TITLE:	Strict Invariance for 5-points Likert Items
    See Millsap & Tein (2004, p.485) for further details 
DATA:	FILE IS example5c.csv;
VARIABLE:	NAMES ARE u1-u8 g;
    USEVARIABLES ARE u1-u8;
	CATEGORICAL ARE u1-u8;
	GROUPING IS g (1=male 2=female);
ANALYSIS: PARAMETERIZATION = THETA; ESTIMATOR = WLSMV;
! Put the chi-square values of the model that we wish to compare with this model
    DIFFTEST=strong5c.dif; ! strict vs. strong
MODEL:
    ! Factor loadings are constrained across groups 
    ! except the marker variables, which are fixed.
    f1 BY u1@1 
        u2 (f21)
        u3 (f31)
        u4 (f41);
    f2 BY u5@1 
        u6 (f62)
        u7 (f72)
        u8 (f82);
        	
    ! All thresholds are constrained across groups. 
    ! Note that thresholds are constrained across groups by default.
    [u1$1] (t11);
    [u1$2] (t12);
    [u1$3] (t13);
    [u1$4] (t14);
    [u2$1] (t21);
    [u2$2] (t22);
    [u2$3] (t23);
    [u2$4] (t24);
    [u3$1] (t31);
    [u3$2] (t32);
    [u3$3] (t33);
    [u3$4] (t34);
    [u4$1] (t41);
    [u4$2] (t42);
    [u4$3] (t43);
    [u4$4] (t44);
    [u5$1] (t51);
    [u5$2] (t52);
    [u5$3] (t53);
    [u5$4] (t54);
    [u6$1] (t61);
    [u6$2] (t62);
    [u6$3] (t63);
    [u6$4] (t64);
    [u7$1] (t71);
    [u7$2] (t72);
    [u7$3] (t73);
    [u7$4] (t74);
    [u8$1] (t81);
    [u8$2] (t82);
    [u8$3] (t83);
    [u8$4] (t84);

    ! Factor variance/covariance are free across groups
    f1*; f2*;
    f1 WITH f2*;

    ! Factor mean of the first group are fixed to zeros
    [f1@0];
    [f2@0];

    ! Unique variances of the all groups are fixed as 1
    u1@1;
    u2@1;
    u3@1;
    u4@1;
    u5@1;
    u6@1;
    u7@1;
    u8@1;

MODEL female: 
    ! Factor loadings are constrained across groups 
    ! except the marker variables, which are fixed.
    f1 BY u1@1 
        u2 (f21)
        u3 (f31)
        u4 (f41);
    f2 BY u5@1 
        u6 (f62)
        u7 (f72)
        u8 (f82);
   
    ! All thresholds are constrained across groups. 
    ! Note that thresholds are constrained across groups by default.
    [u1$1] (t11);
    [u1$2] (t12);
    [u1$3] (t13);
    [u1$4] (t14);
    [u2$1] (t21);
    [u2$2] (t22);
    [u2$3] (t23);
    [u2$4] (t24);
    [u3$1] (t31);
    [u3$2] (t32);
    [u3$3] (t33);
    [u3$4] (t34);
    [u4$1] (t41);
    [u4$2] (t42);
    [u4$3] (t43);
    [u4$4] (t44);
    [u5$1] (t51);
    [u5$2] (t52);
    [u5$3] (t53);
    [u5$4] (t54);
    [u6$1] (t61);
    [u6$2] (t62);
    [u6$3] (t63);
    [u6$4] (t64);
    [u7$1] (t71);
    [u7$2] (t72);
    [u7$3] (t73);
    [u7$4] (t74);
    [u8$1] (t81);
    [u8$2] (t82);
    [u8$3] (t83);
    [u8$4] (t84);


    ! Factor variance/covariance are free across groups
    f1*; f2*;
    f1 WITH f2*;

    ! Factor mean of the second group are free
    [f1*];
    [f2*];

    ! Unique variances are fixed to 1 (equal to the first group)
    u1@1;
    u2@1;
    u3@1;
    u4@1;
    u5@1;
    u6@1;
    u7@1;
    u8@1;
OUTPUT: TECH1; STDYX;
! Save the chi-square values for difference testing with other nested models
SAVEDATA: DIFFTEST=strict5c.dif;