Model variables:
Z(1) = I(T_s in (0,1]) x I(T_c in (1,6])
Z(2) = I(T_s in (0,1]) x I(T_c in (6,12])
Z(3) = I(T_s in (0,1]) x I(T_c > 12)
Z(4) = I(T_s in (1,6]) x I(T_c in (6,12])
Z(5) = I(T_s in (1,6]) x I(T_c > 12)
Z(6) = I(T_s in (6,12]) x I(T_c > 12)
Z(7) = G
Z(8) = AGE
Z(9) = CHICAGO
Z(10) = SANDIEGO
Z(11) = BOSTON
Z(12) = 1


ML model:
Model: ln[f(z|b)], where
Z(1)=I(T_s in (0,1]) x I(T_c in (1,6])
Z(2)=I(T_s in (0,1]) x I(T_c in (6,12])
Z(3)=I(T_s in (0,1]) x I(T_c > 12)
Z(4)=I(T_s in (1,6]) x I(T_c in (6,12])
Z(5)=I(T_s in (1,6]) x I(T_c > 12)
Z(6)=I(T_s in (6,12]) x I(T_c > 12)
Z(7)=G
Z(8)=AGE
Z(9)=CHICAGO
Z(10)=SANDIEGO
Z(11)=BOSTON
Z(12)=1
Z(13)=b(1) {= alpha_s}
Z(14)=b(2).Z(9)+b(3).Z(10)+b(4) {= beta_s'X_s}
Z(15)=b(5) {= alpha_c}
Z(16)=b(6).Z(11)+b(7).Z(8)+b(8) {= beta_c'X_c}
Z(17)=Z(12)/Z(13) {= 1/alpha_s}
Z(18)=Z(7).Z(16) {= G.beta_c'X_c}
Z(19)=EXP[Z(18)] {= exp[G.beta_c'X_c]}
Z(20)=Z(17).Z(14) {= alpha_s^-1 . beta_s'X_s}
Z(21)=-Z(20) {= -alpha_s^-1 . beta_s'X_s}
Z(22)=EXP[Z(21)] {= exp(-alpha_s^-1 . beta_s'X_s)}
Z(23)=Z(12)-Z(19) {= 1-exp[G.beta_c'X_c]}
Z(24)=Z(15).Z(19) {= alpha_c . exp[G.beta_c'X_c]}
Z(25)=-Z(24)
Z(26)=Z(15).Z(22).Z(23) {= c}
Z(27)=1*Z(12)
Z(28)=6*Z(12) {= 6}
Z(29)=12*Z(12) {= 12}
Z(30)=Z(28).Z(25) {= 6.r}
Z(31)=Z(29).Z(25) {= 12.r}
Z(32)=EXP[Z(25)] {= exp(r)}
Z(33)=EXP[Z(30)] {= exp(6.r)}
Z(34)=EXP[Z(31)] {= exp(12.r)}
Z(35)=Z(32)-Z(33) {= exp(r)-exp(6.r)}
Z(36)=Z(33)-Z(34) {= exp(6.r)-exp(12.r)}
Z(37)=LOG[Z(28)] {= ln(6)}
Z(38)=LOG[Z(29)] {= ln(12)}
Z(39)=Z(13).Z(37) {= alpha_s . ln (6)}
Z(40)=Z(13).Z(38) {= alpha_s . ln (12)}
Z(41)=Z(14)+Z(39) {= beta_s'X_s+alpha_s . ln (6)}
Z(42)=Z(14)+Z(40) {= beta_s'X_s+alpha_s . ln (12)}
Z(43)=EXP[Z(14)] {= exp(beta_s'X_s)}
Z(44)=EXP[Z(41)] {= exp(beta_s'X_s+alpha_s . ln (6))}
Z(45)=EXP[Z(42)] {= exp(beta_s'X_s+alpha_s . ln (12))}
Z(46)=-Z(43) {= -exp(beta_s'X_s)}
Z(47)=-Z(44) {= -exp(beta_s'X_s+alpha_s . ln (6))}
Z(48)=-Z(45) {= -exp(beta_s'X_s+alpha_s . ln (12))}
Z(49)=EXP[Z(46)] {= S_s(1|X_s)}
Z(50)=EXP[Z(47)] {= S_s(6|X_s)}
Z(51)=EXP[Z(48)] {= S_s(12|X_s)}
Z(52)=Integral(exp[-Z(26).(ln(1/x)^Z(17)]dx|Z(49)<x<Z(12))
Z(53)=Integral(exp[-Z(26).(ln(1/x)^Z(17)]dx|Z(50)<x<Z(49))
Z(54)=Integral(exp[-Z(26).(ln(1/x)^Z(17)]dx|Z(51)<x<Z(50))
Z(55)=Z(35).Z(52) {= P1}
Z(56)=Z(36).Z(52) {= P2}
Z(57)=Z(34).Z(52) {= P3}
Z(58)=Z(36).Z(53) {= P4}
Z(59)=Z(34).Z(53) {= P5}
Z(60)=Z(34).Z(54) {= P6}
Z(61)=Z(55)+Z(56)+Z(57)+Z(58)+Z(59)+Z(60) {= P1+..+P6}
Z(62)=Z(12)-Z(61) {= P7}
Z(63)=Z(1)+Z(2)+Z(3)+Z(4)+Z(5)+Z(6) {= Y1+..+Y6}
Z(64)=Z(12)-Z(63)
Z(65)=Z(1).Z(55) {= Y1.P1}
Z(66)=Z(2).Z(56) {= Y2.P2}
Z(67)=Z(3).Z(57) {= Y3.P3}
Z(68)=Z(4).Z(58) {= Y4.P4}
Z(69)=Z(5).Z(59) {= Y5.P5}
Z(70)=Z(6).Z(60) {= Y6.P6}
Z(71)=Z(64).Z(62) {= Y7.P7}
Z(72)=Z(65)+Z(66)+Z(67)+Z(68)+Z(69)+Z(70)+Z(71) {= Y1.P1+..+Y7.P7}
Z(73)=.0000000001*Z(12) {= 0.0000000001}
Z(74)=MAXIMUM[Z(72),Z(73)]
Z(75)=LOG[Z(74)] {= Final model}
ln[f(z|b)] = Z(75), where z = (Z(1),..,Z(75))' and b = (b(1),..,b(8))'

