/* Table in Hout (1983: 11). Original source: page 49 of */ /* Featherman D.L., R.M. Hauser. (1978) "Opportunity and Change." */ /* New York: Academic. */ #delimit ; tabi 1414 521 302 643 40 \ 724 524 254 703 48 \ 798 648 856 1676 108 \ 756 914 771 3325 237 \ 409 357 441 1611 1832 ,replace; #delimit cr rename row father rename col son rename pop freq label var father "Father's occupation" label var son "Son's occupation" #delimit ; label def occ 1 "Upper nonmanual" 2 "Lower nonmanual" 3 "Upper manual" 4 "Lower manual" 5 "Farm"; #delimit cr label val father occ label val son occ * structural zeros for quasi independence model gen wt=(father ~=son ) * variable for quasi-independence; gen diag=0 quietly replace diag=father if father==son * a symmetric cross-classification gen sym=0 quietly replace sym=1 if ((father==1 & son==2) | (father==2 & son==1)) quietly replace sym=2 if ((father==1 & son==3) | (father==3 & son==1)) quietly replace sym=3 if ((father==1 & son==4) | (father==4 & son==1)) quietly replace sym=4 if ((father==1 & son==5) | (father==5 & son==1)) quietly replace sym=5 if ((father==2 & son==3) | (father==3 & son==2)) quietly replace sym=6 if ((father==2 & son==4) | (father==4 & son==2)) quietly replace sym=7 if ((father==2 & son==5) | (father==5 & son==2)) quietly replace sym=8 if ((father==3 & son==4) | (father==4 & son==3)) quietly replace sym=9 if ((father==3 & son==5) | (father==5 & son==3)) quietly replace sym=10 if ((father==4 & son==5) | (father==5 & son==4)) * design vectors for crossings parameter model gen v1=(father <= 1 & son > 1) | (father > 1 & son <= 1) gen v2=(father <= 2 & son > 2) | (father > 2 & son <= 2) gen v3=(father <= 3 & son > 3) | (father > 3 & son <= 3) gen v4=(father <= 4 & son > 4) | (father > 4 & son <= 4) tab father son [fw=freq] * An model of independence desmat father son glm freq _x_*, link(log) family(poisson) desrep * save the design matrix of the baseline model renpfix _x_ _z_ * A quasi-independence loglinear model, using structural zeros * (page 23 of "Mobility Tables"). /* 0 1 1 1 1 values of variable "wt" 1 0 1 1 1 1 1 0 1 1 1 1 1 0 1 1 1 1 1 0 */ glm freq _z_* [iweight=wt], link(log) family(poisson) desrep * Quasi-independence using a "dummy factor" to create the design * vectors for the diagonal cells (page 23). /* 1 0 0 0 0 values of variable "diag" 0 2 0 0 0 0 0 3 0 0 0 0 0 4 0 0 0 0 0 5 */ desmat diag glm freq _z_* _x_*, link(log) family(poisson) desrep * Quasi-symmetry using the symmetric cross-classification (page 23) /* 0 1 2 3 4 values of variable "sym" 1 0 5 6 7 2 5 0 8 9 3 6 8 0 10 4 7 9 10 0 */ desmat sym glm freq _z_* _x_*, link(log) family(poisson) desrep * Crossings parameter model (page 35) /* 0 v1 v1 v1 v1 | 0 0 v2 v2 v2 | 0 0 0 v3 v3 | 0 0 0 0 v4 v1 0 0 0 0 | 0 0 v2 v2 v2 | 0 0 0 v3 v3 | 0 0 0 0 v4 v1 0 0 0 0 | v2 v2 0 0 0 | 0 0 0 v3 v3 | 0 0 0 0 v4 v1 0 0 0 0 | v2 v2 0 0 0 | v3 v3 v3 0 0 | 0 0 0 0 v4 v1 0 0 0 0 | v2 v2 0 0 0 | v3 v3 v3 0 0 | v4 v4 v4 v4 0 */ glm freq _z_* v*, link(log) family(poisson) desrep * Crossings parameter model, specified as a pattern of log odds-ratios /* The set of local log odds-ratio for table F can be defined as */ /* log((F[i,j]*F[i+1,j+1])/(F[i,j+1]*F[i+1,j])) */ /* for i=1 to nrow(F)-1, j=1 to ncol(F)-1 */ /* Using the difference contrast for interaction means that para- */ /* meters will correspond with log odds-ratios */ /* The crossings parameter model has a pattern of log odds-ratios */ /* with zeros for all off diagonal cells */ /* It is fitted by creating a design for a saturated model using */ /* the difference contrast for interactions, then deleting all */ /* columns of the design matrix for off-diagonal cells of the set */ /* of local log odds-ratios */ * 1 2 3 4 --> 1 * 5 6 7 8 6 * 9 10 11 12 11 * 13 14 15 16 16 desmat father.son=dif.dif drop _x_2-_x_5 _x_7-_x_10 _x_12-_x_15 glm freq _z_* _x_*, link(log) family(poisson) desrep * Uniform association model: linear by linear association (page 58). desmat father.son=orp(1).orp(1) glm freq _z_* _x_*, link(log) family(poisson) desrep * RC model 1 (unequal row and column effects, page 58) /* Fits a uniform association parameter and row and column effect */ /* parameters. Row and column effect parameters have the */ /* restriction that the first and last categories are zero. */ /* The column of design for the last category must be deleted */ /* "manually". */ #delimit ; desmat father.son=orp(1).orp(1) /* uniform association */ father.son=ind(1).orp(1) /* row effects 2-5, drop 5 */ father.son=orp(1).ind(1); /* col effects 6-9, drop 9 */ #delimit cr drop _x_5 _x_9 glm freq _z_* _x_*, link(log) family(poisson) desrep