SOFTWARE/GAUSS 13
 

GAUSS Applications

Pre-written, customizable GAUSS programs designed to increase user productivity and extend GAUSS functionality in the fields of statistics, finance, engineering, physics, risk analysis and more.

Algorithmic Derivatives
A program for generating GAUSS procedures for computing algorithmic derivatives.
Constrained Maximum Likelihood MT
Constrained Maximum Likelihood MT provides for the estimation of statistical models by maximum likelihood while allowing for the imposition of general constraints on the parameters, linear or nonlinear, equality or inequality, as well as bounds.
Constrained Optimization MT Basic sample statistics including means, frequencies and crosstabs.
Constrained Optimization Solves the nonlinear programming problem subject to general constraints on the parameters. 
CurveFit
Nonlinear curve fitting.
Descriptive Statistics MT
Basic sample statistics including means, frequencies and crosstabs. This application is thread-safe and takes advantage of structures.
Discrete Choice  A statistical package for estimating discrete choice and other models in which the dependent variable is qualitative in some way.
FANPAC MT Comprehensive suite of GARCH (Generalized AutoRegressive Conditional Heteroskedastic) models for estimating volatility.
Linear Programming MT
Solves small and large scale linear programming problems
Linear Regression MT
Least squares estimation.
Loglinear Analysis MT
Analysis of categorical data using loglinear analysis.
Maximum Likelihood MT
Maximum likelihood estimation of the parameters of statistical models; uses structures, allowing calls to be safely nested or called in threaded programs, and some calculations are themselves threaded.
Maximum Likelihood
Maximum likelihood estimation of the parameters of statistical models.
Nonlinear Equations MT
Solves systems of nonlinear equations having as many equations as unknowns.
Optimization MT
Unconstrained optimization; uses structures, allowing calls to be safely nested or called in threaded programs, and some calculations are themselves threaded.
Optimization
Unconstrained optimization.
Time Series MT
Exact ML estimation of VARMAX, VARMA, ARIMAX, ARIMA, and ECM models subject to general constraints on the parameters. Panel data estimation. Unit root and cointegration tests.


Algorithmic Derivatives

The GAUSS AD 1.0 module is an application program for generating GAUSS procedures for computing algorithmic derivatives. A major achievement of AD is improved accuracy for optimization. Numerical derivatives invariably produce a loss of precision. The loss of precision is greater for standard errors than it is for estimates.

At the default tolerance, Constrained Maximum Likelihood (CML) and Maximum Likelihood (Maxlik) can be expected generally to have four or five places of accuracy, whereas standard errors will have about two places. Accuracy essentially doubles with AD. AD works independently of any application to improve derivatives, and it can be used with any application that uses derivatives.

For some types of optimization problems, convergence is accelerated. Iterations are faster and fewer of them are needed to achieve convergence. The types of problems that will see the most improvement are those with a large amount of computation.

Constrained Maximum Likelihood 2.0.6+ and Maximum Likelihood 5.0.7+ have been updated to improve speed with AD.

Available for Windows, LINUX, and Mac. Requires GAUSS Mathematical and Statistical System 6.0 or the GAUSS Engine 6.0.


Constrained Mamximum Lkelihood MT (CMLMT) i

Features
  • Parameter Estimation
  • Statistical Inference – Wald, Bootstrap, Confidence Limits by Inversion
  • Heteroskedastic-consistent Covariance Matrix of Parameters
  • Profile Likelihood
  • Weighted Maximum Likelihood
  • BFGS, DFP, Newton, BHHH descent algorithms
  • Stepbt, Brent, Half Step, Augmented Penalty, BHHH step, Wolfe’s Line Search Methods
  • Numerical Gradient, Hessian
Maximum Likelihood Estimation

Provide a GAUSS procedure for computing the log-likelihood of your statistical model, and Constrained Maximum Likelihood MT does the rest.  Using an iterative Sequential Quadratic Programming method parameter estimates along with standard errors and confidence limits are generated.

Example

Suppose we have a dependent variable that is observed in several ordered categories.  We might estimate coefficients of a regression on this variable using the ordered probit model:



where



and



Assuming we have



wherewhere  is the Normal cumulative distribution function.

The log-likelihood function for this model is



The cmlmt function that performs the estimation takes four arguments, (1) a pointer to the procedure that computes the log-likelihood, (2) a PV parameter structure containing the start values of the parameters, (3) a DS data structure, and (4) a control structure.

GAUSS structures are simply bins containing other objects such as matrices, strings, arrays, etc.  They can be defined by the programmer, but the two of the structures used by cmlmt are defined in the Run-Time Library, and the control structure is defined in the cmlmt library.