.5 <= b(1) <= 1
-1.5 <= b(2) <= -1
-.5 <= b(3) <= 0
0 <= b(4) <= .5
0 <= b(5) <= .2
.25 <= b(6) <= .75
-.2 <= b(7) <= 0
1 <= b(8) <= 2

The log-likelihood function has been maximized using the simplex method
of Nelder and Mead. The algorithm involved is a Visual Basic translation
of the Fortran algorithm involved in:
W.H.Press, B.P.Flannery, S.A.Teukolsky and W.T.Vetterling, 'Numerical
Recipes', Cambridge University Press, 1986, pp. 292-293

Estimation results:
Parameters ML estimate   t-value
                       [p-value]
b(1)          0.861683    12.275
                       [0.00000]
b(2)         -1.226747    -7.410
                       [0.00000]
b(3)         -0.303043    -2.004
                       [0.04507]
b(4)          0.174315     1.761
                       [0.07820]
b(5)          0.038611     7.469
                       [0.00000]
b(6)          0.411872     2.267
                       [0.02341]
b(7)         -0.053659    -3.220
                       [0.00128]
b(8)          1.537895     3.217
                       [0.00129]

[The two-sided p-values are based on the normal approximation]

Log-Likelihood:         -847.842785
n:                              503

Information criteria:      
     Akaike:               3.402953
     Hannan-Quinn:         3.429287
     Schwarz:              3.470080