You can specify the response in the form of a single variable or in the form of a ratio of two variables denoted events/trials.

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1 The GENMOD Procedure MODEL Statement MODEL response = < effects > < /options > ; MODEL events/trials = < effects > < /options > ; You can specify the response in the form of a single variable or in the form of a ratio of two variables denoted events/trials. 1. The first form is applicable to all responses (Table 4.1 (a)). 2. The second form is applicable only to summarized binomial response data (Table 4.1(b)). When each observation in the input data set contains the number of events (for example, successes) and the number of trials from a set of binomial trials, use the events/trials syntax. OPTIONS: DIST D ERROR ERR = keyword DIST= Distribution Default Link Function BINOMIAL BIN B binomial logit GAMMA GAM G gamma inverse ( power(-1) ) IGAUSSIAN IG inverse Gaussian inverse squared ( power(-2) ) MULTINOMIAL MULT multinomial cumulative logit NEGBIN NB negative binomial log NORMAL NOR N normal identity POISSON POI P Poisson log LINK = keyword LINK= CUMCLL CCLL CUMLOGIT CLOGIT CUMPROBIT CPROBIT CLOGLOG CLL IDENTITY ID Link Function cumulative complementary log-log cumulative logit cumulative probit complementary log-log identity 1

2 LOG log LOGIT logit PROBIT probit POWER(number) POW(number) power with = number DATA: Three types of beetles were exposed to different levels (dose) of a toxin. The outcome was survival status. data ldose; infile "G:\Documents\current_projects\Brown\GLM\Data\ldose.csv" firstobs=2 DSD dlm=','; input beetle ldose n y; dose = exp(ldose); run; proc print;run; proc genmod DESCENDING; class beetle / PARAM=REF REF=FIRST ; model y/n = beetle dose / dist=binomial link=logit covb TYPE1; /* lrci SCALE=PEARSON*/ contrast 'no difference between beetles' beetle 1 0, beetle 0 1/ WALD E; /* default is LR test */ contrast 'dose has no effect' dose 1 / E; contrast 'no difference between beetles, and dose has no effect' beetle 1 0, beetle 0 1, dose 1 / E; estimate 'beetle 2 at dose=6' intercept 1 beetle 1 0 dose 6/ E EXP; run; proc logistic; class beetle / PARAM=REF REF=FIRST ; model y/n= beetle dose/ COVB LINK=logit; contrast 'beetle 2 vs 3' beetle 1-1/E ESTIMATE=EXP; contrast 'beetle 1 at dose = 0' INTERCEPT 1 /E ESTIMATE=PARM; contrast 'beetle 2 at dose = 0' INTERCEPT 1 beetle 1 0 /E ESTIMATE=BOTH; run; 2

3 The SAS System 11:17 Thursday, November 6, Obs beetle ldose n y dose The SAS System 11:17 Thursday, November 6, The GENMOD Procedure Model Information Data Set Distribution Link Function Response Variable (Events) Response Variable (Trials) WORK.LDOSE Binomial Logit y n Number of Observations Read 24 Number of Observations Used 24 Number of Events 685 Number of Trials 1433 Class Level Information Design Class Value Variables beetle Parameter Information Parameter Effect beetle Prm1 Intercept Prm2 beetle 2 Prm3 beetle 3 Prm4 dose Criteria For Assessing Goodness Of Fit Criterion DF Value Value/DF 3

4 Deviance Scaled Deviance Pearson Chi-Square Scaled Pearson X Log Likelihood Algorithm converged. The SAS System 11:17 Thursday, November 6, The GENMOD Procedure Estimated Covariance Matrix Prm1 Prm2 Prm3 Prm4 Prm Prm Prm Prm Analysis Of Parameter Estimates Standard 95% Confidence Chi- Parameter DF Estimate Error Limits Square Pr > ChiSq Intercept <.0001 beetle beetle <.0001 dose <.0001 Scale NOTE: The scale parameter was held fixed. LR Statistics For Type 1 Analysis Chi- Source Deviance DF Square Pr > ChiSq Intercept beetle <.0001 dose <.0001 Coefficients for Contrast beetle 2 at dose=6 Label Prm1 Prm2 Prm3 Prm4 beetle 2 at dose= Contrast Estimate Results Standard Chi- Label Estimate Error Alpha Confidence Limits Square Pr > ChiSq beetle 2 at dose= Exp(beetle 2 at dose=6) The SAS System 11:17 Thursday, November 6, The GENMOD Procedure Coefficients for Contrast no difference between beetles Label Row Prm1 Prm2 Prm3 Prm4 no difference between beetles no difference between beetles

