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Page 447 Table 17.1
data depress; set "c:\cama4\depress"; inccat = 0; if income ge 20 then inccat = 1; run; proc freq data = depress; tables sex*inccat / norow nocol nopercent; run;
The FREQ Procedure
Table of SEX by inccat
SEX inccat
Frequency| 0| 1| Total
---------+--------+--------+
1 | 54 | 57 | 111
---------+--------+--------+
2 | 125 | 58 | 183
---------+--------+--------+
Total 179 115 294
Page 448 Table 17.2
NOTE: You can also use proc tabulate to create this table.
data depress; set depress; cesdcat = 0; if cesd ge 11 then cesdcat = 1; run; proc freq data = depress; tables sex *inccat* treat / norow nocol nopercent; run;
The FREQ Procedure
Table 1 of inccat by TREAT
Controlling for SEX=1
inccat TREAT
Frequency| 1| 2| Total
---------+--------+--------+
0 | 20 | 34 | 54
---------+--------+--------+
1 | 21 | 36 | 57
---------+--------+--------+
Total 41 70 111
Table 2 of inccat by TREAT
Controlling for SEX=2
inccat TREAT
Frequency| 1| 2| Total
---------+--------+--------+
0 | 73 | 52 | 125
---------+--------+--------+
1 | 34 | 24 | 58
---------+--------+--------+
Total 107 76 183
Page 449 Table 17.3
proc freq data = depress; tables sex *inccat* cesdcat* treat / norow nocol nopercent; run;
The FREQ Procedure
Table 1 of cesdcat by TREAT
Controlling for SEX=1 inccat=0
cesdcat TREAT
Frequency| 1| 2| Total
---------+--------+--------+
0 | 16 | 23 | 39
---------+--------+--------+
1 | 4 | 11 | 15
---------+--------+--------+
Total 20 34 54
Table 2 of cesdcat by TREAT
Controlling for SEX=1 inccat=1
cesdcat TREAT
Frequency| 1| 2| Total
---------+--------+--------+
0 | 16 | 30 | 46
---------+--------+--------+
1 | 5 | 6 | 11
---------+--------+--------+
Total 21 36 57
Table 3 of cesdcat by TREAT
Controlling for SEX=2 inccat=0
cesdcat TREAT
Frequency| 1| 2| Total
---------+--------+--------+
0 | 48 | 33 | 81
---------+--------+--------+
1 | 25 | 19 | 44
---------+--------+--------+
Total 73 52 125
Table 4 of cesdcat by TREAT
Controlling for SEX=2 inccat=1
cesdcat TREAT
Frequency| 1| 2| Total
---------+--------+--------+
0 | 20 | 20 | 40
---------+--------+--------+
1 | 14 | 4 | 18
---------+--------+--------+
Total 34 24 58
Page 451 middle of the page
proc freq data = depress; tables sex*inccat / norow nocol nopercent expected; run;
The FREQ Procedure
Table of SEX by inccat
SEX inccat
Frequency|
Expected | 0| 1| Total
---------+--------+--------+
1 | 54 | 57 | 111
| 67.582 | 43.418 |
---------+--------+--------+
2 | 125 | 58 | 183
| 111.42 | 71.582 |
---------+--------+--------+
Total 179 115 294
Page 454 top of the page
proc freq data = depress; tables sex*inccat / norow nocol nopercent chisq; run;
The FREQ Procedure
Table of SEX by inccat
SEX inccat
Frequency| 0| 1| Total
---------+--------+--------+
1 | 54 | 57 | 111
---------+--------+--------+
2 | 125 | 58 | 183
---------+--------+--------+
Total 179 115 294
Statistics for Table of SEX by inccat
Statistic DF Value Prob
------------------------------------------------------
Chi-Square 1 11.2104 0.0008
Likelihood Ratio Chi-Square 1 11.1467 0.0008
Continuity Adj. Chi-Square 1 10.4002 0.0013
Mantel-Haenszel Chi-Square 1 11.1723 0.0008
Phi Coefficient -0.1953
Contingency Coefficient 0.1917
Cramer's V -0.1953
Fisher's Exact Test
----------------------------------
Cell (1,1) Frequency (F) 54
Left-sided Pr <= F 6.489E-04
Right-sided Pr >= F 0.9997
Table Probability (P) 3.813E-04
Two-sided Pr <= P 9.068E-04
Sample Size = 294
Page 455 Table 17.7
proc freq data = depress; tables sex*inccat /out=page420 norow nocol nopercent; run; data page420a; set page420; if sex = 1 then sex1 = -1; if sex = 2 then sex1 = 1; if inccat = 0 then inccat1 = -1; if inccat = 1 then inccat1 = 1; run; proc genmod data = page420a; model count= sex1 inccat1 sex1*inccat1 /d=poisson; run; quit;
The GENMOD Procedure
Model Information
Data Set WORK.PAGE420A
Distribution Poisson
Link Function Log
Dependent Variable COUNT
Observations Used 4
Criteria For Assessing Goodness Of Fit
Criterion DF Value Value/DF
Deviance 0 0.0000 .