The PV Parameter Structure

The PV parameter structure is created and filled using GAUSS Run-Time Library functions.  Using these functions the structure can be filled with vectors, matrices, and arrays containing starting parameter values.  Masks can be used to specify fixed versus free parameters.  For example,

struct PV p0;

// creates a default parameter structure
p0 = pvCreate;

p0 = pvPack(p0,.5|.5|.5,”beta”);
p0 = pvPackm(p0,-30|-1|1|30,”tau”,0|1|1|0);


The structure now contains starting values for a 3×1 vector of coefficients called beta,and another 4×1 vector of thresholds called tau. It will be convenient for the calculation of the log-likelihood for the first and last be parameters set to -30 and +30.  The fourth argument is a mask specifying the first and last elements of the vector to be fixed and the remaining elements free parameters to be estimated.

The DS Data Structure

The DS data structure is a general purpose bucket of GAUSS types.  It contains one of each of the types, matrix, array, string, string array, sparse matrix, and scalar.  It is passed to the log-likelihood procedure untouched by cmlmt.  It can be used by programmers in any way they choose to help in computing the log-likelihood.  Typically it is used to pass data to the procedure.  The DS structure can also be reshaped into a vector of structures giving the programmer great flexibility in handling data and other information.
load x[200,5] = data.csv;

struct DS d0;

// creates a 2x1 vector of
// default data structures
d0 = reshape(dsCreate,2,1);  

// dependent variable
d0[1].dataMatrix = x[.,1];   

// independent variables
d0[2].dataMatrix = x[.,2:4];

The cmlmtControl Structure

This structure handles the matrices and strings that control the estimation process such as setting the descent algorithm, the line search method, and so on.  It is also used to specify the constraints.  For example the thresholds need to be constrained in the following way where .  This implies the two free constraints

The programmer will accomplish by specifing two members of the cmlmtControl structure, C and D, to impose this inequality constraint

where x is the vector of parameters being estimated.  Then

struct cmlmtControl c0;

// creates a default structure
c0 = cmlmtControlCreate;

c0.C = { 0  0  0 -1  1  0,
         0  0  0  0 -1  1 };

c0.D = { 0,
         0 };

The first three columns of the matrix c0.C and the vector c0.D are associated with regression coefficients that are unconstrained and the last two are associated with the thresholds.

The Log-likelihood Procedure

The programmer now writes a GAUSS procedure computing a vector of log-likelihood probabilities.  This procedure has three input arguments, the PV parameter structure, the DS data structure, and 3×1 vector the first element of which is nonzero if cmlmt is requesting the vector of log-likelihood probabilities, the second element nonzero if it is requesting the matrix of first derivatives with respect to the parameters, and the third element nonzero if it is requesting the Hessian or array of second derivatives with respect to the parameters.  It has one return argument, a modelResults structure containing the results.

proc orderedProbit(struct PV p, struct DS d, ind);
   local mu, tau, beta, emu, eml;
   struct modelResults mm;

   if ind[1] == 1;
      tau = pvUnpack(p,”tau”);
      beta = pvUnpack(p,”beta”);
      mu = d[2].dataMatrix * beta;
      eml = submat(tau,d[1].dataMatrix,0) – mu;
      emu = submat(tau,d[1].dataMatrix + 1,0) – mu;
      mm.function = ln(cdfn(emu) – cdfn(eml));
   endif;
retp(mm);
endp;

The GAUSS submat function serves to pull out the k-th element of tau for the i-th row of d[1].datamatrix set to k.

Since this procedure doesn’t return a matrix of first derivatives nor an array of second derivatives they will be computed numerically by cmlmt.

The result stored in mm.function is an Nx1 vector of log-probabilities computed by observation.  If we were to have provided analytical derivatives, the first derivatives would be an Nxm matrix of derivatives computed by observation where m is the number of parameters to be estimated, and the second derivatives would be an Nxmxm array of second derivatives computed by observation.  Computing these quantities in this way improves accuracy.  It also allows for the BHHH descent method which is more accurate than other methods permitting a larger convergence tolerance.

It is also possible to return a scalar log-likelihood which is the sum of the individual log-probabilities.  In this case the analytical first derivatives would be a 1xm gradient vector, and the second derivatives a 1xmxm array.  You would also need to set c0.numObs to the number of observations since cmlmt is no longer able to determine the number of observations from the length of the vector of log-probabilities.

The Command File

Finally we put it all together in the command file:

library cmlmt;

// contains the structure definitions
#include cmlmt.sdf;  

// simulating data here
x = rndn(200,3);
b = { .4, .5, .6 };
ystar = x*b;
tau = { -50, -1, 0, 1, 50 };

y = (ystar .> tau[1] .and ystar .<= tau[2]) +
   2 * (ystar .> tau[2] .and ystar .<= tau[3]) +
   3 * (ystar .> tau[3] .and ystar .<= tau[4]) +
   4 * (ystar .> tau[4] .and ystar .<= tau[5]);

struct DS d0;

// creates a 2x1 vector of
// default data structures
d0 = reshape(dsCreate,2,1);  

// dependent variable
d0[1].dataMatrix = y; 

