data modelos;
input OBS  Treatment CPinDiet CalculadoLys LysinDiet Replicate FI TotalEgg EP EW BWI BWF;
datalines;
1	1	7.07	0.33	0.298	1	14.25	4.00	25.00	8.51	131.12	120.16
2	1	7.07	0.33	0.298	2	15.56	3.00	18.75	8.41	146.05	148.69
4	1	7.07	0.33	0.298	4	14.64	3.00	18.75	8.06	129.08	123.27
5	1	7.07	0.33	0.298	5	15.44	5.00	31.25	8.51	149.46	134.11
7	1	7.07	0.33	0.298	7	16.00	4.00	25.00	8.71	141.43	140.95
9	2	10.61	0.49	0.447	2	17.89	8.00	50.00	8.21	165.79	147.85
10	2	10.61	0.49	0.447	3	15.69	8.00	50.00	7.90	133.82	124.52
11	2	10.61	0.49	0.447	4	16.17	7.00	43.75	9.22	152.67	149.97
12	2	10.61	0.49	0.447	5	20.92	8.00	50.00	8.61	140.61	154.90
13	2	10.61	0.49	0.447	6	21.96	7.00	43.75	9.04	147.78	150.60
14	2	10.61	0.49	0.447	7	19.29	6.00	37.50	8.45	144.83	122.07
15	3	14.14	0.66	0.596	1	22.64	15.00	93.75	10.02	151.93	147.11
16	3	14.14	0.66	0.596	2	22.01	14.00	87.50	9.64	168.75	167.24
17	3	14.14	0.66	0.596	3	22.72	10.00	62.50	9.82	155.92	151.38
18	3	14.14	0.66	0.596	4	23.59	11.00	68.75	11.16	160.61	173.05
20	3	14.14	0.66	0.596	6	23.65	9.00	56.25	9.02	161.45	152.08
22	4	17.68	0.82	0.745	1	25.16	15.00	93.75	10.54	158.10	162.65
23	4	17.68	0.82	0.745	2	22.76	9.00	56.25	10.35	171.19	171.87
25	4	17.68	0.82	0.745	4	23.41	14.00	87.50	10.29	157.39	156.79
26	4	17.68	0.82	0.745	5	23.43	14.00	87.50	10.95	168.07	175.63
27	4	17.68	0.82	0.745	6	23.02	14.00	87.50	10.75	166.19	165.25
28	4	17.68	0.82	0.745	7	21.52	7.00	43.75	10.20	168.01	161.22
29	5	24.75	1.15	1.043	1	25.07	12.00	75.00	10.60	170.33	158.22
30	5	24.75	1.15	1.043	2	26.02	14.00	87.50	10.17	174.10	178.97
31	5	24.75	1.15	1.043	3	25.67	15.00	93.75	10.84	157.11	155.47
33	5	24.75	1.15	1.043	5	25.31	16.00	100.00	10.59	172.23	159.94
34	5	24.75	1.15	1.043	6	24.06	16.00	100.00	10.99	160.00	158.56
35	5	24.75	1.15	1.043	7	24.30	14.00	87.50	10.67	164.02	166.42
36	6	28.28	1.32	1.192	1	25.57	15.00	93.75	10.84	164.34	159.65
37	6	28.28	1.32	1.192	2	23.15	15.00	93.75	10.22	178.06	176.58
38	6	28.28	1.32	1.192	3	23.12	13.00	81.25	10.35	166.23	154.79
40	6	28.28	1.32	1.192	5	25.17	16.00	100.00	10.77	170.51	170.71
41	6	28.28	1.32	1.192	6	24.99	12.00	75.00	10.67	178.45	193.59
42	6	28.28	1.32	1.192	7	23.61	18.00	100.00	9.89	178.28	174.14
43	7	35.35	1.65	1.489	1	22.41	10.00	62.50	11.55	158.87	159.10
44	7	35.35	1.65	1.489	2	23.74	15.00	93.75	11.44	162.53	180.55
45	7	35.35	1.65	1.489	3	24.27	14.00	87.50	10.39	174.69	178.18
46	7	35.35	1.65	1.489	4	23.90	15.00	93.75	11.95	173.80	179.40
47	7	35.35	1.65	1.489	5	24.63	12.00	75.00	11.62	162.90	177.07
48	7	35.35	1.65	1.489	6	21.79	16.00	100.00	10.88	184.29	179.84
49	7	35.35	1.65	1.489	7	23.85	13.00	81.25	10.64	165.50	179.56
;
run;
*Determination of parameters;