Scaled Deviance 0 0.0000 .
Pearson Chi-Square 0 0.0000 .
Scaled Pearson X2 0 0.0000 .
Log Likelihood 990.9040
Algorithm converged.
Analysis Of Parameter Estimates
Standard Wald 95% Confidence Chi-
Parameter DF Estimate Error Limits Square Pr > ChiSq
Intercept 1 4.2302 0.0619 4.1089 4.3515 4670.40 <.0001
sex1 1 0.2142 0.0619 0.0929 0.3355 11.97 0.0005
inccat1 1 -0.1785 0.0619 -0.2998 -0.0571 8.31 0.0039
sex1*inccat1 1 -0.2055 0.0619 -0.3268 -0.0842 11.02 0.0009
Scale 0 1.0000 0.0000 1.0000 1.0000
NOTE: The scale parameter was held fixed.
Page 460 in the middle
ods listing close;
proc genmod data = tab427;
class sex inccat treat;
model count = sex|inccat|treat/ d = poisson ;
ods output modelfit = temp1;
run;
proc genmod data = tab427;
class sex inccat treat;
model count = sex|inccat|treat@1/ d = poisson ;
ods output modelfit = temp2;
run;
proc genmod data = tab427;
class sex inccat treat;
model count = sex|inccat|treat@2/ d = poisson ;
ods output modelfit = temp3;
run;
proc genmod data = tab427;
class sex inccat treat;
model count = sex|inccat|treat@1 sex*inccat/ d = poisson ;
ods output modelfit = temp4;
run;
proc genmod data = tab427;
class sex inccat treat;
model count = sex|inccat|treat@1 sex*inccat sex*treat/ d = poisson ;
ods output modelfit = temp5;
run;
ods listing;
data modelfit;
set temp1 temp2 temp3 temp4 temp5;
mydf = lag(df);
if Criterion="Log Likelihood";
keep mydf value ;
run;
data modelfit;
set modelfit;
retain full_ll;
retain full_df;
if _n_ = 1 then do;
full_ll= value;
full_df = mydf;
end;
diff_ll = 2*(full_ll - value);
diff_df = mydf - full_df;
pvalue = 1 - probchi(diff_ll, diff_df);
keep value diff_ll diff_df pvalue;
run;
proc print data = modelfit;
run;
Obs Value diff_ll diff_df pvalue 1 589.8050 0.0000 0 . 2 577.7669 24.0763 4 0.00008 3 589.8045 0.0012 1 0.97262 4 583.3402 12.9296 3 0.00479 5 589.8044 0.0012 2 0.99938
Page 461 table in the middle of the page
ods listing close; proc freq data = depress; tables sex*inccat*treat /list out=tab427; run; proc genmod data = tab427; class sex inccat treat; model count = / d = poisson ; ods output modelfit = temp1; run; * all main effect terms; proc genmod data= tab427; class sex inccat treat; model count = sex inccat treat / d=poisson; ods output modelfit = temp2; run; /*row number 2 is comparing the model below with the model above*/ * all two-way interactions; proc genmod data= tab427; class sex inccat treat; model count = sex|inccat|treat@2 / d=poisson; ods output modelfit = temp3; run; /*row number 3 is comparing the model below with the model above*/ * all terms included; proc genmod data= tab427; class sex inccat treat; model count = sex|inccat|treat@3 / d=poisson; ods output modelfit = temp4; run; data modelcom; set temp1 temp2 temp3 temp4; mydf = lag(df); if Criterion="Log Likelihood" or criterion = "Pearson Chi-Square"; keep criterion mydf value myvalue; run; proc sort data = modelcom; by criterion; run; data modelcom1; set modelcom; if criterion = "Log Likelihood" then do; lagvalue=lag(value); lagdf = lag(mydf); chisq = 2*(value-lagvalue); df = lagdf - mydf ; pvalue = 1-probchi(chisq, df); end; else do ; lagvalue=lag(value); lagdf = lag(mydf); chisq = lagvalue - value; df = lagdf - mydf ; pvalue = 1-probchi(chisq, df); end; keep df chisq pvalue; if chisq ~=.; run; ods listing; proc print data = modelcom1; run;
Obs chisq df pvalue 1 31.8710 3 0.00000 2 24.0752 3 0.00002 3 0.0012 1 0.97262 4 36.6679 3 0.00000 5 24.6507 3 0.00002 6 0.0012 1 0.97262
Page 462
Partial association
ods listing close;
proc genmod data= tab427;
class sex inccat treat;
model count = sex|inccat|treat@2 / d=poisson;
ods output modelfit = temp1;
run;
/*this model gives loglikelihood of 584.4699 with df of 10*/
proc genmod data= tab427;
class sex inccat treat;
model count = inccat|treat sex|treat / d=poisson;
ods output modelfit = temp2;
run;
/*this model gives loglikelihood of 589.8044 with df of 10*/
proc genmod data= tab427;
class sex inccat treat;
model count = sex|inccat sex|treat / d=poisson;
ods output modelfit = temp3;
run;
/*this model gives loglikelihood of 583.5791 with df of 10*/
proc genmod data= tab427;
class sex inccat treat;
model count = sex|inccat inccat|treat / d=poisson;
ods output modelfit = temp4;
run;
proc print data = temp1;
run;
ods listing;
data pg428;
set temp1 temp2 temp3 temp4;
mydf = lag(df);
if criterion = "Log Likelihood";
keep value mydf;
run;
data page428;
set pg428;
retain whole wholedf;
if _n_ = 1 then do;
whole = value;
wholedf = mydf;
end;
else do;
chisq = 2*(whole - value);
df = mydf - wholedf;
pvalue = 1 -probchi(chisq , df);
end;
keep df chisq pvalue;
if chisq ~=.;
run;
proc print data = page428;
run;
Obs chisq df pvalue 1 10.6691 1 0.00109 2 0.0001 1 0.99336 3 12.4508 1 0.00042
Marginal association
NOTE: Look at the Likelihood ratio chi-squares
proc freq data = tab427; weight count; tables sex*inccat /chisq; tables sex*treat /chisq; tables inccat*treat /chisq; run;
The FREQ Procedure
Table of SEX by inccat
SEX inccat
Frequency|
Percent |
Row Pct |
Col Pct | 0| 1| Total
---------+--------+--------+
1 | 54 | 57 | 111
| 18.37 | 19.39 | 37.76
| 48.65 | 51.35 |
| 30.17 | 49.57 |
---------+--------+--------+
2 | 125 | 58 | 183
| 42.52 | 19.73 | 62.24
| 68.31 | 31.69 |
| 69.83 | 50.43 |
---------+--------+--------+
Total 179 115 294
60.88 39.12 100.00
Statistics for Table of SEX by inccat