// independent variables
d0[2].dataMatrix = x; 

struct PV p0;

// creates a default parameter structure
p0 = pvCreate;

p0 = pvPack(p0,.5|.5|.5,"beta");
p0 = pvPackm(p0,-30|-1|0|1|30,"tau",0|1|1|1|0);

struct cmlmtControl c0;

// creates a default structure
c0 = cmlmtControlCreate; 

c0.C = { 0  0  0 -1  1  0,
         0  0  0  0 -1  1 };

c0.D = { 0,
         0};

struct cmlmtResults out;

out = cmlmt(&orderedProbit,p0,d0,c0);

// prints the results
call cmlmtprt(out);

proc orderedProbit(struct PV p, struct DS d, ind);
   local mu, tau, beta, emu, eml;
   struct modelResults mm;

   if ind[1] == 1;
      tau = pvUnpack(p,"tau");
      beta = pvUnpack(p,"beta");
      mu = d[2].dataMatrix * beta;
      eml = submat(tau,d[1].dataMatrix,0) - mu;
      emu = submat(tau,d[1].dataMatrix + 1,0) - mu;
      mm.function = ln(cdfn(emu) - cdfn(eml));
   endif;

retp(mm);
endp;

This program produces the following output:

================================================================

CMLMT Version 2.0.7         3/30/2012   1:29 pm

=================================================================

return code =    0

normal convergence

Log-likelihood        -15.1549

Number of cases     200

Covariance of the parameters computed by the following method:

ML covariance matrix

Parameters    Estimates     Std. err.  Est./s.e.  Prob.    Gradient

------------------------------------------------------------------

beta[1,1]    4.2060        0.2385      17.634   0.0000      0.0000

beta[2,1]    5.3543        0.2947      18.166   0.0000      0.0000

beta[3,1]    6.2839        0.2789      22.531   0.0000      0.0000

tau[2,1]   -10.7561        0.7437     -14.462   0.0000      0.0000

tau[3,1]    -0.0913        0.2499      -0.365   0.7148      0.0000

tau[4,1]    10.6693        0.5697      18.727   0.0000      0.0000

Correlation matrix of the parameters

1     0.52064502     0.54690534    -0.46731768    0.046211496    0.57202935

0.52064502     1     0.58363048    -0.47574225   -0.061765839    0.65959766

0.54690534     0.58363048     1    -0.5169026    -0.0059238287   0.69077806

-0.46731768   -0.47574225    -0.5169026      1    0.0046253798  -0.44858539

0.046211496  -0.061765839   -0.0059238287   0.0046253798    1  -0.01457591

0.57202935    0.65959766     0.69077806    -0.44858539     -0.01457591   1

Wald Confidence Limits

0.95 confidence limits

Parameters    Estimates     Lower Limit   Upper Limit   Gradient

----------------------------------------------------------------------

beta[1,1]    4.2060        3.7355        4.6764        0.0000

beta[2,1]    5.3543        4.7730        5.9356        0.0000

beta[3,1]    6.2839        5.7338        6.8339        0.0000

tau[2,1]   -10.7561      -12.2230       -9.2893        0.0000

tau[3,1]    -0.0913       -0.5842        0.4015        0.0000

tau[4,1]    10.6693        9.5457       11.7929        0.0000

Number of iterations    135

Minutes to convergence     0.00395


Constrained Optimization MT (COMT) solves the Nonlinear Programming problem, subject to general constraints on the parameters – linear or nonlinear, equality or inequality, using the Sequential Quadratic Programming method in combination with several descent methods selectable by the user:
  • Newton-Raphson
  • quasi-Newton (BFGS and DFP)
  • Scaled quasi-Newton
There are also several selectable line search methods. A Trust Region method is also available which prevents saddle point solutions. Gradients can be user-provided or numerically calculated. COMT is fast and can handle large, time-consuming problems because it takes advantage of the speed and number-crunching capabilities of GAUSS. It is thus ideal for large scale Monte Carlo or bootstrap simulations.

New Features
  • Internally threaded functions
  • Uses structures
  • Improved algorithm
  • Allows for computing a subset of the derivatives analytically, and for combining the calculation of the function and derivatives, thus reducing calculations in common between function and derivatives
Threading in COMT

If you have a multi-core processor you may take advantage of COMT’s internally threaded functions. An important advantage of threading occurs in computing numerical derivatives. If the derivatives are computed numerically, threading will significantly decrease the time of computation.
Example

We ran a time trial of a covariance-structure model on a quad-core machine. As is the case for most real world problems, not all sections of the code are able to be run in parallel. Therefore, the theoretical limit for speed increase is much less than (single-threaded execution time)/(number of cores).

Even so, the execution time of our program was cut dramatically:

Single-threaded execution time: 35.42 minutes
Multi-threaded execution time: 11.79 minutes

That is a nearly 300% speed increase!