data modelos; set modelos;
LysIntake=(LysInDiet/100*FI)*1000;
CPIntake=(CPInDiet/100*FI)*1000;
EO=EP/100*EW;
dLys=((EO*13/100)*(6.81/100))*1000; *CP 13% and Lys in Egg 6.81% in CP;
BW=((BWI+BWF)/2)/1000;
MBW=BW**0.67;
ChangBW=BWF-BWI;
FCR=FI/EO;
dz=TotalEggs/12;
FCRdz=FI/dz;
MBWLysIntake=LysIntake/MBW;
MBWEO=EO/MBW;
a1=(LysIntake-59*MBW)/EO;      /*/ RLM /*/
a2=(LysIntake-67*MBW)/EO;     /*/ Broken line /*/
a3=(LysIntake-133*MBW)/EO;   /*/ M1 /*/
a4=(LysIntake-149*MBW)/EO;  /*/ M2 /*/
a5=(LysIntake-139*MBW)/EO; /*/ M4 /*/
a6=(LysIntake-192*MBW)/EO;/*/ M5 /*/
Linear1=MBW*(27*MBWEO+57*MBW);
Linear2=MBW*(18*MBWEO+67*MBW);
NonLinear1 = 133*MBW+MBW*((log(36.7)-log(36.7-MBWEO))/0.0046); * Lysm*MBW + (log(Rmax – log(Rmax – EO)))/k;
*NonLinear2 = 133*MBW+MBW*((log(36.7)-log(36.7-MBWEO))/0.0046);
*NonLinear3 = 133*MBW+MBW*((log(36.7)-log(36.7-MBWEO))/0.0046);
*NonLinear4 = 133*MBW+MBW*((log(36.7)-log(36.7-MBWEO))/0.0046);
run; 
proc print; run;

*Response table and ANOVA and significance for linear and quadratic effect;

*This procedure must be repeated for all variables;


PROC MIXED DATA=modelos;
class treatment replicate;
model variables=treatment;
random replicate/type=ar(1) sub=replicate;
contrast "ef.lin" treatment -3 -2 -1 0 1 2 3;
contrast "ef.qua" treatment 5 0 -3 -4 -3 0 5;
run;
*Description of the maximum and minimum response for arginine deposition in the
egg, maintenance requirement and total efficiency of arginine utilization;

*Model 1. Linear regression model;

proc reg data=modelos;
model   MBWLysIntake=  MBWEO MBW/noint;
run;
proc nlmixed data=modelos;
parms  a=26  Lysm=50;
model MBWEO~normal(((MBWLysIntake-Lysm*MBW)/a)+ avar, errvar);
random avar~normal(0, Replicatevar) subject=Replicate;
predict ((MBWLysIntake-Lysm*MBW)/a)+ avar out=ppp;
ods output dimensions=ddd;
run;
proc nlin data=modelos;
parms a=39 Lysm=49;
model  MBWEO=(MBWLysIntake-Lysm*MBW)/a;
run;
data ppp; set ppp; 
resid=MBWEO-pred; 
run;
proc means noprint data=ppp; where MBWEO ne .;
var MBWEO resid;
output out=mmm uss=totss sserr css=ctotss rss1 n=nobs; run;
data ddd; set ddd; if descr='parameters'; run;
data mmm; merge mmm ddd;
rsquare =(ctotss-sserr)/ctotss;
adjrsquare = 1 -(sserr/(41-4-1))/(ctotss/41-1); run;
proc print; run;
proc reg data=ppp;
model resid=pred;
run;proc print; run;

*Model 2. Broken-line model;

proc nlmixed data=modelos
parms rmax=30 u=0.698 r=500;
z1=(mbwlysintake<r)*(r-mbwlysintake);
model mbweo~normal (rmax+u*(z1) + rmaxvar, errvar);
random rmaxvar~normal(0, rpvar) subject=replicate;
predict rmax+u*(z1) + rmaxvar out=ppp;
ods output dimensions=ddd;
run;

*Model 3. Monomolecular model with four parameters;
 
proc nlin data=modelos;
parms  Rmax=32 Rmin=5 k=0.01178 Lysm=170;
model MBWEO=(Rmax-Rmin)*(1-exp(-k*(MBWLysIntake-Lysm)));
run;
proc nlmixed data=modelos;
parms  Rmax=35 Rmin=5 k=0.01178 Lysm=178;
model MBWEO~normal((Rmax-Rmin)*(1-exp(-k*(MBWLysIntake-Lysm)))+ Rmaxvar, errvar);
random Rmaxvar~normal(0, Replicatevar) subject=Replicate;
predict (Rmax-Rmin)*(1-exp(-k*(MBWLysIntake-Lysm)))+ Rmaxvar out=ppp;
ods output dimensions=ddd;
run;
data ppp; set ppp; 
resid=MBWEO-pred; 
run;
proc means noprint data=ppp; where MBWEO ne .;
var MBWEO resid;
output out=mmm uss=totss sserr css=ctotss rss1 n=nobs; run;
data ddd; set ddd; if descr='parameters'; run;
data mmm; merge mmm ddd;
rsquare =(ctotss-sserr)/ctotss;
adjrsquare = 1 -(sserr/(41-4-1))/(ctotss/41-1); run;
proc print; run;
proc reg data=ppp;
model resid=pred;
run;proc print; run;