Statistic DF Value Prob
------------------------------------------------------
Chi-Square 1 11.2104 0.0008
Likelihood Ratio Chi-Square 1 11.1467 0.0008
Continuity Adj. Chi-Square 1 10.4002 0.0013
Mantel-Haenszel Chi-Square 1 11.1723 0.0008
Phi Coefficient -0.1953
Contingency Coefficient 0.1917
Cramer's V -0.1953
Fisher's Exact Test
----------------------------------
Cell (1,1) Frequency (F) 54
Left-sided Pr <= F 6.489E-04
Right-sided Pr >= F 0.9997
Table Probability (P) 3.813E-04
Two-sided Pr <= P 9.068E-04
Sample Size = 294
The FREQ Procedure
Table of SEX by TREAT
SEX TREAT
Frequency|
Percent |
Row Pct |
Col Pct | 1| 2| Total
---------+--------+--------+
1 | 41 | 70 | 111
| 13.95 | 23.81 | 37.76
| 36.94 | 63.06 |
| 27.70 | 47.95 |
---------+--------+--------+
2 | 107 | 76 | 183
| 36.39 | 25.85 | 62.24
| 58.47 | 41.53 |
| 72.30 | 52.05 |
---------+--------+--------+
Total 148 146 294
50.34 49.66 100.00
Statistics for Table of SEX by TREAT
Statistic DF Value Prob
------------------------------------------------------
Chi-Square 1 12.8149 0.0003
Likelihood Ratio Chi-Square 1 12.9284 0.0003
Continuity Adj. Chi-Square 1 11.9680 0.0005
Mantel-Haenszel Chi-Square 1 12.7713 0.0004
Phi Coefficient -0.2088
Contingency Coefficient 0.2044
Cramer's V -0.2088
Fisher's Exact Test
----------------------------------
Cell (1,1) Frequency (F) 41
Left-sided Pr <= F 2.578E-04
Right-sided Pr >= F 0.9999
Table Probability (P) 1.568E-04
Two-sided Pr <= P 4.627E-04
Sample Size = 294
The FREQ Procedure
Table of inccat by TREAT
inccat TREAT
Frequency|
Percent |
Row Pct |
Col Pct | 1| 2| Total
---------+--------+--------+
0 | 93 | 86 | 179
| 31.63 | 29.25 | 60.88
| 51.96 | 48.04 |
| 62.84 | 58.90 |
---------+--------+--------+
1 | 55 | 60 | 115
| 18.71 | 20.41 | 39.12
| 47.83 | 52.17 |
| 37.16 | 41.10 |
---------+--------+--------+
Total 148 146 294
50.34 49.66 100.00
Statistics for Table of inccat by TREAT
Statistic DF Value Prob
------------------------------------------------------
Chi-Square 1 0.4776 0.4895
Likelihood Ratio Chi-Square 1 0.4777 0.4895
Continuity Adj. Chi-Square 1 0.3267 0.5676
Mantel-Haenszel Chi-Square 1 0.4759 0.4903
Phi Coefficient 0.0403
Contingency Coefficient 0.0403
Cramer's V 0.0403
Fisher's Exact Test
----------------------------------
Cell (1,1) Frequency (F) 93
Left-sided Pr <= F 0.7912
Right-sided Pr >= F 0.2838
Table Probability (P) 0.0750
Two-sided Pr <= P 0.5504
Sample Size = 294
Page 463 We were unable to reproduce the stepwise analysis using proc genmod.
Page 464
NOTE: The type1 option on the model statement gives us the first order terms and this is the model to compare against the three-way terms.