The DS Structure

COMT uses the DS and PV structures that are available in the GAUSS Run-Time Library.

The DS structure is completely flexible, allowing you to pass anything you can think of into your procedure. There is a member of the structure for every GAUSS data type.

struct DS {
scalar type;
matrix dataMatrix;
array dataArray;
string dname;
string array vnames;
};

The PV Structure

The PV structure revolutionizes how you pass the parameters into the procedure. No longer do you have to struggle to get the parameter vector into matrices for calculating the function and its derivatives, trying to remember, or figure out, which parameter is where in the vector.

If your log-likelihood uses matrices or arrays,you can store them directly into the PV structure and remove them as matrices or arrays with the parameters already plugged into them. The PV structure can handle matrices and arrays in which some of their elements are fixed and some free. It remembers the fixed parameters and knows where to plug in the current values of the free parameters. It can also handle symmetric matrices in which parameters below the diagonal are repeated above the diagonal.

b0 – Mean paramters.
garch – GARCH parameters.
arch – ARCH parameters.
omega – Constant in variance equation.

There is no longer any need to use global variables. Anything the procedure needs can be passed into it through the DS structure. And these new applications uses control structures rather than global variables. This means, in addition to thread safety, that it is straightforward to nest calls to COMT inside of a call to COMT, QNewtonmt, QProgmt, or EQsolvemt.




 Available for Windows, Mac, Linux and Solaris. Requires GAUSS/GAUSS Light version 10 or higher.


Constrained Optimization (CO)

CO is an applications module written in the GAUSS programming language. It solves the Nonlinear Programming problem, subject to general constraints on the parameters - linear or nonlinear, equality or inequality, using the Sequential Quadratic Programming method in combination with several descent methods selectable by the user - Newton-Raphson, quasi-Newton (BFGS and DFP), and scaled quasi-Newton. There are also several selectable line search methods. A Trust Region method is also available which prevents saddle point solutions. Gradients can be user-provided or numerically calculated.

CO is fast and can handle large, time-consuming problems because it takes advantage of the speed and number-crunching capabilities of GAUSS. It is thus ideal for large scale Monte Carlo or bootstrap simulations.

Example

A Markowitz mean/variance portfolio allocation analysis on a thousand or more securities would be an example of a large scale problem CO could handle.

CO also contains a special technique for semi-definite problems, and thus it will solve the Markowitz portfolio allocation problem for a thousand stocks even when the covariance matrix is computed on fewer observations than there are securities.

Because CO handles general nonlinear functions and constraints, it can solve a more general problem than the Markowitz problem. The efficient frontier is essentially a quadratic programming problem where the Markowitz Mean/Variance portfolio allocation model is solved for a range of expected portfolio returns which are then plotted against the portfolio risk measured as the standard deviation:



where l is a conformable vector of ones, and where is the observed covariance matrix of the returns of a portfolio of securities, and µ are their observed means.

This model is solved for



and the efficient frontier is the plot of rk on the vertical axis against



on the horizontal axis. The portfolio weights in Wk describe the optimum distribution of portfolio resources across the securities given the amount of risk to return one considers reasonable.

Because of CO's ability to handle nonlinear constraints, more elaborate models may be considered. For example, this model frequently concentrates the allocation into a minority of the securities. To spread out the allocation one could solve the problem subject to a maximum variance for the weights, i.e., subject to



where  is a constant setting a ceiling on the sums of squares of the weights.

correlation matrix



This data was taken from from Harry S. Marmer and F.K. Louis Ng, "Mean-Semivariance Analysis of Option-Based Strategies: A Total Asset Mix Perspective", Financial Analysts Journal, May-June 1993.

An unconstrained analysis produced the results below:



It can be observed that the optimal portfolio weights are highly concentrated in T-bills.

Now let us constrain w´w to be less than, say, .8. We then get:



The constraint does indeed spread out the weights across the categories, in particular stocks seem to receive more emphasis.



Efficient portfolio for these analyses

We see there that the constrained portfolio is riskier everywhere than the unconstrained portfolio given a particular portfolio return.

In summary, CO is well-suited for a variety of financial applications from the ordinary to the highly sophisticated, and the speed of GAUSS makes large and time-consuming problems feasible.

CO is an advanced GAUSS Application and comes as GAUSS source code.

GAUSS Applications are modules written in GAUSS for performing specific modeling and analysis tasks. They are designed to minimize or eliminate the need for user programming while maintaining flexibility for non-standard problems.

Available for Windows, Mac, Linux and Solaris. Requires GAUSS/GAUSS Light version 8.0 or higher.

CurveFit Given data and a procedure for computing the function, CurveFit will find a best fit of the data to the function in the least squares sense.

