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help for ^nl vbgf^                                                [STB-53: sg128]
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Nonlinear least squares VBGF parameter estimation
-------------------------------------------------

   ^nl vbgf^ sizevar agevar [weight] [^if^ exp] [^in^ range]
              [ ^, l^evel^(^#^)^ ^i^nit^(^...^)^ ^ln^lsq^(^#^)^ ^lea^ve ^eps(^#^)^
              ^nolo^g ^tr^ace ^it^erate^(^#^)^ fcn_options ]


sizevar is the dependent variable with individual or mean size values.

agevar is the independent variable with age for each size.

^aweights^ and ^fweight^s are allowed; see help ^weights^.

^nl vbgf^ as being an application of ^nl^ shares the features of all estimation 
   commands; see help ^est^.


The syntax of ^predict^ following ^nl vbgf^ is

   predict [type] newvarname [^if^ exp] [^in^ range] [, { ^y^hat | ^r^esiduals }]


^yhat^ and ^residuals^ are available both in and out of sample; type "^predict^ ...
^if e(sample)^ ..." if wanted only for the estimation sample.


Description
-----------

This command uses Stata's nl program to fit a von Bertalanffy Growth Function
(VBGF) to the dependent variable wich is size or mean size by least squares. 
The VBGF is in the separate program nlvbgf.ado. As an application of the nl
procedure included in Stata, the ^nl vbgf^ program shares all the options for
^nl^ (see help ^nl^).


Options
-------

^level(^#^)^ specifies the confidence level, in percent, for confidence intervals
    of the coefficients; see help ^level^.

^init(^...^)^ specifies initial values for parameters that are to be used to over-
    ride the default initial values.

^lnlsq(^#^)^ fits the model defined in fcn by 'log least squares', defined as with
    shifted lognormal errors. In other words, ln(depvar-#) is assumed normally
    distributed. Sums of squares and deviance are adjusted to the same scale as
    depvar.

^leave^ leaves behind after estimation a set of new variables with the same names
    as the estimated parameters containing the derivative of E(y) with respect
    to the parameter.

^eps(^#^)^ specifies the convergence criterion for successive parameter estimates
    and for the residual sum of squares. Default: 1e-5 (.00001).

^nolog^ suppresses the iteration log.

^trace^ expands the iteration log to provide more details, including values of
    the parameters at each step of the process.

^iterate(^#^)^ specifies the maximum number of iterations before giving up and
    defaults to 100.

fcn_options refer to any options allowed by nlfcn.


Options for ^predict^
-------------------

^yhat^, the default, calculates the fitted values.

^residuals^ calculates the residuals.


nlvbgf
------

^nl vbgf^ uses the function defined by nlvbgf.  In nlvbgf the parameters of the 
problem and set default initial values are determined, and it permit to 
evaluate the function for a given set of parameter estimates.

The nlvbgf is:

program define nlvbgf
   version 6.0
      if "`1'"=="?"  {
         global S_2 /*
*/ "von Bertalanffy growth function, $S_E_depv=b0*(1-exp(-b1*(`2'-b2)))"
         global S_1 "b0 b1 b2"
         local exp "[$S_E_wgt $S_E_exp]"
         global b0=500
         global b1=1
         global b2=0.1
         exit
      }
      replace `1'= $b0*(1-exp(-$b1*(`2'-$b2)))
end


Examples
--------

Having ^mlen^ a variable with mean size (or individual size) at each ^age^, 
you type:

   ^. nl vbgf mlen age^

Notice that the initial values of the parameters were provided in the nlvbgf
program.  You can, however, override them.  To estimate a model using 600 
for the initial value of b0 (L_inf) rather than 500, you can type

   ^. nl vbgf mlen age, init(b0 = 600)^

To also change the initial value of b1 (K) from 1 to .5, and b2 (t_0) 
from .1 to .2, you type:

   ^. nl vbgf mlen age, init(b0 = 600, b1 = .5, b2 = 0.2)^


Author
------

Isaias H. Salgado-Ugarte
Universidad Nacional Autonoma de Mexico
Facultad de Estudios Superiores Zaragoza
Biologia, Guelatao 66 Col. Ejercito de Oriente
Iztapalapa 09230, Mexico D.F., Mexico
(Fax 52-5-773-0151)
e-mail: isalgado@@servidor.unam.mx


Also see
--------

 Manual:  ^[U] 23 Estimation and post-estimation commands^,
          ^[U] 29 Overview of model estimation in Stata^,
          ^[R] nl^
On-line:  help for @nl@, @est@, @postest@, @ml@, @regress@, @bevholt@