DF Value Prob
------------------------------------------------------
Chi-Square 2 16.3723 0.0003
Likelihood Ratio Chi-Square 2 18.4774 <.0001
Mantel-Haenszel Chi-Square 1 14.4765 0.0001
Phi Coefficient 0.2883
Contingency Coefficient 0.2770
Cramer's V 0.2883
Sample Size = 197
Table of ses by sector
ses(Socioeconomic Status)
sector(Area of City)
Frequency|
Row Pct |
Col Pct | 1| 2| Total
---------+--------+--------+
High | 38 | 39 | 77
| 49.35 | 50.65 |
| 32.20 | 49.37 |
---------+--------+--------+
Middle | 27 | 23 | 50
| 54.00 | 46.00 |
| 22.88 | 29.11 |
---------+--------+--------+
Low | 53 | 17 | 70
| 75.71 | 24.29 |
| 44.92 | 21.52 |
---------+--------+--------+
Total 118 79 197
Statistics for Table of ses by sector
Statistic DF Value Prob
------------------------------------------------------
Chi-Square 2 11.5803 0.0031
Likelihood Ratio Chi-Square 2 11.9927 0.0025
Mantel-Haenszel Chi-Square 1 10.3971 0.0013
Phi Coefficient 0.2425
Contingency Coefficient 0.2356
Cramer's V 0.2425
Sample Size = 197
Table of ses by gotfever
ses(Socioeconomic Status)
gotfever
Frequency|
Row Pct |
Col Pct |No |Yes | Total
---------+--------+--------+
High | 53 | 24 | 77
| 68.83 | 31.17 |
| 38.13 | 41.38 |
---------+--------+--------+
Middle | 35 | 15 | 50
| 70.00 | 30.00 |
| 25.18 | 25.86 |
---------+--------+--------+
Low | 51 | 19 | 70
| 72.86 | 27.14 |
| 36.69 | 32.76 |
---------+--------+--------+
Total 139 58 197
Statistics for Table of ses by gotfever
Statistic DF Value Prob
------------------------------------------------------
Chi-Square 2 0.2961 0.8624
Likelihood Ratio Chi-Square 2 0.2977 0.8617
Mantel-Haenszel Chi-Square 1 0.2819 0.5954
Phi Coefficient 0.0388
Contingency Coefficient 0.0387
Cramer's V 0.0388
Sample Size = 197
Table of sector by gotfever
sector(Area of City)
gotfever
Frequency|
Row Pct |
Col Pct |No |Yes | Total
---------+--------+--------+
1 | 95 | 23 | 118
| 80.51 | 19.49 |
| 68.35 | 39.66 |
---------+--------+--------+
2 | 44 | 35 | 79
| 55.70 | 44.30 |
| 31.65 | 60.34 |
---------+--------+--------+
Total 139 58 197
Statistics for Table of sector by gotfever
Statistic DF Value Prob
------------------------------------------------------
Chi-Square 1 14.0238 0.0002
Likelihood Ratio Chi-Square 1 13.8852 0.0002
Continuity Adj. Chi-Square 1 12.8548 0.0003
Mantel-Haenszel Chi-Square 1 13.9526 0.0002
Phi Coefficient 0.2668
Contingency Coefficient 0.2578
Cramer's V 0.2668
Fisher's Exact Test
----------------------------------
Cell (1,1) Frequency (F) 95
Left-sided Pr <= F 0.9999
Right-sided Pr >= F 1.797E-04
Table Probability (P) 1.290E-04
Two-sided Pr <= P 2.360E-04
Sample Size = 197
_______________________________________________________________________________
Log-linear on Dengue fever data 3
Model with just selected 2-way relationships
11:00 Monday, November 22, 2004
The CATMOD Procedure
Data Summary
Response agegrp*ses*sector*gotfev Response Levels 36
Weight Variable None Populations 1
Data Set MEXICO Total Frequency 197
Frequency Missing 0 Observations 197
Maximum Likelihood Analysis
Sub -2 Log Convergence Parameter Estimates
Iteration Iteration Likelihood Criterion 1 2 3
------------------------------------------------------------------------------
0 0 1411.9065 1.0000 0 0 0
1 0 1327.4244 0.0598 -0.0863 0.0508 0.4112
2 0 1318.7325 0.006548 -0.3476 0.1630 0.4727
3 0 1318.5067 0.000171 -0.4024 0.1921 0.5028
4 0 1318.5055 9.7208E-7 -0.4074 0.1946 0.5052
5 0 1318.5055 4.623E-11 -0.4074 0.1946 0.5052
Maximum Likelihood Analysis
Parameter Estimates
Iteration 4 5 6 7 8 9
---------------------------------------------------------------------------
0 0 0 0 0 0 0
1 0.3198 -0.0914 0.1726 -0.2386 0.1980 -0.2132
2 0.5100 -0.1859 0.2308 -0.2080 0.0946 -0.2315
3 0.5632 -0.2136 0.2280 -0.2070 0.0988 -0.2249
4 0.5682 -0.2161 0.2279 -0.2070 0.0987 -0.2249
5 0.5682 -0.2161 0.2279 -0.2070 0.0987 -0.2249
Maximum Likelihood Analysis
Parameter Estimates
Iteration 10 11
---------------------------------
0 0 0
1 -0.1371 0.3198
2 -0.1343 0.2950
3 -0.1317 0.2974
4 -0.1317 0.2974
5 -0.1317 0.2974
Maximum likelihood computations converged.
