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When declaring parameters in the parameters block using Dim(), you can specify a type to automatically apply structural constraints. These constraints ensure that parameters remain within their valid mathematical space during estimation.

Details

Standard Types:

  • "vector", "matrix", "array": Standard unconstrained containers. Use lower and upper for element-wise bounds.

Ordering Constraints:

  • "ordered": A vector where $x_1 < x_2 < ... < x_K$.

  • "positive_ordered": A vector where $0 < x_1 < x_2 < ... < x_K$.

Constrained Vectors:

  • "simplex": A vector where all elements are >= 0 and sum(x) = 1.

  • "centered": A vector of length K where sum(x) = 0. (Estimated using K-1 degrees of freedom).

Correlation and Covariance Matrices:

  • "corr_matrix": A symmetric, positive-definite correlation matrix (diagonal elements are 1).

  • "cov_matrix": A symmetric, positive-definite covariance matrix.

  • "CF_corr": The Cholesky factor of a correlation matrix.

  • "CF_cov": The Cholesky factor of a covariance matrix (diagonal elements are positive).

Special Structural Matrices:

  • "lower_tri": A lower-triangular matrix.

  • "positive_lower_tri": A lower-triangular matrix with positive diagonal elements.

  • "centered_matrix": A matrix where each column sums to zero.

  • "centered_tri": A triangular matrix with column-wise sum-to-zero constraints (often used for identification in factor analysis).