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Constructing variance matrices from other variance matrices


tex2html_wrap_inline33790 tex2html_wrap_inline33790 Syntax

BD>var : v(S tex2html_wrap_inline33794 ,B tex2html_wrap_inline33794 ,B tex2html_wrap_inline33798 )=[(E tex2html_wrap_inline33794 )][v(S tex2html_wrap_inline33798 ,B tex2html_wrap_inline35146 ,B tex2html_wrap_inline35148 )] tex2html_wrap_inline35150 [(E tex2html_wrap_inline33798 )][r(S tex2html_wrap_inline35146 ,B tex2html_wrap_inline35156 ,B tex2html_wrap_inline35158 )] tex2html_wrap_inline34586 (E tex2html_wrap_inline35162 ) tex2html_wrap_inline34586 ... tex2html_wrap_inline33712

where tex2html_wrap_inline35086 are the names of bases which must already exist, tex2html_wrap_inline35088 are valid equations, and tex2html_wrap_inline35090 are belief store numbers.

tex2html_wrap_inline33806 tex2html_wrap_inline33806

This usage of the VAR:  command is used to construct variance matrices from linear combinations of other variance and/or correlation matrices. The naming part indicates that the beliefs being specified are the covariances for belief store number tex2html_wrap_inline34400 between the collection of elements tex2html_wrap_inline35092 and the collection of elements tex2html_wrap_inline35094 . (If tex2html_wrap_inline35096 then tex2html_wrap_inline35098 may be omitted.) The optional coefficients in the linear combination are the equations tex2html_wrap_inline34844 which must be enclosed within round brackets.

The matrices in the linear combination are either variance matrices or correlation matrices. For example, the syntax v(S tex2html_wrap_inline33798 ,B tex2html_wrap_inline35146 ,B tex2html_wrap_inline35148 ) refers to the variance-covariance matrix specified between the collection of elements tex2html_wrap_inline35102 and the collection of elements tex2html_wrap_inline35104 for belief store number tex2html_wrap_inline35180 . (If tex2html_wrap_inline35106 then tex2html_wrap_inline35108 may be omitted.) r(S tex2html_wrap_inline35146 ,B tex2html_wrap_inline35156 ,B tex2html_wrap_inline35158 ) refers to the correlation matrix specified between the collection of elements tex2html_wrap_inline35110 and the collection of elements tex2html_wrap_inline35112 for belief store number tex2html_wrap_inline35188 . (If tex2html_wrap_inline35114 then tex2html_wrap_inline35116 may be omitted.) Where a correlation matrix is indicated, the corresponding covariance matrix is accessed and the correlations calculated temporarily.

The matrices involved in the command must be conformable. You should be careful when you use commands of this kind when the collections in the definition part are neither the same as, nor disjoint to, the collections in the naming part. This is because [B/D] assumes all variance-covariance matrices to be symmetric and thus stores only part of the matrix. Consequently, asymmetries in what you attempt may result in unintended misspecifications. See §6.8.5 for an illustration of this kind of problem. These problems do not arise when (1) tex2html_wrap_inline35118 is disjoint to tex2html_wrap_inline35120 and (2) tex2html_wrap_inline35122 , and similarly for any other pair of collections appearing in the definition part. It is perfectly possible for tex2html_wrap_inline35124 and tex2html_wrap_inline35126 as the definition part is evaluated entirely before being stored.

If an equation such as tex2html_wrap_inline35128 is found without being the coefficient of a succeeding matrix, a matrix of conformable dimensions of scalars all equal to the value of the equation tex2html_wrap_inline35128 is added or subtracted as necessary.


next up previous contents index
Next: Direct numerical specification of Up: Declaring variances and covariances Previous: Declaring single covariances

David Wooff
Wed Oct 21 15:14:31 BST 1998