Maximum Likelihood Analysis of Variance
Source DF Chi-Square Pr > ChiSq
--------------------------------------------------
agegrp 2 6.92 0.0314
gotfever 1 28.12 <.0001
agegrp*gotfever 2 14.08 0.0009
ses 2 5.94 0.0514
sector 1 1.37 0.2424
ses*sector 2 11.13 0.0038
sector*gotfever 1 13.44 0.0002
Likelihood Ratio 24 10.18 0.9938
_______________________________________________________________________________
Log-linear on Dengue fever data 4
Saturated model 11:00 Monday, November 22, 2004
The CATMOD Procedure
Data Summary
Response agegrp*ses*sector*gotfev Response Levels 36
Weight Variable None Populations 1
Data Set MEXICO Total Frequency 197
Frequency Missing 0 Observations 197
Maximum Likelihood Analysis
Sub -2 Log Convergence Parameter Estimates
Iteration Iteration Likelihood Criterion 1 2 3
------------------------------------------------------------------------------
0 0 1411.9065 1.0000 0 0 0
1 0 1333.0577 0.0558 -0.0863 0.0508 0.1726
2 0 1309.1189 0.0180 -0.2863 0.1403 0.2158
3 0 1308.3283 0.000604 -0.3299 0.1690 0.2239
4 0 1308.3252 2.4154E-6 -0.3312 0.1697 0.2244
5 0 1308.3252 7.295E-11 -0.3312 0.1697 0.2244
Maximum Likelihood Analysis
Parameter Estimates
Iteration 4 5 6 7 8 9
---------------------------------------------------------------------------
0 0 0 0 0 0 0
1 -0.2386 -0.3096 0.1472 0.1929 -0.1726 0.1980
2 -0.2401 -0.2834 0.1956 0.1625 -0.2084 0.1289
3 -0.2426 -0.2764 0.2166 0.1486 -0.1989 0.1243
4 -0.2424 -0.2758 0.2173 0.1483 -0.1994 0.1238
5 -0.2424 -0.2758 0.2174 0.1483 -0.1994 0.1238
Maximum Likelihood Analysis
Parameter Estimates
Iteration 10 11 12 13 14 15
---------------------------------------------------------------------------
0 0 0 0 0 0 0
1 0.1066 0.0609 -0.2132 -0.1371 0.0457 0.0152
2 0.0597 0.0852 -0.2166 -0.1388 0.1186 0.0639
3 0.0601 0.0895 -0.2022 -0.1393 0.1193 0.0828
4 0.0593 0.0900 -0.2019 -0.1390 0.1201 0.0836
5 0.0593 0.0900 -0.2019 -0.1390 0.1202 0.0836
Maximum Likelihood Analysis
Parameter Estimates
Iteration 16 17 18 19 20 21
---------------------------------------------------------------------------
0 0 0 0 0 0 0
1 3.984E-17 0.0609 0.4112 0.3198 -0.0914 0.0305
2 -0.1017 0.1447 0.4955 0.5278 -0.2379 0.0378
3 -0.1017 0.1371 0.5089 0.5398 -0.2471 0.0382
4 -0.1023 0.1371 0.5089 0.5397 -0.2472 0.0386
5 -0.1023 0.1371 0.5089 0.5397 -0.2472 0.0386
Maximum Likelihood Analysis
Parameter Estimates
Iteration 22 23 24 25 26 27
---------------------------------------------------------------------------
0 0 0 0 0 0 0
1 -0.1066 -0.1675 0.0152 0.1523 -0.0305 0.3198
2 0.001349 -0.1054 -0.0458 0.0993 -0.0390 0.2948
3 0.004996 -0.0907 -0.0311 0.1001 -0.0551 0.2960
4 0.005608 -0.0900 -0.0306 0.0997 -0.0555 0.2956