5 Coefficients for Contrast dose has no effect Label Row Prm1 Prm2 Prm3 Prm4 dose has no effect Coefficients for Contrast no difference between beetles, and dose has no effect Label Row Prm1 Prm2 Prm3 Prm4 no difference between beetles, and dose has no effect no difference between beetles, and dose has no effect no difference between beetles, and dose has no effect Contrast Results Chi- Contrast DF Square Pr > ChiSq Type no difference between beetles <.0001 dose has no effect <.0001 LR no difference between beetles, and dose has no effect <.0001 LR The SAS System 11:17 Thursday, November 6, Model Information Data Set Response Variable (Events) Response Variable (Trials) Model Optimization Technique WORK.LDOSE y n binary logit Fisher's scoring Number of Observations Read 24 Number of Observations Used 24 Sum of Frequencies Read 1433 Sum of Frequencies Used 1433 Response Profile Ordered Binary Total Value Outcome Frequency 1 Event Nonevent 748 Class Level Information Design Class Value Variables beetle Model Convergence Status Convergence criterion (GCONV=1E-8) satisfied. Model Fit Statistics 5

6 Intercept Intercept and Criterion Only Covariates AIC SC Log L The SAS System 11:17 Thursday, November 6, Testing Global Null Hypothesis: BETA=0 Test Chi-Square DF Pr > ChiSq Likelihood Ratio <.0001 Score < <.0001 Type 3 Analysis of Effects Effect DF Chi-Square Pr > ChiSq beetle <.0001 dose <.0001 Analysis of Maximum Likelihood Estimates Standard Parameter DF Estimate Error Chi-Square Pr > ChiSq Intercept <.0001 beetle beetle <.0001 dose <.0001 Odds Ratio Estimates Point 95% Effect Estimate Confidence Limits beetle 2 vs beetle 3 vs dose Association of Predicted Probabilities and Observed Responses Percent Concordant 86.5 Somers' D Percent Discordant 11.4 Gamma Percent Tied 2.2 Tau-a Pairs c The SAS System 11:17 Thursday, November 6, Estimated Covariance Matrix Parameter Intercept beetle2 beetle3 dose Intercept beetle beetle dose

7 Coefficients of Contrast beetle 2 vs 3 Parameter Row1 Intercept 0 beetle2 1 beetle3-1 dose 0 Coefficients of Contrast beetle 1 at dose = 0 Parameter Row1 Intercept 1 beetle2 0 beetle3 0 dose 0 Coefficients of Contrast beetle 2 at dose = 0 Parameter Row1 Intercept 1 beetle2 1 beetle3 0 dose 0 Contrast Test Results Contrast DF Chi-Square Pr > ChiSq beetle 2 vs <.0001 beetle 1 at dose = <.0001 beetle 2 at dose = <.0001 The SAS System 11:17 Thursday, November 6, Contrast Rows Estimation and Testing Results Standard Contrast Type Row Estimate Error Alpha Confidence Limits beetle 2 vs 3 EXP beetle 1 at dose = 0 PARM beetle 2 at dose = 0 PARM beetle 2 at dose = 0 EXP E E E E-11 Contrast Rows Estimation and Testing Results Contrast Type Row Chi-Square Pr > ChiSq beetle 2 vs 3 EXP <.0001 beetle 1 at dose = 0 PARM <.0001 beetle 2 at dose = 0 PARM <.0001 beetle 2 at dose = 0 EXP <

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