Special Features

  • Weight observations
  • Multiple dependent variables
  • Bootstrap estimation
  • Histogram and surface plots of bootstrapped coefficients
  • Profile t, and profile likelihood trace plots
  • Levenberg-Marquardt descent method
  • Polak-Ribiere conjugate gradient descent method
  • Ability to activate and inactivate coefficients
  • Heteroskedastic-consistent covariance matrix of coefficients

Bootstrap Estimation

CurveFit includes special procedures for computing bootstrapped estimates. One procedure produces a mean vector and covariance matrix of the bootstrapped coefficients. Another generates histogram plots of the distribution of the coefficients and surface plots of the parameters in pairs. The plots are especially valuable for nonlinear models because the distributions of the coefficients may not be unimodal or symmetric. 

Profile t, and Profile Likelihood Trace Plots

Also included in the module is a procedure that generates profile t trace plots and profile likelihood trace plots using methods described in Bates and Watts, "Nonlinear Regression Analysis and its Applications". Ordinary statistical inference can be very misleading in nonlinear models. These plots are superior to usual methods in assessing the statistical significance of coefficients in nonlinear models.

Descent Methods

The primary descent method for the single dependent variable is the classical Levenberg-Marquardt method. This method takes advantage of the structure of the nonlinear least squares problem, providing a robust and swift means for convergence to the minimum. If, however, the model contains a large number of coefficients to be estimated, this method can be burdensome because of the requirement for storing and computing the information matrix. For such models the Polak-Ribiere version of the conjugate gradient method is provided, which does not require the storage or computation of this matrix.

Multiple Dependent Variables

CurveFit allows multiple dependent variables using a criterion function permitting the interpretation of the estimated coefficients as either maximum likelihood estimates or as Bayesian estimates with a noninformative prior. This feature is useful for estimating the parameters of "compartment" models, i.e., models arising from linear first order differential equations. 

Available for Windows, Mac, Linux and Solaris. Requires GAUSS/GAUSS Light version 8.0 or higher.

Descriptive Statistics (MT 1.0)

The procedures in Descriptive Statistics MT 1.0 provide basic statistics for the variables in GAUSS data sets. These statistics describe and test univariate and multivariate features of the data and provide information for further analysis. Descriptive Statistics MT 1.0 is a new product that is thread-safe and takes advantage of structures. 

  • Includes methods for analyzing and generating contingency
    tables and statistics for them.
  • Includes new routines to compute descriptive statistics,
    including both univariate and multivariate skew and kurtosis.
  • Includes support for variable names of up to 32 characters.
  • Includes support for date variables where applicable.
  • You can now choose between two report types-all variables
    in a single table or individual reports for each variable-and
    you can choose which statistics to include in the report and
    the order in which they appear.
Descriptive Statistics MT 1.0 has methods for analyzing and generating contingency tables and producing statistics for them:
  • Chi-Squared (Pearson and Likelihood Ratio)
  • Phi
  • Cramer's V
  • Spearman s Rho
  • Goodman-Krustal's Gamma Kendall's Tau-B Stuart s Tau-C Somer's D
  • Lamda
Descriptive Statistics MT 1.0 also has methods for generating frequency distributions with statistics, skew and kurtosis, and tests for differences of means.

Available for Windows, Mac, Linux and Solaris. Requires GAUSS/GAUSS Light version 8.0 or higher.


Discrete Choice is a package for the fitting of a variety of models with categorical dependent variables. These models are particularly useful for researchers in the social, behavioral, and biomedical sciences, as well as economics, public choice, education, and marketing.

Output for these models includes full information maximum likelihood estimates with either standard and quasi-maximum likelihood inference. In addition, estimates of marginal effects are computed either as partials of the probabilities with respect to the means of the exogenous variables or optionally as the average partials of the probabilities with respect to the exogenous variables.

Models
Nested logit model
  • Is derived from the assumption that residuals have a generalized extreme value distribution and allows for a general pattern of dependence among the responses thus avoiding the IIA problem, i.e., the "independence of irrelevant alternatives."
Conditional logit model
  • Includes both variables that are attributes of the responses as well as, optionally, exogenous variables that are properties of cases.
Multinomial logit model
  • Qualitative responses are each modeled with a separate set of regression coefficients
Adjacent category multinomial logit model
  • The log-odds of one category versus the next higher category is linear in the cutpoints and explanatory variables
Stereotype multinomial logit model
  • The coefficients of the regression in each category are linear functions of a reference regression
Poisson regression, left or right truncated, left or right censored, or zero-inflated models
  • Estimates model with Poisson distributed dependent variable. This includes censored models - the dependent variable is not observed but independent variables are available - and truncated models where not even the independent variables are observed. Also, a zero-inflated Poisson model can be estimated where the probability of the zero category is a mixture of a Poisson consistent probability and an excess probability. The mixture coefficient can be a function of independent variables.
Negative binomial regression, left or right truncated, left or right censored, or zero-inflated models
  • Estimates model with negative binomial distributed dependent variable. This includes censored models - the dependent variable is not observed but independent variables are available - and truncated models where not even the independent variables are observed. Also, a zero-inflated negative binomial model can be estimated where the probability of the zero category is a mixture of a negative binomial consistent probability and an excess probability. The mixture coefficient can be a function of independent variables.
Logit, probit models
  • Estimates dichotomous dependent variable with either Normal or extreme value distributions
Ordered logit, probit models
  • Estimates model with an ordered qualitative dependent variable with Normal or extreme value distributions
Available for Windows, Mac, Linux and Solaris. Requires GAUSS/GAUSS Light version 8.0 or higher.


