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# Models with regression variables

A regression variable is a variable x that depends on time but is not defined in the model but rather is defined in the data set in the case of Monolix. In the data set the regression variable is represented by vector $x=\left(x_1, x_2, ..., x_m \right)$  and a vector $\left(t_1, t_2, ..., t_m \right)$, where $x_j=x(t_j)$ is the value of x at time $t_j$.

Note that x is only defined at time points $\left(t_1, t_2, ..., t_m \right)$. For the model evaluation the regression variable must be available at any time t. For this reason the value of the regression variable at any time t is obtained by interpolation. In the current version of Mlxtran, interpolation is performed by using the last given value:

$x(t)=x_j~~\text{for}~~t_j \leq t < t_{j+1}$.

Regression variables are used in the Mlxtran model by defining them as a list in the regressor block of the [LONGITUDINAL] section:

[LONGITUDINAL]
input = {reg_var1, reg_var2, ....}
reg_var1 = {use = regressor}
reg_var2 = {use = regressor}
...

For each regression variable defined in the regressor list of the Monolix Mlxtran model, there must be a column in the data set defined as a regressor column X. Regressors in the data set and in the Monolix Mlxtran model are matched by order, not by name.

Example of regression variables used in Monolix