Estimate Quasi-Binomial Model with GENMOD Procedure in SAS

This article is originally published at https://statcompute.wordpress.com

In my previous post (https://statcompute.wordpress.com/2015/11/01/quasi-binomial-model-in-sas/), I’ve shown why there is an interest in estimating Quasi-Binomial models for financial practitioners and how to estimate with GLIMMIX procedure in SAS.

In the demonstration below, I will show an example how to estimate a Quasi-Binomial model with GENMOD procedure by specifying VARIANCE and DEVIANCE. While the CPU time for model estimation is a lot faster with GENMOD than with GLIMMIX, additional steps are necessary to ensure the correct statistical inference.

ods listing close;
ods output modelfit = fit;
ods output parameterestimates = parm1;
proc genmod data = kyphosis;
  model y = age number start / link = logit noscale;
  variance v = _mean_ * (1 - _mean_);
  deviance d = (-2) * log((_mean_ ** _resp_) * ((1 - _mean_) ** (1 - _resp_)));
run;
ods listing;

proc sql noprint;
select
  distinct valuedf format = 12.8, df format = 8.0 into :disp, :df
from
  fit
where 
  index(criterion, "Pearson") > 0;

select
  value format = 12.4 into :ll
from
  fit
where
  criterion = "Log Likelihood";

select
  sum(df) into :k
from
  parm1;
quit;

%let aic = %sysevalf((-&ll + &k) * 2); 
%let bic = %sysevalf(-&ll * 2 + &k * %sysfunc(log(&df + &k)));

data parm2 (keep = parameter estimate stderr2 df t_value p_value);
  set parm1;
  where df > 0;

  stderr2 = stderr * (&scale ** 0.5);
  df = &df;
  t_value = estimate / stderr2;
  p_value = (1 - probt(abs(t_value), &df)) * 2;
run;

title;
proc report data = parm2 spacing = 1 headline nowindows split = "*";
  column(" Parameter Estimate of Quasi-Binomial Model "
         parameter estimate stderr2 t_value df p_value);
  compute before _page_;
    line @5 "Fit Statistics";
	line " ";
	line @3 "Quasi Log Likelihood: %sysfunc(round(&ll, 0.01))";
	line @3 "Quasi-AIC (smaller is better): %sysfunc(round(&aic, 0.01))";
	line @3 "Quasi-BIC (smaller is better): %sysfunc(round(&bic, 0.01))";
	line @3 "(Dispersion Parameter for Quasi-Binomial is %sysfunc(round(&disp, 0.0001)))";
	line " ";
  endcomp;
  define parameter / "Parmeter" width = 10 order order = data;
  define estimate  / "Estimate" width = 10 format = 10.4;
  define stderr2   / "Std Err"  width = 10 format = 10.4;
  define t_value   / "T Value"  width = 10 format = 10.2;
  define df        / "DF"       width = 5  format = 4.0;
  define p_value   / "Pr > |t|" width = 10 format = 10.4;
run;
quit;
  
/*
    Fit Statistics

  Quasi Log Likelihood: -30.69
  Quasi-AIC (smaller is better): 69.38
  Quasi-BIC (smaller is better): 78.96
  (Dispersion Parameter for Quasi-Binomial is 0.9132)

          Parameter Estimate of Quasi-Binomial Model
 Parmeter     Estimate    Std Err    T Value    DF   Pr > |t|
 ------------------------------------------------------------
 Intercept     -2.0369     1.3853      -1.47    77     0.1455
 Age            0.0109     0.0062       1.77    77     0.0800
 Number         0.4106     0.2149       1.91    77     0.0598
 Start         -0.2065     0.0647      -3.19    77     0.0020
*/

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