5 0.005609 -0.0899 -0.0306 0.0997 -0.0555 0.2956
Maximum Likelihood Analysis
Parameter Estimates
Iteration 28 29 30 31 32 33
---------------------------------------------------------------------------
0 0 0 0 0 0 0
1 -0.0152 2.456E-17 -0.0305 -0.0457 -0.1371 -0.0761
2 -0.1062 0.0139 -0.0526 0.0783 -0.0454 -0.1532
3 -0.1116 0.0109 -0.0497 0.0804 -0.0332 -0.1368
4 -0.1125 0.0114 -0.0494 0.0811 -0.0323 -0.1365
5 -0.1125 0.0114 -0.0494 0.0811 -0.0323 -0.1365
Maximum Likelihood Analysis
Parameter Estimates
Iteration 34 35
---------------------------------
0 0 0
1 0.1218 3.655E-17
2 0.0797 0.0450
3 0.0760 0.0267
4 0.0756 0.0265
5 0.0756 0.0265
Maximum likelihood computations converged.
Maximum Likelihood Analysis of Variance
Source DF Chi-Square Pr > ChiSq
----------------------------------------------------------
agegrp 2 4.23 0.1205
ses 2 3.52 0.1724
agegrp*ses 4 2.02 0.7325
sector 1 1.50 0.2206
agegrp*sector 2 1.40 0.4966
ses*sector 2 6.03 0.0490
agegrp*ses*sector 4 2.06 0.7253
gotfever 1 25.36 <.0001
agegrp*gotfever 2 11.25 0.0036
ses*gotfever 2 0.12 0.9394
agegrp*ses*gotfever 4 0.54 0.9695
sector*gotfever 1 8.56 0.0034
agegrp*sector*gotfever 2 0.66 0.7201
ses*sector*gotfever 2 0.30 0.8598
agegrp*ses*sector*gotfev 4 0.81 0.9375
Likelihood Ratio 0 . .
_______________________________________________________________________________
Log-linear on Dengue fever data 5
Reproduce Goodness of fit LR Chisquare = 10.18 with 24 df
11:00 Monday, November 22, 2004
G PVAL
G = 10.1803 , df = 24, p = 0.9937627
_______________________________________________________________________________
Log-linear on Dengue fever data 6
Reduced model for testing agegrp by gotfever
11:00 Monday, November 22, 2004
The CATMOD Procedure
Data Summary
Response agegrp*ses*sector*gotfev Response Levels 36
Weight Variable None Populations 1
Data Set MEXICO Total Frequency 197
Frequency Missing 0 Observations 197
Maximum Likelihood Analysis
Sub -2 Log Convergence Parameter Estimates
Iteration Iteration Likelihood Criterion 1 2 3
------------------------------------------------------------------------------
0 0 1411.9065 1.0000 0 0 0
1 0 1340.6702 0.0505 -0.0863 0.0508 0.1726
2 0 1336.9981 0.002739 -0.0883 0.0515 0.2309
3 0 1336.9829 0.0000113 -0.0883 0.0515 0.2279
4 0 1336.9829 1.67E-10 -0.0883 0.0515 0.2279
Maximum Likelihood Analysis
Parameter Estimates
Iteration 4 5 6 7 8 9
---------------------------------------------------------------------------
0 0 0 0 0 0 0
1 -0.2386 0.1980 -0.2132 -0.1371 0.4112 0.3198
2 -0.2080 0.0943 -0.2317 -0.1343 0.4145 0.2963
3 -0.2070 0.0987 -0.2249 -0.1317 0.4118 0.2974
4 -0.2070 0.0987 -0.2249 -0.1317 0.4118 0.2974
Maximum likelihood computations converged.