FANPAC MT 3.0

FANPAC MT is a set of threadsafe keyword commands and procedures for the econometric analysis of financial data. More specifically, the estimation of parameters of time series models via the maximum likelihood method. The package is divided into two parts:

The package is divided into two parts:
  • Easy-to-program keyword commands which simplify the modeling process
  • GAUSS procedures, which can be called directly to perform the computations, allowing for great flexibility

New features

FANPAC MT 3.0 gives econometricians and financial professionals access to many new multivariate models, which provide a better fit for some financial problems. New models/features are listed in orange.


fanpacmt3.0


Available for Windows, Mac, Linux and Solaris. Requires GAUSS/GAUSS Light version 8.0 or higher.



Linear Programming MT

Linear Programming MT Module solves the standard linear programming problem with the following NEW and CUTTING-EDGE features:

  • Thread-safe Execution: Control variables are model matrices are contained in structures allowing thread-safe execution of programs.
  • Sparse matrices: Linear Programming MT exploits sparse matrix technology permitting the analysis of problems with very large constraint matrices. The size of a problem that can be analyzed is dependent on the speed and amount of memory on the computer, but problems with two to three thousand constraints and more than six thousand variables have been tested on ordinary PC's.
  • MPS files: procedures are available for translating MPS formatted files.

Other Product Features

LPMT is designed to solve small and large scale linear programming problems. LPMT can be initialized with a starting value, such as the solution to a previous problem which is similar to the one being solved. This feature can dramatically reduce the number of iterations required to find a feasible starting point.

Features
  • Upper and lower finite bounds can be provided for variables and constraints
  • Problem type (minimization or maximization)
  • Constraint types (<=, >=, =)
  • Choice of tolerances
  • Pivoting rules
Computes
  • The value of the variables and the objective function upon termination, and returns the dual variables
  • State of each constraint
  • Uniqueness and quality of solution
  • Multiple optimal solutions if they exist
  • Number of iterations required
  • A final basis
  • Can generate iterations log and/or final report, if requested

Available for Windows, Mac, Linux and Solaris. Requires GAUSS/GAUSS Light version 8.0 or higher.

Linear Regression MT

The Linear Regression MT application module is a set of procedures for estimating single equations or a simultaneous system of equations. It allows constraints on coefficients, calculates het-con standard errors, and includes two-stage least squares, three-stage least squares, and seemingly unrelated regression. It is thread-safe and takes advantage of structures found in later versions of GAUSS. 

Features

  • Calculates heteroskedastic-consistent standard errors, and performs both influence and collinearity diagnostics inside the ordinary least squares routine (OLS)
  • All regression procedures can be run at a specified data range
  • Performs multiple linear hypothesis testing with any form
  • Estimates regressions with linear restrictions
  • Accommodates large data sets with multiple variables
  • Stores all important test statistics and estimated coefficients in an efficient manner
  • Both three-stage least squares and seemingly unrelated regression can be estimated iteratively
  • Thorough Documentation
  • The comprehensive user's guide includes both a well-written tutorial and an informative reference section. Additional topics are included to enrich the usage of the procedures. These include:
    • Joint confidence region for beta estimates
    • Tests for heteroskedasticity
    • Tests of structural change
    • Using ordinary least squares to estimate a translog cost function
    • Using seemingly unrelated regression to estimate a system of cost share equations
    • Using three-stage least squares to estimate Klein's Model I
Available for Windows, Mac, Linux and Solaris. Requires GAUSS/GAUSS Light version 8.0 or higher.

Loglinear Analysis MT

The Loglinear Analysis MT application module (LOGLIN) contains procedures for the analysis of categorical data using loglinear analysis. This application is thread-safe and takes advantage of structures.

The estimation is based on the assumption that the cells of the K-way table are independent Poisson random variables. The parameters are found by applying the Newton-Raphson method using an algorithm found in A. Agresti (1984) Analysis of Ordinal Categorical Data.

You may construct your own design matrix or use LOGLIN procedures to compute one for you. You may also select the type of constraint and the parameters. 

Features

  • Fits a hierarchical model given fit configurations
  • Will fit all 3-way hierarchical models of a table
  • Provides for cell weights
  • LOGLIN can estimate most of the models described in such texts as Y.M.M. Bishop, S.E. Fienberg, and P.W. Holland (1975) Discrete Multivariate Analysis, S. Haberman (1979) Analysis of Qualitative Data, Vols. 1 and 2, as well as the book by A. Agresti.

