Stata 13 help for maximize

Title

[R] maximize -- Details of iterative maximization

Syntax

Maximum likelihood optimization

mle_cmd ... [, options]

Set default maximum iterations

set maxiter # [, permanently]

options Description ------------------------------------------------------------------------- difficult use a different stepping algorithm in nonconcave regions technique(algorithm_spec) maximization technique iterate(#) perform maximum of # iterations; default is iterate(16000) [no]log display an iteration log of the log likelihood; typically, the default trace display current parameter vector in iteration log gradient display current gradient vector in iteration log showstep report steps within an iteration log hessian display current negative Hessian matrix in iteration log showtolerance report the calculated result that is compared to the effective convergence criterion tolerance(#) tolerance for the coefficient vector; see Options for the defaults ltolerance(#) tolerance for the log likelihood; Options for the defaults nrtolerance(#) tolerance for the scaled gradient; Options for the defaults qtolerance(#) when specified with algorithms bhhh, dfp, or bfgs, the q-H matrix is used as the final check for convergence rather than nrtolerance() and the H matrix; seldom used nonrtolerance ignore the nrtolerance() option from(init_specs) initial values for the coefficients ------------------------------------------------------------------------- where algorithm_spec is

algorithm [ # [ algorithm [#] ] ... ]

algorithm is {nr | bhhh | dfp | bfgs}

and init_specs is one of

matname [, skip copy ]

{ [eqname:]name = # | /eqname = # } [...]

# [# ...], copy

Description

All Stata commands maximize likelihood functions using moptimize() and optimize(); see Methods and formulas in [R] maximize. Commands use the Newton-Raphson method with step halving and special fixups when they encounter nonconcave regions of the likelihood. For details, see [M-5] moptimize and [M-5] optimize. For more information about programming maximum likelihood estimators in ado-files, see [R] ml and Gould, Pitblado, and Poi (2010).

set maxiter specifies the default maximum number of iterations for estimation commands that iterate. The initial value is 16000, and # can be 0 to 16000. To change the maximum number of iterations performed by a particular estimation command, you need not reset maxiter; you can specify the iterate(#) option. When iterate(#) is not specified, the maxiter value is used.

Maximization options

difficult specifies that the likelihood function is likely to be difficult to maximize because of nonconcave regions. When the message "not concave" appears repeatedly, ml's standard stepping algorithm may not be working well. difficult specifies that a different stepping algorithm be used in nonconcave regions. There is no guarantee that difficult will work better than the default; sometimes it is better and sometimes it is worse. You should use the difficult option only when the default stepper declares convergence and the last iteration is "not concave" or when the default stepper is repeatedly issuing "not concave" messages and producing only tiny improvements in the log likelihood.

technique(algorithm_spec) specifies how the likelihood function is to be maximized. The following algorithms are allowed. For details, see Gould, Pitblado, and Poi (2010).

technique(nr) specifies Stata's modified Newton-Raphson (NR) algorithm.

technique(bhhh) specifies the Berndt-Hall-Hall-Hausman (BHHH) algorithm.

technique(dfp) specifies the Davidon-Fletcher-Powell (DFP) algorithm.

technique(bfgs) specifies the Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm.

The default is technique(nr).

You can switch between algorithms by specifying more than one in the technique() option. By default, an algorithm is used for five iterations before switching to the next algorithm. To specify a different number of iterations, include the number after the technique in the option. For example, specifying technique(bhhh 10 nr 1000) requests that ml perform 10 iterations with the BHHH algorithm followed by 1000 iterations with the NR algorithm, and then switch back to BHHH for 10 iterations, and so on. The process continues until convergence or until the maximum number of iterations is reached.

iterate(#) specifies the maximum number of iterations. When the number of iterations equals iterate(), the optimizer stops and presents the current results. If convergence is declared before this threshold is reached, it will stop when convergence is declared. Specifying iterate(0) is useful for viewing results evaluated at the initial value of the coefficient vector. Specifying iterate(0) and from() together allows you to view results evaluated at a specified coefficient vector; however, not all commands allow the from() option. The default value of iterate(#) for both estimators programmed internally and estimators programmed with ml is the current value of set maxiter, which is iterate(16000) by default.

log and nolog specify whether an iteration log showing the progress of the log likelihood is to be displayed. For most commands, the log is displayed by default, and nolog suppresses it. For a few commands (such as the svy maximum likelihood estimators), you must specify log to see the log.

trace adds to the iteration log a display of the current parameter vector.

gradient adds to the iteration log a display of the current gradient vector.

showstep adds to the iteration log a report on the steps within an iteration. This option was added so that developers at StataCorp could view the stepping when they were improving the ml optimizer code. At this point, it mainly provides entertainment.

hessian adds to the iteration log a display of the current negative Hessian matrix.

showtolerance adds to the iteration log the calculated value that is compared with the effective convergence criterion at the end of each iteration. Until convergence is achieved, the smallest calculated value is reported.

shownrtolerance is a synonym of showtolerance.

