Maximum Likelihood MT (maxlikmt)
==================================
A maximum likelihood package for **GAUSS**.

Description
----------------
MaxlikMT provides a suite of flexible, efficient and trusted tools for the solution of the maximum likelihood problem with bounds on the parameters.

Installation
--------------
Please `contact us <https://www.aptech.com/contact-us>`_ with to request pricing and installation information.

If you already own **maxlikMT**, you can use the `GAUSS Package Manager <https://www.aptech.com/blog/gauss-package-manager-basics/>`_ to install maxlikMT as well.

Requires GAUSS/GAUSS Light version 17 or higher.

Key Features
------------------------------

Statistical Inference
+++++++++++++++++++++++++++++++
**maxlikmt** provides methods for statistical inference of weighted or unweighted, bounded or unbounded maximum likelihood models.

* Inverted Hessian covariance matrix
* Heteroskedastic-consistent covariance matrix
* Wald confidence limits
* Likelihood ratio statistics
* Bootstrap
* Likelihood profile and Profile ‘t’ traces

Descent methods
+++++++++++++++++++++++++++++++

* BFGS (Broyden, Fletcher, Goldfarb and Powell)
* BHHH (Berndt, Hall, Hall, and Hausman)
* DFP (Davidon, Fletcher and Powell)
* Newton 

Line search methods
+++++++++++++++++++++++++++++++

* STEPBT
* Brent’s method
* Half
* Strong Wolfe’s conditions

Advantages
--------------------------------
Flexible
+++++++++++++++++

* Bounded parameters.
* Specify fixed and free parameters.
* Dynamic algorithm switching.
* Compute all, a subset, or none of the derivatives numerically.
* Easily pass data other than the model parameters as extra input arguments. New!
* Methods to simply create matrices needed for log-likelihood computation from subsets of the parameters.

Efficient
+++++++++++++++

* Threaded and thread-safe.
* Option to avoid computations that are the same for the log-likelihood function and derivatives.
* The tremendous speed of user-defined procedures in **GAUSS** speeds up your estimation.

Trusted
+++++++++++
For more than 30 years, leading researchers have trusted the efficient and numerically sound code in the **GAUSS** maximum likelihood estimation tools to keep them at the forefront of their fields.

Available Optimization Controls
--------------------------------
Optimization controls are set to default values that few users ever need to change.  However, **maxlikmt** is fully customizable and the flexible optimization options can be a great help when tackling more difficult problems.

Control Options
+++++++++++++++++++++++++++++++

.. list-table::
    :widths: auto

   * - Parameter bounds
     - Simple parameter bounds of the type: lower_bd ≤ x_i ≤ upper_bd.
   * - Descent algorithms
     - BFGS, DFP, Newton, and BHHH.
   * - Algorithm switching
     - Specify descent algorithms to switch between based upon the number of elapsed iterations, a minimum change in the objective function, or line search step size.
   * - Weights
     - Observation weights.
   * - Covariance matrix type
     - Compute a ML covariance matrix, a QML covariance matrix, or none.
   * - Alpha
     - Probability level for statistical tests.
   * - Line search method
     - STEPBT (quadratic and cubic curve fit), Brent’s method, BHHHStep, half-step or Strong Wolfe’s Conditions.
   * - Active parameters
     - Control which parameters are active (to be estimated) and which should be fixed to their start value.
   * - Gradient Method
     - Either compute an analytical gradient, or have **maxlikmt** compute a numerical gradient using the forward, central, or backwards difference method.
   * - Hessian Method
     - Either compute an analytical Hessian, or have **maxlikmt** compute a numerical Hessian using the forward, central, or backwards difference method.
   * - Gradient check
     - Compares the analytical gradient computed by the user-supplied function with the numerical gradient to check the analytical gradient for correctness.
   * - Random seed
     - Starting seed value used by the random line search method to allow for repeatable code.
   * - Print output
     - Controls whether (or how often) iteration output is printed and whether a final report is printed.
   * - Gradient step
     - Advanced feature: Controls the increment size for computing the step size for numerical first and second derivatives.
   * - Random search radius
     - The radius of the random search if attempted.
   * - Maximum iterations
     - Maximum iterations to converge.
   * - Maximum elapsed time
     - Maximum number of minutes to converge.
   * - Maximum random search attempts
     - Maximum allowed number of random line search attempts.
   * - Convergence tolerance
     - Convergence is achieved when the direction vector changes less than this amount.


.. toctree::
    :maxdepth: 2
    :hidden:
    :caption: Maximum Likelihood Documents

    user-guide
    command-reference
    mlmt-examples