/*first order terms*/
proc genmod data = tab427;
class sex inccat treat cesdcat;
model count = sex inccat treat cesdcat sex|inccat|treat|cesdcat@3 / d = poisson link=log type1 ;
ods output modelfit = three;
run;
ods listing close;
/*term stc*/
proc genmod data = tab427;
class sex inccat treat cesdcat;
model count = sex|inccat|treat|cesdcat@2
sex*inccat*treat sex*inccat*cesdcat inccat*treat*cesdcat / d = poisson link=log ;
ods output modelfit = stc;
run;
/*term itc*/
proc genmod data = tab427;
class sex inccat treat cesdcat;
model count = sex|inccat|treat|cesdcat@2
sex*inccat*treat sex*inccat*cesdcat sex*treat*cesdcat / d = poisson link=log ;
ods output modelfit = itc;
run;
/*term isc*/
proc genmod data = tab427;
class sex inccat treat cesdcat;
model count = sex|inccat|treat|cesdcat@2
sex*inccat*treat inccat*treat*cesdcat sex*treat*cesdcat / d = poisson link=log ;
ods output modelfit = isc;
run;
/*term ist*/
proc genmod data = tab427;
class sex inccat treat cesdcat;
model count = sex|inccat|treat|cesdcat@2
inccat*sex*cesdcat inccat*treat*cesdcat sex*treat*cesdcat / d = poisson link=log;
ods output modelfit = ist;
run;
ods listing;
data threecom;
set three ist isc itc stc;
if Criterion="Deviance" ;
keep criterion df value ;
run;
data table430_part3;
set threecom;
retain a;
if _n_ =1 then a = Value;
else do;
lrchisq = value - a;
pvalue = 1-probchi(lrchisq, 1);
end;
keep lrchisq pvalue;
if _n_ >1;
run;
/*comparison model*/
ods listing close;
proc genmod data = tab427;
class sex inccat treat cesdcat;
model count = sex|inccat|treat|cesdcat@2 / d = poisson link=log ;
ods output modelfit = two;
run;
/*term si*/
proc genmod data = tab427;
class sex inccat treat cesdcat;
model count = sex inccat treat cesdcat
inccat*treat inccat*cesdcat
sex*treat sex*cesdcat treat*cesdcat / d = poisson link=log ;
ods output modelfit = si;
run;
/*term it*/
proc genmod data = tab427;
class sex inccat treat cesdcat;
model count = sex inccat treat cesdcat
sex*inccat inccat*cesdcat
sex*treat sex*cesdcat treat*cesdcat / d = poisson link=log ;
ods output modelfit = it;
run;
/*term ic*/
proc genmod data = tab427;
class sex inccat treat cesdcat;
model count = sex inccat treat cesdcat
sex*inccat inccat*treat
sex*treat sex*cesdcat treat*cesdcat / d = poisson link=log ;
ods output modelfit = ic;
run;
/*term st*/
proc genmod data = tab427;
class sex inccat treat cesdcat;
model count = sex inccat treat cesdcat
inccat*sex inccat*treat inccat*cesdcat
sex*cesdcat treat*cesdcat / d = poisson link=log ;
ods output modelfit = st;
run;
/*term sc*/
proc genmod data = tab427;
class sex inccat treat cesdcat;
model count = sex inccat treat cesdcat
inccat*sex inccat*treat inccat*cesdcat
sex*treat treat*cesdcat / d = poisson link=log ;
ods output modelfit = sc;
run;
/*term tc*/
proc genmod data = tab427;
class sex inccat treat cesdcat;
model count = sex inccat treat cesdcat
inccat*sex inccat*treat inccat*cesdcat
sex*treat sex*cesdcat / d = poisson link=log ;
ods output modelfit = tc;
run;
ods listing;
data twocom;
set two si it ic st sc tc;
if Criterion="Deviance" ;
keep criterion df value ;
run;
data table430_part2;
set twocom;
retain a;
if _n_ =1 then a = Value;
else do;
lrchisq = value - a;
pvalue = 1-probchi(lrchisq, 1);
end;
keep lrchisq pvalue;
if _n_ >1;
run;
proc print data = table430_part2;
run;
NOTE: This output gives the first four rows of the table.
