4.2 Linear constraints

Your model can have linear constraints within all the parameters except \(\mathbf{Q}\), \(\mathbf{R}\) and \(\boldsymbol{\Lambda}\). For example \(1+2a-3b\) is a linear constraint. When entering this value for you matrix, you specify this as "1+2*a+-3*b". NOTE: \(+\)’s join parts so \(+-3*b\) to specify \(-3b\). Anything after * is a parameter. So 1*1 has a parameter called "1". Example, let’s specify the following matrices: \[\begin{equation*} \mathbf{B} = \begin{bmatrix}b-0.1&0\\ 0&b+0.1\end{bmatrix}\quad \mathbf{Q} = \begin{bmatrix}q_{11}&0\\ 1&0\end{bmatrix}\quad \mathbf{Z} = \begin{bmatrix}z_1-z_2&2 z_1\\ 0&z_1\\ z_2&0\end{bmatrix} \end{equation*}\]

This would be specified as (notice "1*z1+-1*z2" for z1-z2):

B1 <- matrix(list("-0.1+1*b",0,0,"0.1+1*b"),2,2)
Q1 <- matrix(list("q11",0,0,1),2,2)
Z1 <- matrix(list("1*z1+-1*z2",0,"z2","2*z1","z1",0),3,2)
model.list <- list(B=B1,U=U1,Q=Q1,Z=Z1,A=A1,R=R1,x0=pi1,V0=V1,tinitx=0)