Compare AIC Using PROC MIXED
--------------------------------

AIC: -2*log(Likelihood(hat(beta))) + 2p
BIC: -2*log(Likelihood(hat(beta))) + p*log(N)

Example 1
------------

DATA SET1;
INPUT GENDER $ HEIGHT WEIGHT AGE;
/* Compare AIC*/
HEIGHT2=HEIGHT**2;
DATALINES;
M 68 155 23
F 61  99 20
F 63 115 21
M 70 205 45
M 69 170  .
F 65 125 30
M 72 220 48
;

###Only Height
PROC MIXED DATA=SET1;                
MODEL WEIGHT=HEIGHT;         
RUN;

-2 Res Log Likelihood            45.4
AIC (smaller is better)          47.4
AICC (smaller is better)         48.8
BIC (smaller is better)          47.0



###HEIGHT and HEIGHT**2
PROC MIXED DATA=SET1;                
MODEL WEIGHT=HEIGHT HEIGHT2;         
RUN;

 -2 Res Log Likelihood           42.2
AIC (smaller is better)          44.2 <----Smaller
AICC (smaller is better)         46.2
BIC (smaller is better)          43.6 <----Smaller

---------------------
Example 2
------------

### HR=a+b*DOSE+e
DATA HEART;
INPUT DOSE HR;
DATALINES;
 2 60
 2 58
 4 63
 4 62
 8 67
 8 65      
16 70
16 70
32 74
32 73
;

PROC MIXED DATA=HEART;
MODEL HR=DOSE;   
RUN;



-2 Res Log Likelihood            44.6
AIC (smaller is better)          46.6
AICC (smaller is better)         47.2
BIC (smaller is better)          46.7



### HR=a+b*log(DOSE)+e,   <--Dose on log-scale.
DATA HEART;
INPUT DOSE HR;
LDOSE=LOG(DOSE); 
DATALINES;
 2 60
 2 58
 4 63-2 Res Log Likelihood            23.7
                               AIC (smaller is better)          25.7
                               AICC (smaller is better)         26.4
                               BIC (smaller is better)          25.8
 4 62
 8 67
 8 65
16 70
16 70
32 74
32 73
;


PROC MIXED DATA=HEART;
MODEL HR=LDOSE;  
RUN;

-2 Res Log Likelihood            23.7
AIC (smaller is better)          25.7 <---------Smaller
AICC (smaller is better)         26.4 <---------Smaller
BIC (smaller is better)          25.8