<some output omitted>
LR Statistics For Type 1 Analysis
Chi-
Source Deviance DF Square Pr > ChiSq
Intercept 115.4069
SEX 97.5936 1 17.81 <.0001
inccat 83.5495 1 14.04 0.0002
TREAT 83.5358 1 0.01 0.9071
cesdcat 34.8139 1 48.72 <.0001
SEX*inccat 23.6672 1 11.15 0.0008
SEX*TREAT 10.7389 1 12.93 0.0003
inccat*TREAT 10.7388 1 0.00 0.9934
SEX*inccat*TREAT 10.7376 1 0.00 0.9726
SEX*cesdcat 7.0589 1 3.68 0.0551
inccat*cesdcat 5.8929 1 1.17 0.2802
SEX*inccat*cesdcat 5.6357 1 0.26 0.6120
TREAT*cesdcat 5.3193 1 0.32 0.5738
SEX*TREAT*cesdcat 4.7877 1 0.53 0.4659
inccat*TREAT*cesdcat 0.0452 1 4.74 0.0294
NOTE: The output below gives the rest of the table. It is the output from the two proc prints above. The ods listing close statements tell SAS not to print the output of the proc genmods.
Obs lrchisq pvalue 1 0.00830 0.92743 2 0.00995 0.92053 3 4.74251 0.02943 4 1.22709 0.26797 Obs lrchisq pvalue 1 9.9063 0.00165 2 0.0019 0.96527 3 1.1678 0.27986 4 11.9764 0.00054 5 2.3418 0.12595 6 0.3171 0.57333
Page 468 at the bottom
proc freq data= depress; tables sex*treat*inccat/list out=page435; run; data page435a; set page435; if sex = 1 then sex1= 1; if sex = 2 then sex1 = -1; if treat =1 then treat1 = 1; if treat = 2 then treat1 = -1; if inccat = 0 then inccat1 = -1; if inccat = 1 then inccat1 = 1; run; proc genmod data= page435a; model count = sex1 treat1 inccat1 sex1*treat1 sex1*inccat1 treat1*inccat1 /d = poisson; run;
The GENMOD Procedure
Model Information
Data Set WORK.PAGE435A
Distribution Poisson
Link Function Log
Dependent Variable COUNT
Observations Used 8
Criteria For Assessing Goodness Of Fit
Criterion DF Value Value/DF
Deviance 1 0.0012 0.0012
Scaled Deviance 1 0.0012 0.0012
Pearson Chi-Square 1 0.0012 0.0012
Scaled Pearson X2 1 0.0012 0.0012
Log Likelihood 793.5897
Algorithm converged.
Analysis Of Parameter Estimates
Standard Wald 95% Confidence Chi-
Parameter DF Estimate Error Limits Square Pr > ChiSq
Intercept 1 3.5121 0.0636 3.3875 3.6367 3051.83 <.0001
sex1 1 -0.2246 0.0636 -0.3491 -0.1000 12.48 0.0004
treat1 1 -0.0481 0.0627 -0.1711 0.0748 0.59 0.4431
inccat1 1 -0.1784 0.0620 -0.2999 -0.0570 8.29 0.0040
sex1*treat1 1 -0.2194 0.0630 -0.3429 -0.0958 12.11 0.0005
sex1*inccat1 1 0.2056 0.0633 0.0815 0.3297 10.54 0.0012
treat1*inccat1 1 0.0005 0.0623 -0.1217 0.1227 0.00 0.9934
Scale 0 1.0000 0.0000 1.0000 1.0000
NOTE: The scale parameter was held fixed.
Page 470 top of the page
data depress437; set depress; treat1 = treat -1; sex1 = sex - 1; run; proc logistic data = depress437 desc; model treat1 = inccat sex1; run;
The LOGISTIC Procedure
Analysis of Maximum Likelihood Estimates
Standard Wald
Parameter DF Estimate Error Chi-Square Pr > ChiSq
Intercept 1 0.5360 0.2347 5.2149 0.0224
inccat 1 -0.00208 0.2494 0.0001 0.9934
sex1 1 -0.8774 0.2522 12.1067 0.0005
Odds Ratio Estimates
Point 95% Wald
Effect Estimate Confidence Limits
inccat 0.998 0.612 1.627
sex1 0.416 0.254 0.682
Association of Predicted Probabilities and Observed Responses
Percent Concordant 34.7 Somers' D 0.202
Percent Discordant 14.4 Gamma 0.412
Percent Tied 50.9 Tau-a 0.102
Pairs 21608 c 0.601
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