I am trying to run a Bayesian logistic regression model, where two parameters need to be constrained to be equal. This model compares two groups in an IRT model, each with its own latent variable theta(the regressor), and each group has its own set of binomial responses, with the response probability determined by theta. I need to constrain some responses to be equal across the groups. I have some code below, based on the SAS Press book 'Bayesian Analysis of Item Response Theory' by Stone and Zhu. However, they don't have the parameter constraint that I need, which I am trying to specify. Here is my code. The reposnse data is in the variable x[5], denoting responses to 5 items. The parameters b1[5] and b2[5] are paameters for the item responses for groups 1 and 2 that are allowed to differ. However, responses to the first item have a parameter constraint - their coefficients ItemOne1 and ItemOne2 should be constrained equal across the two groups. The mu and mu_g parameters are the means of the latent regressor theta for the two groups. proc mcmc data=lsat_g outpost=lsat_bayes seed=23 nthreads=1 nbi=5000 nmc=20000; array ItemOne[2] ItemOne1 ItemOne2; array b1[4]; array b2[4]; array x[5];array mu[2] 0 mu_g; parms ItemOne: 0; parms a1 a2 1; parms b1: b2: 0; prior b1: b2: ~ normal(0, var=16); prior a1 a2 ~ lognormal(0, var=9); parms mu_g 0; prior mu_g ~ normal(0, var=1); beginnodata; /* if (ItemOne1 - ItemOne2 = 0.) then lp = lpdfnorm(ItemOne1,0,4);*/ /* else lp = .;*/ lp = lpdfnorm(ItemOne1,0,4); prior ItemOne1 ItemOne2 ~ general(lp); endnodata; random theta ~ normal(mu[group], var=1) subject=_obs_; llike=0; do j=1 to 5; if group=1 and j=1 then do; prob = logistic(a1*(theta-ItemOne1)); llike = llike + x[j] * log(prob) + (1 - x[j]) * log(1 - prob); end; else if group=1 and j > 1 then do; prob = logistic(a1*(theta-b1[j-1])); llike = llike + x[j] * log(prob) + (1 - x[j]) * log(1 - prob); end; else if group =2 and j = 1 then do; prob = logistic(a2*(theta-ItemOne2)); llike = llike + x[j] * log(prob) + (1 - x[j]) * log(1 - prob); end; else if group =2 and j > 1 then do; prob = logistic(a2*(theta-b2[j-1])); llike = llike + x[j] * log(prob) + (1 - x[j]) * log(1 - prob); end; end; model general(llike); run;   I tried to specify the equality cnstraint based on some example code for conjoint analysis, and my model runs. My results adon't seem to agree with the frequentist model I ran using Proc IRT. The beta coefficients estimates b1 and b2 should not be too different, while my Proc MCMC resutlts make them to be so, unlike Proc IRT. Is my syntax correct? How can I force ItemOne1 and ItemOne2 to be equal, while allowing the theta regressor to have different means (mu and mu_g) for the two groups?   I am including the data generating code as well here. /* SAS program to create the LSAT SAS dataset */ data lsat; input x @5 (x1-x5) (1.) freq; do i=1 to freq; output; end; drop x i freq; datalines; 1 00000 3 2 00001 6 3 00010 2 4 00011 11 5 00100 1 6 00101 1 7 00110 3 8 00111 4 9 01000 1 10 01001 8 11 01010 0 12 01011 16 13 01100 0 14 01101 3 15 01110 2 16 01111 15 17 10000 10 18 10001 29 19 10010 14 20 10011 81 21 10100 3 22 10101 28 23 10110 15 24 10111 80 25 11000 16 26 11001 56 27 11010 21 28 11011 173 29 11100 11 30 11101 61 31 11110 28 32 11111 298 ; run; /* create the LSAT_G data set assumes lsat sas dataset in work library */ data lsat_g; set lsat; if mod(_n_,2)=0 then group=1; else group=2; run; ... View more