Parameters

The [parameters] block defines all model parameters: fixed effects (theta), between-subject variability (omega), and residual error (sigma).

Theta (Fixed Effects)

theta NAME(initial_value, lower_bound, upper_bound)

• NAME: Parameter name (used in [individual_parameters] expressions)
• initial_value: Starting value for estimation
• lower_bound: Lower bound constraint (must be > 0; parameters are log-transformed internally)
• upper_bound: Upper bound constraint

Example:

theta TVCL(0.134, 0.001, 10.0)
theta TVV(8.1, 0.1, 500.0)
theta TVKA(1.0, 0.01, 50.0)

Omega (Between-Subject Variability)

Diagonal omega

omega NAME ~ variance

• NAME: Random effect name (used in [individual_parameters] as ETA_XXX)
• variance: Initial variance estimate (diagonal element of the omega matrix)

Example:

omega ETA_CL ~ 0.07
omega ETA_V  ~ 0.02
omega ETA_KA ~ 0.40

Each variance represents the between-subject variability for that parameter. The coefficient of variation (CV%) is approximately sqrt(variance) * 100 for log-normally distributed parameters. For example, omega ETA_CL ~ 0.09 corresponds to ~30% CV.

Block omega (correlated random effects)

To estimate correlations between random effects, use block_omega:

block_omega (NAME1, NAME2, ...) = [lower_triangle_values]

The values are the lower triangle of the covariance matrix, specified row-wise. For a 2x2 block:

block_omega (ETA_CL, ETA_V) = [var_CL, cov_CL_V, var_V]

For a 3x3 block:

block_omega (ETA_CL, ETA_V, ETA_KA) = [var_CL, cov_CL_V, var_V, cov_CL_KA, cov_V_KA, var_KA]

You can mix diagonal and block omega specifications. Diagonal omegas specify uncorrelated random effects, while block omegas estimate the full covariance sub-matrix:

block_omega (ETA_CL, ETA_V) = [0.09, 0.02, 0.04]
omega ETA_KA ~ 0.40

This estimates a 3x3 omega where ETA_CL and ETA_V are correlated (2x2 block), but ETA_KA is uncorrelated with both.

Declaration order

The order of omega and block_omega lines in the [parameters] block determines the ETA indexing throughout the model: in the omega matrix and all output. For example:

block_omega (ETA_CL, ETA_V) = [0.09, 0.02, 0.04]
omega ETA_KA ~ 0.40

produces ETA order [ETA_CL, ETA_V, ETA_KA] (indices 1, 2, 3), while:

omega ETA_KA ~ 0.40
block_omega (ETA_CL, ETA_V) = [0.09, 0.02, 0.04]

produces [ETA_KA, ETA_CL, ETA_V] (indices 1, 2, 3). The [individual_parameters] block should list assignments in the same order for clarity, though the parameter mapping is by name, not position.

Sigma (Residual Error)

sigma NAME ~ value

• NAME: Residual error parameter name (referenced in [error_model])
• value: Initial value

Example:

sigma PROP_ERR ~ 0.01
sigma ADD_ERR  ~ 1.0

The interpretation of sigma depends on the error model:

Complete Examples

Diagonal omega (no correlations):

[parameters]
  theta TVCL(0.134, 0.001, 10.0)
  theta TVV(8.1, 0.1, 500.0)
  theta TVKA(1.0, 0.01, 50.0)

  omega ETA_CL ~ 0.07
  omega ETA_V  ~ 0.02
  omega ETA_KA ~ 0.40

  sigma PROP_ERR ~ 0.01

Block omega (correlated CL and V):

[parameters]
  theta TVCL(0.134, 0.001, 10.0)
  theta TVV(8.1, 0.1, 500.0)
  theta TVKA(1.0, 0.01, 50.0)

  block_omega (ETA_CL, ETA_V) = [0.09, 0.02, 0.04]
  omega ETA_KA ~ 0.40

  sigma PROP_ERR ~ 0.01