Maximum Likelihood Analysis of Variance
Source DF Chi-Square Pr > ChiSq
--------------------------------------------------
agegrp 2 0.74 0.6907
ses 2 5.94 0.0514
sector 1 1.37 0.2424
ses*sector 2 11.13 0.0038
gotfever 1 25.77 <.0001
sector*gotfever 1 13.44 0.0002
Likelihood Ratio 26 28.66 0.3269
_______________________________________________________________________________
Log-linear on Dengue fever data 7
LR Chisquare for agegrp by gotfever. Compare Wald chisq = 14.08
11:00 Monday, November 22, 2004
G PVAL
G = 18.4774 , df = 2, p = 0.0000972
/**************************** deathpen2.sas *********************************/
options linesize=79 pagesize=35 noovp formdlim='_';
title 'Race & Death Penalty: Am. Soc. Review 1981, 46, 918-927';
title2 'Log-linear analysis with sampling zeros';
data deathrow;
input deathp $ victrace $ defrace $ numbr;
label defrace = 'Race of Defendant'
victrace = 'Race of Victim'
deathp = 'Death Penalty';
if numbr=0 then numbr=1.0E-20; /* That's the zero cell freq */
/* proc catmod assumes all zeros are structural */
datalines;
Yes White White 19
Yes White Black 11
Yes Black Black 6
Yes Black White 0
No White White 132
No White Black 52
No Black White 9
No Black Black 97
;
proc catmod;
title3 'Test any association among vars with goodness of fit test';
model deathp*victrace*defrace=_response_
/ nodesign noprofile noresponse noparm;
loglin deathp victrace defrace;
weight numbr;
proc catmod;
title3 'Model with all 2-way relationships';
model deathp*victrace*defrace=_response_
/ nodesign noprofile noresponse noparm;
loglin deathp|victrace deathp|defrace victrace|defrace;
weight numbr;
/* Now test each relationship in turn. Start with deathp|defrace */
proc catmod;
title3 'Test deathp by defrace';
model deathp*victrace*defrace=_response_
/ nodesign noprofile noresponse noparm;
loglin deathp|victrace victrace|defrace;
weight numbr;
proc iml;
title2 'LR Chisquare for deathp by defrace';
G = 961.76247 - 960.58132; pval = 1-probchi(G,1);
print "G = " G ", df = 1, p = " pval;
/* Now I'd use this as a new full model and test the other two relationships.*/
_______________________________________________________________________________
Race & Death Penalty: Am. Soc. Review 1981, 46, 918-927 1
Log-linear analysis with sampling zeros
Test any association among vars with goodness of fit test
22:02 Sunday, November 21, 2004
The CATMOD Procedure
Data Summary
Response deathp*victrace*defrace Response Levels 8
Weight Variable numbr Populations 1
Data Set DEATHROW Total Frequency 326
Frequency Missing 0 Observations 8
Maximum Likelihood Analysis
Sub -2 Log Convergence Parameter Estimates
Iteration Iteration Likelihood Criterion 1 2 3
------------------------------------------------------------------------------
0 0 1355.7959 1.0000 0 0 0
1 0 1108.0806 0.1827 0.7791 -0.3129 0.0184
2 0 1098.0538 0.009049 1.0000 -0.3237 0.0184
3 0 1097.8102 0.000222 1.0418 -0.3237 0.0184
4 0 1097.8099 2.2821E-7 1.0432 -0.3237 0.0184
5 0 1097.8099 2.699E-13 1.0432 -0.3237 0.0184
Maximum likelihood computations converged.