Available for Windows, Mac, Linux and Solaris. Requires GAUSS/GAUSS Light version 8.0 or higher.

Maximum Likelihood (MaxlikMT) MT 2.0

MaxlikMT 2.0 contains a set of procedures for the solution of the maximum likelihood problem with bounds on parameters.

Major Features of MaxLikMT

  • Structures
  • Simple bounds
  • Hypothesis testing for models with bounded parameters
  • Log-likelihood function
  • AlgorithmSecant algorithms
  • Line search methods
  • Weighted maximum likelihood
  • Active and inactive parameters
  • Bounds
In MaxlikMT, the same procedure computing the log-likelihood or objective function will be used to compute analytical derivatives as well if they are being provided. Its return argument is a maxlikmtResults structure with three members, a scalar, or Nx1 vector containing the log-likelihood (or objective), a 1xK vector, or NxK matrix of first derivatives, and a KxK matrix or NxKxK array of second derivatives (it needs to be an array if the log-likelihood is weighted).

Of course the derivatives are optional, or even partially optional, i.e., you can compute a subset of the derivatives if you like and the remaining will be computed numerically. This procedure will have an additional argument which tells the function which to compute, the log-likelihood or objective, the first derivatives, or the second derivatives, or all three. This means that calculations in common will not have to be redone.

Available for Windows, Mac, Linux and Solaris. Requires GAUSS/GAUSS Light version 10 or higher; Linux requires version 10.0.4 or higher.


Maximum Likelihood (MAXLIK)

MAXLIK performs maximum likelihood estimation of the parameters of statistical models. All you provide is a GAUSS function to calculate the log-likelihood for a set of observations. MAXLIK does the rest.

Major Features of Maximum Likelihood
  • More than 25 user-selectable options control the optimization
  • Fast Procedures: FASTMAX, FASTBoot, FASTBayes, FASTProfile, and FASTPflCLimits can speed convergence times up to 800 percent over earlier versions of MAXLIK, depending on the type of problem.
  • "Kiss-Monster" random numbers used in the bootstrap procedure and random line search algorithm.
  • The bootstrap and random line search procedures use the new "Kiss-Monster" random number generator. It has a period of 10^8859, long enough for serious Monte Carlo work.
  • Descent algorithms include: BFGS (Broyden-Fletcher-Goldfarb-Shanno), DFP (Davidon-Fletcher-Powell), Newton, steepest descent, PRCG (Polak-Ribiere-type conjugate gradient), and BHHH (Berndt-Hall-Hall-Hausman)
  • Step-length methods include: STEPBT, BRENT, BHHHSTEP, and a step-halving method
  • A "switching" method may also be selected which switches the algorithm during the iterations according to three criteria: number of iterations, failure of the function to decrease within a tolerance, or decrease of the line search step length below a tolerance
Improved Algorithm

MAXLIK implements the Cholesky factorization, solve, and update methods for the BFGS, DFP, and Newton algorithms. Event Count and Duration Regression

An included COUNT module (by Gary King, Harvard University) estimates limited dependent variable models. These procedures provide maximum likelihood estimator s for parametric regression models of events data, i.e., models with dependent variables that are measured either as event counts or as durations between events.
Available for Windows, Mac, Linux and Solaris. Requires GAUSS/GAUSS Light version 8.0 or higher.

Nonlinear Equations MT

The Nonlinear Equations MT applications module (NLSYS) solves systems of nonlinear equations where there are as many equations as unknowns. This application is thread-safe and takes advantage of structures found in later versions of GAUSS.

The functions must be continuous and differentiable. You may provide a function for calculating the Jacobian, if desired. Otherwise NLSYS will compute the Jacobian numerically. You can also select from two descent algorithms, the Newton method or the secant update method, and from two step-length methods, a quadratic/cubic method, or the hookstep method.

Available for Windows, Mac, Linux and Solaris. Requires GAUSS/GAUSS Light version 8.0 or higher.

Optimization MT (OPMT) 1.0

OPMT is intended for the optimization of functions. It has many features, including a wide selection of descent algorithms, step-length methods, and "on-the-fly" algorithm switching. Default selections permit you to use Optimization with a minimum of programming effort. All you provide is the function to be optimized and start values, and OPMT does the rest.

Special Features in Optimization MT 1.0

  • Internally threaded.

  • Uses structures. 

  • Allows for placing bounds on the parameters. 

  • Allows for computing a subset of the derivatives analytically, and for combining the calculation of the function and derivatives, thus reducing calculations in common between function and derivatives.

  • More than 25 options can be easily specified by the user to control the optimization
  • Descent algorithms include: BFGS, DFP, Newton, steepest descent, and PRCG
  • Step length methods include: STEPBT, BRENT, and a step-halving method
  • A "switching" method may also be selected which switches the algorithm during the iterations according to two criteria: number of iterations, or failure of the function to decrease within a tolerance

Available for Windows, Mac, Linux and Solaris. Requires GAUSS/GAUSS Light version 10 or higher.