*Model 4. Monomolecular model with three parameters;

proc nlmixed data=modelos;
parms  Rmax=36 k=0.016 Lysm=150;
model MBWEO~normal(Rmax*(1-exp(-k*(MBWLysIntake-Lysm)))+ Rmaxvar, errvar);
random Rmaxvar~normal(0, Replicatevar) subject=Replicate;
predict Rmax*(1-exp(-k*(MBWLysIntake-Lysm)))+ Rmaxvar out=ppp;
ods output dimensions=ddd;
run;
data ppp; set ppp; 
resid=MBWEO-pred; 
run;
proc means noprint data=ppp; where MBWEO ne .;
var MBWEO resid;
output out=mmm uss=totss sserr css=ctotss rss1 n=nobs; run;
data ddd; set ddd; if descr='parameters'; run;
data mmm; merge mmm ddd;
rsquare =(ctotss-sserr)/ctotss;
adjrsquare = 1 -(sserr/(41-4-1))/(ctotss/41-1); run;
proc print; run;
proc reg data=ppp;
model resid=pred;
run;proc print; run;

*Model 5. Monomolecular model with three parameters;

proc nlmixed data=modelos;
parms  Rmax=36 k=0.016 Rmin=110;
model MBWEO~normal(Rmax*(1-exp(-k*(MBWLysIntake)) - Rmin)+ Rmaxvar, errvar);
random Rmaxvar~normal(0, Replicatevar) subject=Replicate;
predict Rmax*(1-exp(-k*(MBWLysIntake)) - Rmin)+ Rmaxvar out=ppp;
ods output dimensions=ddd;
run;
data ppp; set ppp; 
resid=MBWEO-pred; 
run;
proc means noprint data=ppp; where MBWEO ne .;
var MBWEO resid;
output out=mmm uss=totss sserr css=ctotss rss1 n=nobs; run;
data ddd; set ddd; if descr='parameters'; run;
data mmm; merge mmm ddd;
rsquare =(ctotss-sserr)/ctotss;
adjrsquare = 1 -(sserr/(41-4-1))/(ctotss/41-1); run;
proc print; run;
proc reg data=ppp;
model resid=pred;
run;proc print; run;

*Model 6. Monomolecular model with four parameters;

proc nlmixed data=modelos;
parms  Rmin=110 Range=160 k=0.016 Lysm=450;
model MBWEO~normal(Rmin+Range*(1-exp(-exp(-k*(MBWLysIntake-Lysm))) + Rmaxvar, errvar);
random Rmaxvar~normal(0, Replicatevar) subject=Replicate;
predict Rmin+Range*(1-exp(-exp(-k*(MBWLysIntake-Lysm))) + Rmaxvar out=ppp;
ods output dimensions=ddd;
run;
data ppp; set ppp; 
resid=MBWEO-pred; 
run;
proc means noprint data=ppp; where MBWEO ne .;
var MBWEO resid;
output out=mmm uss=totss sserr css=ctotss rss1 n=nobs; run;
data ddd; set ddd; if descr='parameters'; run;
data mmm; merge mmm ddd;
rsquare =(ctotss-sserr)/ctotss;
adjrsquare = 1 -(sserr/(41-4-1))/(ctotss/41-1); run;
proc print; run;
proc reg data=ppp;
model resid=pred;
run;proc print; run;

*Model 7. Monomolecular model with three parameters;

proc nlmixed data=modelos;
parms  Rmax=230 k=0.016 Lysm=380;
model MBWEO~normal(Rmax*(1-exp(-exp(-k*(MBWLysIntake-Lysm))) + Rmaxvar, errvar);
random Rmaxvar~normal(0, Replicatevar) subject=Replicate;
predict Rmax*(1-exp(-exp(-k*(MBWLysIntake-Lysm))) + Rmaxvar out=ppp;
ods output dimensions=ddd;
run;
data ppp; set ppp; 
resid=MBWEO-pred; 
run;
proc means noprint data=ppp; where MBWEO ne .;
var MBWEO resid;
output out=mmm uss=totss sserr css=ctotss rss1 n=nobs; run;
data ddd; set ddd; if descr='parameters'; run;
data mmm; merge mmm ddd;
rsquare =(ctotss-sserr)/ctotss;
adjrsquare = 1 -(sserr/(41-4-1))/(ctotss/41-1); run;
proc print; run;
proc reg data=ppp;
model resid=pred;
run;proc print; run;

*Model 8. Monomolecular model with four parameters;

proc nlmixed data=modelos;
parms  Rmax=350 Rmin=110 k=0.016 Lysm=380;
model MBWEO~normal(Rmax-(Rmax-Rmin)*(1-exp(-k*(MBWLysIntake-Lysm))) + Rmaxvar, errvar);
random Rmaxvar~normal(0, Replicatevar) subject=Replicate;
predict Rmax-(Rmax-Rmin)*(1-exp(-k*(MBWLysIntake-Lysm))) + Rmaxvar out=ppp;
ods output dimensions=ddd;
run;
data ppp; set ppp; 
resid=MBWEO-pred; 
run;
proc means noprint data=ppp; where MBWEO ne .;
var MBWEO resid;
output out=mmm uss=totss sserr css=ctotss rss1 n=nobs; run;
data ddd; set ddd; if descr='parameters'; run;
data mmm; merge mmm ddd;
rsquare =(ctotss-sserr)/ctotss;
adjrsquare = 1 -(sserr/(41-4-1))/(ctotss/41-1); run;
proc print; run;
proc reg data=ppp;
model resid=pred;
run;proc print; run;