_______________________________________________________________________________
Race & Death Penalty: Am. Soc. Review 1981, 46, 918-927 2
Log-linear analysis with sampling zeros
Test any association among vars with goodness of fit test
22:02 Sunday, November 21, 2004
The CATMOD Procedure
Maximum Likelihood Analysis of Variance
Source DF Chi-Square Pr > ChiSq
--------------------------------------------------
deathp 1 139.40 <.0001
victrace 1 30.82 <.0001
defrace 1 0.11 0.7397
Likelihood Ratio 4 137.93 <.0001
_______________________________________________________________________________
Race & Death Penalty: Am. Soc. Review 1981, 46, 918-927 3
Log-linear analysis with sampling zeros
Model with all 2-way relationships
22:02 Sunday, November 21, 2004
The CATMOD Procedure
Data Summary
Response deathp*victrace*defrace Response Levels 8
Weight Variable numbr Populations 1
Data Set DEATHROW Total Frequency 326
Frequency Missing 0 Observations 8
Maximum Likelihood Analysis
Sub -2 Log Convergence
Iteration Iteration Likelihood Criterion
-------------------------------------------------
0 0 1355.7959 1.0000
1 0 1007.3817 0.2570
2 0 966.58695 0.0405
3 0 960.82256 0.005964
4 0 960.58234 0.000250
5 0 960.58132 1.0681E-6
6 0 960.58132 3.562E-11
Maximum Likelihood Analysis
Parameter Estimates
Iteration 1 2 3 4 5 6
---------------------------------------------------------------------------
0 0 0 0 0 0 0
1 0.7791 -0.3129 -0.1656 0.0184 0.0307 0.5583
_______________________________________________________________________________
Race & Death Penalty: Am. Soc. Review 1981, 46, 918-927 4
Log-linear analysis with sampling zeros
Model with all 2-way relationships
22:02 Sunday, November 21, 2004
The CATMOD Procedure
Maximum Likelihood Analysis
Parameter Estimates
Iteration 1 2 3 4 5 6
---------------------------------------------------------------------------
2 1.0319 -0.5367 0.1184 0.2993 0.0163 0.7490
3 1.1522 -0.7969 0.2911 0.4564 -0.1057 0.8166
4 1.1968 -0.8500 0.3278 0.4784 -0.1098 0.8387
5 1.2000 -0.8540 0.3310 0.4794 -0.1101 0.8395
6 1.2001 -0.8540 0.3311 0.4794 -0.1101 0.8395
Maximum likelihood computations converged.
Maximum Likelihood Analysis of Variance
Source DF Chi-Square Pr > ChiSq
--------------------------------------------------
deathp 1 100.06 <.0001
victrace 1 33.83 <.0001
deathp*victrace 1 6.50 0.0108
defrace 1 14.87 0.0001
deathp*defrace 1 1.21 0.2722
victrace*defrace 1 77.29 <.0001
Likelihood Ratio 1 0.70 0.4025
_______________________________________________________________________________
Race & Death Penalty: Am. Soc. Review 1981, 46, 918-927 5
Log-linear analysis with sampling zeros
Test deathp by defrace
22:02 Sunday, November 21, 2004
The CATMOD Procedure
Data Summary
Response deathp*victrace*defrace Response Levels 8
Weight Variable numbr Populations 1
Data Set DEATHROW Total Frequency 326
Frequency Missing 0 Observations 8
Maximum Likelihood Analysis
Sub -2 Log Convergence
Iteration Iteration Likelihood Criterion
---------------------------------------------------
0 0 1355.7959 1.0000
1 0 1011.0092 0.2543
2 0 966.42214 0.0441
3 0 961.92902 0.004649
4 0 961.76311 0.000172
5 0 961.76247 6.6622E-7
6 0 961.76247 1.515E-11
Maximum Likelihood Analysis
Parameter Estimates
Iteration 1 2 3 4 5
--------------------------------------------------------------------------
0 0 0 0 0 0
1 0.7791 -0.3129 -0.1656 0.0184 0.5583
_______________________________________________________________________________
Race & Death Penalty: Am. Soc. Review 1981, 46, 918-927 6
Log-linear analysis with sampling zeros
Test deathp by defrace
22:02 Sunday, November 21, 2004
The CATMOD Procedure
Maximum Likelihood Analysis
Parameter Estimates
Iteration 1 2 3 4 5
--------------------------------------------------------------------------
2 1.0385 -0.5414 0.1306 0.3155 0.7534
3 1.1347 -0.7481 0.2279 0.3760 0.8130
4 1.1688 -0.7956 0.2620 0.3904 0.8274
5 1.1713 -0.7986 0.2645 0.3908 0.8279
6 1.1714 -0.7986 0.2645 0.3908 0.8279
Maximum likelihood computations converged.
Maximum Likelihood Analysis of Variance
Source DF Chi-Square Pr > ChiSq
--------------------------------------------------
deathp 1 102.17 <.0001
victrace 1 33.59 <.0001
deathp*victrace 1 5.21 0.0225
defrace 1 17.05 <.0001
victrace*defrace 1 76.52 <.0001
Likelihood Ratio 2 1.88 0.3903
_______________________________________________________________________________
Race & Death Penalty: Am. Soc. Review 1981, 46, 918-927 7
LR Chisquare for deathp by defrace
22:02 Sunday, November 21, 2004
G PVAL
G = 1.18115 , df = 1, p = 0.277122