Optimization

Optimization is intended for the optimization of functions. It has many features, including a wide selection of descent algorithms, step-length methods, and "on-the-fly" algorithm switching. Default selections permit you to use Optimization with a minimum of programming effort. All you provide is the function to be optimized and start values, and Optimization does the rest.

Features
  • More than 25 options can be easily specified by the user to control the optimization
  • Descent algorithms include: BFGS, DFP, Newton, steepest descent, and PRCG
  • Step length methods include: STEPBT, BRENT, and a step-halving method
  • A "switching" method may also be selected which switches the algorithm during the iterations according to two criteria: number of iterations, or failure of the function to decrease within a tolerance
Improved Algorithm

Optimization implements the numerically superior Cholesky factorization, solve and update methods for the BFGS, DFP, and Newton algorithms. The Hessian, or its estimate, are updated rather than the inverse of the Hessian, and the descent is computed using a solve. This results in better accuracy and improved convergence over previous methods.

Available for Windows, Mac, Linux and Solaris. Requires GAUSS/GAUSS Light version 8.0 or higher.

Time Series MT 1.0

Time Series MT 1.0 is the newest time series application available for GAUSS. This new product will streamline the creation of large GAUSS programs that utilize Time Series models.

Features

  • LSDV - Least Squares Dummy Variable model for multivariate data with bias correction of the parameters

  • Switch - Hamilton's Regime-Switching Regression model

  • SVARMAX - Seasonal VARMAX model: SVARMAX(p,d,q,P,D,Q)s

  • TSCS - Time Series Cross-Sectional Regression models
  • Thread-safe
  • Structured output

Autoregressive Models

  • Computes estimates of the parameters and standard errors for a regression model with autoregressive errors.
Matrices
  • Portmanteau Statistics
  • Forecasting: Univariate and Multivariate
  • Univariate Simulation
Switching Regression
  • Bayesian prior
  • Constraints on transition probabilities
Additional Features
  • Exact full information maximum likelihood (FIML) estimation of VARMAX and VARMA, ARIMAX, ARIMA, ECM models.
    • Impose general linear and nonlinear and equality and inequality constraints on the parameters. Find Lagrangean values associated with each constraint. Return ACF indicator matrices, together with other summary information, including Akaike, Schwarz, and Bayesian information criteria. Compute forecasts from VARMAX and VARMA models.
  • Exact maximum likelihood estimation of ECM models.
    • Unit root and cointegration tests, DF, ADF, Phillips-Perron, and Johansen's Trace and Maximum Eigenvalue tests.
  • Estimation of VAR models.
    • Compute parameter estimates and standard errors for a regression model with autoregressive errors. Can be used for models for which the Cochrane-Orcutt or similar procedures are used. Also computes autocovariances and autocorrelations of the error term.
  • ARIMA Models
    • The Time Series module includes tools for estimating general ARIMA (p,d,q) models using an exact MLE procedure based on C. Ansley (Biometrika 1979, pp. 59-65). Procedures for computing forecasts, theoretical autocovariances, sample autocorrelations, and partial autocorrelations (using Durbin's algorithm), as well as for simulating ARIMA models are provided.
  • Time-Series Cross-Sectional Regression Models: TSCS
    • This module provides procedures to compute estimates for "pooled time-series cross-sectional" models. The assumption is that there are multiple observations over time on a set of cross-sectional units (e.g., people, firms, countries).

      For example, the analyst may have data for a cross-section of individuals each measured over 10 time periods. While these models were devised to study a cross-section of units over multiple time periods, they also correspond to models in which there are data for groups such as schools or firms with measurements on multiple observations within the group (e.g., students, teachers, employees).

      The specific model that can be estimated with this program is a regression model with variable intercepts. That is, a model with individual-specific effects. The regression parameters for the exogenous variables are assumed to be constant across cross-sectional units. The intercept varies across individuals. This program provides three estimators:
      • Fixed-effects OLS estimator (analysis of covariance estimator)
      • Constrained OLS estimator
      • Random effects estimator using GLS
                     A Hausman test is computed to show whether the error components (random
                     effects) model is the correct specification. In addition to providing the
                     analysis of computed. The first partial squared correlation shows the
                     percentage of variation in the dependent variable that can be explained by
                     the set of independent variables while holding constant the group variables.
                     The second shows the extent to which variation in the dependent variable can
                     be accounted for by the group variable after the other independent variables
                     have been statistically held constant.

           A key feature of this program is that it allows for a variable number of
           time-series observations per cross-sectional unit. For instance, there
           might be 5 time-series observations for the first individual, 10 for the
           second, and so on. This is useful when there are missing values.

Available for Windows, Mac, Linux and Solaris. Requires GAUSS/GAUSS Light version 8.0 or higher.

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