# Help System (web edition)

By the ESTIMATE operation also maximum likelihood estimates for
parameters of a user-defined univariate distribution can be
computed.
The distribution has to be defined by a MODEL specification
of the form:
10  *MODEL <name of model>
11  *LOGDENSITY=<logarithm of the density function>
All other specifications are same as in ESTIMATE for regression
models.
Example on the next page:

.......................................................................
Estimation of a logit model:
FILE CREATE TEST,24,3,64,7,10000 / Creating file TEST (10000 cases)
FIELDS:
1 N 4 X1
2 N 4 X2
3 N 1 Y
END

VAR X1,X2,Y TO TEST / Making simulated data values
X1=rand(2002) X2=rand(2002) Y=int(rand(2002)+1/(1+exp(3-2*X1-3*X2)))
Y is 1 with probability 1/(1+exp(3-2*X1-3*X2)) and Y=0 otherwise.

Estimation of the model on the next page:

Estimation of the logit model:
{P}=1/(1+exp(C+a*X1+b*X2)) / Shorthand notation for the model function

MODEL LM1
LOGDENSITY=Y*log({P})+(1-Y)*log(1-{P})

ESTIMATE TEST,LM1,CUR+1 / METHOD=M PRIND=0
Estimated parameters of model LM1:
C=2.87264 (0.0711958)
a=-1.99688 (0.0807001)
b=-2.75048 (0.0835568)
n=10000 log(L)=-5830.526990 nf=56
Correlations:
C      a      b
C           1.000 -0.714 -0.749
a          -0.714  1.000  0.188
b          -0.749  0.188  1.000