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[此贴子已经被作者于2005-1-15 13:29:24编辑过]

Procedure For Computing Likelihood Function

The user must provide a procedure for computing the log-likelihood for either one observation, or for a matrix of observations. The procedure must have two input arguments, first, a vector of parameter values, and second, one or more rows of the data matrix. The output argument is the log-likelihood for the observation or observations in the second argument evaluated at the parameters values in the first argument. Suppose that the function procedure has been named fct, the following considerations apply:

 FORMAT logl=fct(x,y) INPUT x - vector of parameters of model y - one or more rows of the data set (if the data set has been transformed, or if vars /= 0, i.e., there is selection, then y is a transformed, selected observation) if __row == 1, one row of the data set if __row >= 2, if data set is stored in memory then all of the data set will be passed to FCT; if data set is stored in GAUSS data file then __row will be passed to passed to FCT. if __row <= 0, For data set is stored in memory same as __row>= 2, for GAUSS data file the maximum number of rows that will fit in memory will be computed by MAXLIK. if _max_Lag >= 1, a matrix of observations, the first is the i-_max_Lag row, and the final row is the i-th row. OUTPUT logl - the log-likelihood if __row == 1 or _max_Lag >= 1, a scalar value for a given observation, otherwise a vector of log-likelihoods.

REMARKS

If you have written the procedure such that it must compute the log-likelihood of one observation at a time then you must set __row = 1. But if you are able to write the procedure so that a vector of log-likelihoods may be returned then set __row=0; If you are getting "insufficient memory" messages when the data are being read from a GAUSS data file then either set __row ==1 or to some positive value. Also, if the data set is stored in a GAUSS data set and the selected data set will fit into memory, then MAXLIK will read it in and store it before beginning the iterations. In this case the setting of __row will follow the rules of a data set stored in memory. Significant reduction in computation time may be achieved when the data set can be stored in memory and procedure is written to compute vectors of log-probabilities.

Calling MAXLIK Recursively

The procedure that computes the log-likelihood may itself call MAXLIK. When calling MAXLIK recursively the following considerations apply:

If a data set is being analyzed and it is to be transformed or deleted for missing data or cases are to be selected, then this can be done only on the outermost version of MAXLIK, i.e., the version called in the original command file. Variable selection (as opposed to case selection) can be done on any level through the second argument in the call to each version of MAXLIK. Data sets can be opened by nested versions of MAXLIK. If a nested version of MAXLIK is going to use the data set opened by the outer version of MAXLIK then pass a null string (i.e., "") in the first argument in the call. If it is going to analyze a different data set from the outer version then pass it the data set name in a string. You may also load and store a data set in memory in the command file and pass it as the first argument in the nested call to MAXLIK.

Before the call to the nested version of MAXLIK, the global variables may be re-set by calling MAXCLR. You must not use MAXSET because that will clear information about the data sets opened and processed in the outer version. The only differences between MAXSET and MAXCLR are references to these globals.

You may also want to disable the keyboard control of the nested versions. This is done by setting the global _max_key = 0 after the call to MAXCLR and before the call to the nested MAXLIK.

Maximum Likelihood

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.

Platform: Windows, LINUX and UNIX.

Requirements: GAUSS/GAUSS Light version 3.6.18 or higher.

[此贴子已经被作者于2005-1-15 13:33:08编辑过]