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| AD 1.0 (Algorithmic Derivatives) | A program for generating GAUSS procedures for computing algorithmic derivatives. |
| Constrained Maximum Likelihood | Solves the general maximum likelihood problem subject to general constraints on the parameters. |
| Constrained Optimisation | Solves the Nonlinear Programming problem, subject to general constraints on the parameters. |
| CurveFit | Nonlinear curve fitting. |
| Descriptive statistics | Basic sample statistics including means, frequencies and crosstabs. This application is backwards compatible with programs written with Descriptive Statistics 3.1 |
| 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 scale linear programming problems. |
| Linear Regression MT | Least squares estimation. |
| Loglinear Analysis MT | Analysis of categorical data using loglinear analysis. |
| Maximum Likelihood | Maximum likelihood estimation of the parameters of statistical models. |
| Nonlinear Equations MT | Solves systems of nonlinear equations where there are as many equations as unknowns. |
| Optimisation | General optimization. |
| Time Series | Time-Series Cross-Sectional Regression Models, Autoregression Models and ARIMA-estimation. |
Gauss Third Party Applications
AD 1.0 (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 mprovement 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.
Platforms : Windows, LINUX and UNIX.
Requirements: Requires GAUSS Mathematical and Statistical System 6.0 or the GAUSS
Engine 6.0.
- 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
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.Platform: Windows, LINUX and UNIX.Requirements: GAUSS/GAUSS Light version 3.2 or higher.
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
- 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
- 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.
- Includes new routines to compute descriptive statistics,
- 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.
Platforms: Windows, LINUX and UNIX.
Requirements: Requires GAUSS Mathematical and Statistical System 6.0 or the GAUSS Engine 6.0.
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."
- Includes both variables that are attributes of the responses as well as, optionally, exogenous variables that are properties of cases.
- Qualitative responses are each modeled with a separate set of regression coefficients
- The log-odds of one category versus the next higher category is linear in the cutpoints and explanatory variables
- The coefficients of the regression in each category are linear functions of a reference regression
- 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.
- 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.
- Estimates dichotomous dependent variable with either Normal or extreme value distributions
- Estimates model with an ordered qualitative dependent variable with Normal or extreme value distributions
- 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.
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
- 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
Requirements: GAUSS/GAUSS Light version 4.0 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
- Joint confidence region for beta estimates
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.
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
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.
Platform: Windows, LINUX and UNIX.Requirements: GAUSS/GAUSS Light version 3.6.18 or higher.
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.
Platform: Windows, LINUX, Mac, and UNIX. Requirements: GAUSS/GAUSS Engine/GAUSS Light version 6.0 or higher.
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
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.
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
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.
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