LINEAR_CAP_AND_LAG_MODEL
========================

Python object: ``phenotypic.schema._linear_cap_and_lag_model.LINEAR_CAP_AND_LAG_MODEL``

Fitted parameters of the double-softplus growth model (with saturation).

Output columns are **metric-qualified**: each header is
``LinearCapAndLagModel_<metric>_<parameter>``, where ``<metric>`` records
the measurement the model was fit on (``self.on`` with its category prefix
stripped, e.g. ``Shape_Area`` → ``Area``). For example, fitting on
``Shape_Area`` emits ``LinearCapAndLagModel_Area_v`` (post-lag growth rate)
and ``LinearCapAndLagModel_Area_s0`` (initial size). The labels below are
the ``<parameter>`` segment; the ``<metric>`` infix is filled in at fit
time.

.. list-table:: Category: **LinearCapAndLagModel**
   :header-rows: 1

   * - Column label
     - Description
     - Type
   * - ``LinearCapAndLagModel_v``
     - The post-lag phase growth rate.
     - :bdg-ref-success:`Tier 1 · Direct phenotype <measurement-tiers>`
   * - ``LinearCapAndLagModel_s0``
     - The initial size
     - :bdg-ref-success:`Tier 1 · Direct phenotype <measurement-tiers>`
   * - ``LinearCapAndLagModel_lambda``
     - The duration of the lag phase
     - :bdg-ref-success:`Tier 1 · Direct phenotype <measurement-tiers>`
   * - ``LinearCapAndLagModel_alpha``
     - lag phase transition sharpness
     - :bdg-ref-primary:`Tier 2 · Descriptive trait <measurement-tiers>`
   * - ``LinearCapAndLagModel_smax``
     - Carrying capacity used by the model. Either the user-provided scalar or the per-group observed maximum.
     - :bdg-ref-success:`Tier 1 · Direct phenotype <measurement-tiers>`
   * - ``LinearCapAndLagModel_beta``
     - Saturation transition sharpness. Fitted per-group when a saturation shoulder is detected and ``beta`` is ``None`` at construction; held at the user-provided scalar (or the module default) when no shoulder is present.
     - :bdg-ref-primary:`Tier 2 · Descriptive trait <measurement-tiers>`
   * - ``LinearCapAndLagModel_mode``
     - Fit variant selected per-group: 'fixed_beta' (beta held at the user-provided or module-default value) or 'fitted_beta' (beta fitted as a 5th free parameter when a saturation shoulder is detected).
     - :bdg-ref-secondary:`Quality <measurement-classification>`