Gauss Applications are software packages written using the Gauss programming language. Some of these applications have been developed by Aptech Systems and are described below. Others have been developed by third-parties and are known as Third-Party Applications. You need Gauss to be able to run the Applications. They are purchasable as add-ons to Gauss.

Gauss Applications are available for the Windows and UNIX versions of GAUSS:

Gauss Third Party Applications

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
  
• Activate and inactivate coefficients
  
• Heteroskedastic-consistent covariance matrix of coefficients
  

Bootstrap Estimation
CurveFit includes special procedures for computing boot-strapped estimates. One procedure produces a mean vector and covariance matrix of the boot-strapped coefficients, while 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 uni-modal 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, and these plots provide a means for assessing the statistical significance of coefficients in nonlinear models that is superior to the usual methods.

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.

Requires GAUSS/GAUSS Light version 3.6 or greater.

Available for Windows NT, Windows 95, 98, 2000, XP and UNIX versions of GAUSS.

Descriptive Statistics

The procedures in DSTAT provide basic sample statistics of the variables in GAUSS data sets. These statistics describe the numerical characteristics of random variables, and provide information for further analysis.

Features

• Handles large data sets
  
• Accommodates both character and numeric variables
  
• All statistics calculated are accessible for later use
  
• Provides statistics for an entire data set or specified data range
  

Main Functions

• Calculates the means of a set of variables
  
• Calculates the extreme values of a set of variables
  
• Computes the covariance matrix of a set of variables
  
• Computes the correlation matrix of a set of variables
  
• Creates contingency tables
  
• Computes statistics and measure of fits for a contingency table
  
• Computes frequency distributions for a set of variables
• Tests the differences of means between two groups
  

Requires GAUSS/GAUSS Light version 3.6 or greater.

Available for Windows NT, Windows 95, 98, 2000, XP and UNIX versions of GAUSS.

Linear Programming
The Linear Programming module (SIMPLEX) is designed to solve small scale linear programming problems.

Features

• Upper and lower finite bounds can be provided for variables and constraints
  
• Problem type (minimization or maximization)
  
• Constraint types (æ,Ñ,=)
  
• Choice of tolerances
  
• Pivoting rules
  
• Output can be adjusted using global variables
  

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.
  

SIMPLEX 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.

Requires GAUSS/GAUSS Light version 3.6 or greater.

Available for Windows NT, Windows 95, 98, 2000, XP and UNIX versions of GAUSS.

Linear Regression

The Linear Regression module is a set of procedures for estimating single equations or a simultaneous system of equations. It allows constraints on coefficients, het-con standard errors. Includes two-stage least squares, three-stage least squares, and seemingly unrelated regression.

Features

• Calculates Heteroskedastic-consistent Standard Errors, and performs both influence and collinearity diagnostics inside the Ordinary Least Squares routine.
  
• 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.
  
• All important test statistics and estimated coefficients are stored in an efficient manner.
  
• Both Three-Stage Least Squares and Seemingly Unrelated Regression can be estimated iteratively.
  

Thorough Documentation

• A 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.
  

Requires GAUSS/GAUSS Light version 3.6 or greater.

Available for Windows NT, Windows 95, 98, 2000, XP and UNIX versions of GAUSS.

The Loglinear Analysis module contains procedures for the analysis of categorical data using loglinear analysis.

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 Analysis of Ordinal Categorical Data by A. Agresti.

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.
  

Requires GAUSS/GAUSS Light version 3.6 or greater.

Available for Windows NT, Windows 95, 98, 2000, XP and UNIX versions of GAUSS.

Maximum Likelihood 5.0

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

Features

• More than 25 options can be easily specified by the user to control the optimization
  
• 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 two criteria: number of iterations, or failure of the function to decrease within a tolerance
  

Improved Algorithm

• MAXLIK implements the numerically superior Cholesky factorization, solve, and update methods for the BFGS, DFP, and Newton algorithms.
  
• Event Count and Duration Regression:
  
• COUNT is included in this module for estimating the Limited Dependent Variable model. These procedures provide maximum likelihood estimators 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.
  

Requires GAUSS/GAUSS Light version 3.6 or greater.

Available for Windows NT, Windows 95, 98, 2000, XP and UNIX versions of GAUSS.

Nonlinear Equations

The Nonlinear Equations module solves systems of nonlinear equations where there are as many equations as unknowns. The new version utilizes new GAUSS functions, significantly increasing accuracy and computational speed.

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.

Optimization

OPTMUM 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 OPTMUM with a minimum of programming effort. All you provide is the function to be optimized and start values, and OPTMUM 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, and BRENT , a step-halving method may also be used
  
• 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

OPTMUM 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.

Requires GAUSS/GAUSS Light version 3.6 or greater.

Available for Windows NT, Windows 95, 98, 2000, XP and UNIX versions of GAUSS.

Quantal Response

Quantal Response is a statistical package which provides a set of procedures for estimating models in which the dependent variable is qualitative in some way. These models are particularly useful for researchers in the social, behavioral, and biomedical sciences, as well as economics, public choice, education, and marketing.

Features

• Efficiently handles large data sets
  
• Estimates unknown parameters
  
• Provides a variety of goodness-of-fit measures
  
• All regression procedures can be run at a specified data range
  
• Performs multiple linear hypothesis testing with any form
  
• Accommodates both numeric and character variables
  

Main Models

• LOGIT: Estimates multinomial logit model, in which qualitative choices have more than two categories
  
• ORDERED: Estimates the ordered logit or ordered probit models in which the choice variable is inherently ordered
  
• PROBIT: Estimates the binomial probit model
  
• PSNREG: Estimates the poisson regression model
  
• QTEST: Tests the linear hypotheses
  

Requires GAUSS/GAUSS Light version 3.6 or greater.

Available for Windows NT, Windows 95, 98, 2000, XP and UNIX versions of GAUSS.

Time Series

Time-Series Cross-Sectional Regression Models, Autoregression Models and ARIMA-estimation.

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 covariance and GLS estimates, two multiple partial-squared correlations are computed. The first partial correlation (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 estimate 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.

Autoregression Models
Computes estimates of the parameters 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 also includes tools for estimating general ARIMA (p,d,1,q) models using an exact MLE procedure based on C. Ansley (Biometrika 1979, p. 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.

Requires GAUSS/GAUSS Light version 3.6 or greater.

Available for Windows NT, Windows 95, 98, 2000, XP and UNIX versions of GAUSS.