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imposing the restriction on parameter in simulteonus nonlinear equations

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imposing the restriction on parameter in simulteonus nonlinear equations

Hello

 

I am working on Simultaneous nonlinear equations but I don’t know how I can impose the matrix restriction on the parameters, my model as follows:

 

Proc model data= test;

Parms     βir0 βir1 αirir αirus

               βus0 βus1 αusir  αusus;

Exogenous pirt pust y cir cus; 

/* system equations*/ 

Qirt= βir0+ βir1*y+ αirir*Pirt+αirus*Pust; 

Qust= βus0+ βus1*y+ αusir*Pirt+αusus*Pust;

Qirt= αirir*(Cir-pirt);

Qust= αusus*(Cus-pust;


Fit  Qirt Qust  / fiml;
run

 

And this is matrix of parameters that I have

 

λ11  λ12  λ13   λ14
λ21 λ22   λ23   λ24
λ31   0   λ33    0
0   λ42   0    λ44

 

and this the restriction on this parameter

 


λ11        1

λ12        0

λ13    - αirir

λ14    -αirus

λ21      0

λ22      1

λ23     -αusir

λ24    - αusus

λ31       1

λ33       αirir

λ42       1

λ44       αusus

 

 

Anyone can help me for how can I impose this restriction on above-mentioned model? I am so grateful of you in advance

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