------------------------------------------------------------------------------- Below we describe the three convergence tolerances. Convergence is declared when the nrtolerance() criterion is met and either the tolerance() or the ltolerance() criterion is also met.

tolerance(#) specifies the tolerance for the coefficient vector. When the relative change in the coefficient vector from one iteration to the next is less than or equal to tolerance(), the tolerance() convergence criterion is satisfied.

tolerance(1e-4) is the default for estimators programmed with ml.

tolerance(1e-6) is the default.

ltolerance(#) specifies the tolerance for the log likelihood. When the relative change in the log likelihood from one iteration to the next is less than or equal to ltolerance(), the ltolerance() convergence is satisfied.

ltolerance(0) is the default for estimators programmed with ml.

ltolerance(1e-7) is the default.

nrtolerance(#) specifies the tolerance for the scaled gradient. Convergence is declared when g*inv(H)*g' < nrtolerance(). The default is nrtolerance(1e-5).

qtolerance(#) when specified with algorithms bhhh, dfp, or bfgs uses the q-H matrix as the final check for convergence rather than nrtolerance() and the H matrix.

Beginning with Stata 12, by default, Stata now computes the H matrix when the q-H matrix passes the convergence tolerance, and Stata requires that H be concave and pass the nrtolerance() criterion before concluding convergence has occurred.

qtolerance() provides a way for the user to obtain Stata's earlier behavior.

nonrtolerance specifies that the default nrtolerance() criterion be turned off.

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

from() specifies initial values for the coefficients. Not all estimators in Stata support this option. You can specify the initial values in one of three ways: by specifying the name of a vector containing the initial values (for example, from(b0), where b0 is a properly labeled vector); by specifying coefficient names with the values (for example, from(age=2.1 /sigma=7.4)); or by specifying a list of values (for example, from(2.1 7.4, copy)). from() is intended for use when you are doing bootstraps (see [R] bootstrap) and in other special situations (for example, with iterate(0)). Even when the values specified in from() are close to the values that maximize the likelihood, only a few iterations may be saved. Poor values in from() may lead to convergence problems.

skip specifies that any parameters found in the specified initialization vector that are not also found in the model be ignored. The default action is to issue an error message.

copy specifies that the list of values or the initialization vector be copied into the initial-value vector by position rather than by name.

Option for set maxiter

permanently specifies that, in addition to making the change right now, the maxiter setting be remembered and become the default setting when you invoke Stata.

Remarks

Only in rare circumstances would you ever need to specify any of these options, except nolog. The nolog option is useful for reducing the amount of output appearing in log files.

Stored results

Maximum likelihood estimators store the following in e():

Scalars e(N) number of observations; always stored e(k) number of parameters; always stored e(k_eq) number of equations in e(b); usually stored e(k_eq_model) number of equations in overall model test; usually stored e(k_dv) number of dependent variables; usually stored e(df_m) model degrees of freedom; always stored e(r2_p) pseudo-R-squared; sometimes stored e(ll) log likelihood; always stored e(ll_0) log likelihood, constant-only model; stored when constant-only model is fit e(N_clust) number of clusters; stored when vce(cluster clustvar) is specified; see [U] 20.21 Obtaining robust variance estimates e(chi2) chi-squared; usually stored e(p) significance of model of test; usually stored e(rank) rank of e(V); always stored e(rank0) rank of e(V) for constant-only model; stored when constant-only model is fit e(ic) number of iterations; usually stored e(rc) return code; usually stored e(converged) 1 if converged, 0 otherwise; usually stored

Macros e(cmd) name of command; always stored e(cmdline) command as typed; always stored e(depvar) names of dependent variables; always stored e(wtype) weight type; stored when weights are specified or implied e(wexp) weight expression; stored when weights are specified or implied e(title) title in estimation output; usually stored by commands using ml e(clustvar) name of cluster variable; stored when vce(cluster clustvar) is specified; see [U] 20.21 Obtaining robust variance estimates e(chi2type) Wald or LR; type of model chi-squared test; usually stored e(vce) vcetype specified in vce(); stored when command allows vce() e(vcetype) title used to label Std. Err.; sometimes stored e(opt) type of optimization; always stored e(which) max or min; whether optimizer is to perform maximization or minimization; always stored e(ml_method) type of ml method; always stored by commands using ml e(user) name of likelihood-evaluator program; always stored e(technique) from technique() option; sometimes stored e(singularHmethod) m-marquardt or hybrid; method used when Hessian is singular; sometimes stored (1) e(crittype) optimization criterion; always stored (1) e(properties) estimator properties; always stored e(predict) program used to implement predict; usually stored

Matrices e(b) coefficient vector; always stored e(Cns) constraints matrix; sometimes stored e(ilog) iteration log (up to 20 iterations); usually stored e(gradient) gradient vector; usually stored e(V) variance-covariance matrix of the estimators; always stored e(V_modelbased) model-based variance; only stored when e(V) is neither the OIM nor OPG variance

Functions e(sample) marks estimation sample; always stored -------------------- 1. Type ereturn list, all to view these results; see [P] return.

See Stored results in the manual entry for any maximum likelihood estimator for a list of returned results.

Reference

Gould, W. W., J. Pitblado, and B. P. Poi. 2010. Maximum Likelihood Estimation with Stata. 4th ed. College Station, TX: Stata Press.


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