Maximum Likelihood MT (maxlikmt)

A maximum likelihood package for GAUSS.


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


Please contact us with to request pricing and installation information.

If you already own maxlikMT, you can use the GAUSS Package Manager to install maxlikMT as well.

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


  • Brent’s method

  • Half

  • Strong Wolfe’s conditions



  • 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.


  • 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.


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

: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.


Observation weights.

Covariance matrix type

Compute a ML covariance matrix, a QML covariance matrix, or none.


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.