The mxMatrix function creates MxMatrix objects, which consist of five matrices and a type argument. The values matrix is made up of numeric elements whose usage and capabilities in other functions are defined by the free matrix. If an element is specified as a fixed parameter in the free matrix, then the element in the values matrix is treated as a constant value and cannot be altered or updated by an objective function when included in an mxRun function. If an element is specified as a free parameter in the free matrix, the element in the value matrix is considered a starting value and can be changed by an objective function when included in an mxRun function. Element labels beginning with 'data.'
can be used if the MxMatrix is to be used in an MxModel object that has a raw dataset (i.e., an MxData object of type="raw"
). Such a label instructs OpenMx to use a particular column of the raw dataset to fill in the value of that element. For historical reasons, the variable contained in that column is called a "definition variable." For example, if an MxMatrix element has the label 'data.x'
, then OpenMx will use the first value of the data column named "x" when evaluating the fitfunction for the first row, and will use the second value of column "x" when evaluating the fitfunction for the second row, and so on. After the call to mxRun()
, the values for elements labeled with 'data.x'
are returned as the value from the first (i.e., first before any automated sorting is done) element of column "x" in the data.
Objects created by the mxMatrix()
function are of a specific type, which specifies the number and location of parameters in the labels matrix and the starting values in the values matrix. Input values, free, and labels matrices must be of appropriate shape and have appropriate values for the matrix type requested. Nine types of matrices are supported:
Diag |
matrices must be square, and only elements on the principal diagonal may be specified as free parameters or take non-zero values. All other elements are required to be fixed parameters with a value of 0. |
|
Full
matrices may be either rectangular or square, and all elements in the matrix may be freely estimated. This type is the default for the mxMatrix() function. |
|
Iden
matrices must be square, and consist of no free parameters. Matrices of this type have a value of 1 for all entries on the principal diagonal and the value 0 in all off-diagonal entries. |
|
Lower
matrices must be square, with a value of 0 for all entries in the upper triangle and no free parameters in the upper triangle. |
|
Sdiag
matrices must be square, with a value of 0 for all entries in the upper triangle and along the diagonal. No free parameters in the upper triangle or along the diagonal. |
|
Symm
matrices must be square, and elements in the principle diagonal and lower triangular portion of the matrix may be free parameters of any value. Elements in the upper triangular portion of the matrix are constrained to be equal to those in the lower triangular portion, such that the value and parameter specificiation of the element in row i and column j is identical to to the value and specification of the element in row j and column i. |
|
Stand
matrices are symmetric matrices (see 'Symm') with 1's along the main diagonal. |
|
Unit
matrices may be either rectangular or square, and contain no free parameters. All elements in matrices of this type have a value of 1 for all elements. |
|
Zero
matrices may be either rectangular or square, and contain no free parameters. All elements in matrices of this type have a value of 0 for all elements. |
When type is Lower or Symm, then the arguments to free, values, labels, lbound, or ubound may be vectors of length $N * (N + 1) / 2$, where N is the number of rows and columns of the matrix. When type is Sdiag or Stand, then the arguments to free, values, labels, lbound, or ubound may be vectors of length $N * (N - 1) / 2$.