Fitting a two-parameter inverse Gaussian distribution by maximum likelihood
invgaussfit varname [weight] [if exp] [in range] [, muvar(varlist1) lambdavar(varlist2) robust cluster(clustervar) level(#) maximize_options ]
by ... : may be used with invgaussfit; see help by.
fweights and aweights are allowed; see help weights.
invgaussfit fits by maximum likelihood a two-parameter inverse Gaussian distribution to a distribution of a variable varname. The distribution has probability density function for variable x > 0, location parameter m > 0 and scale parameter l > 0 of (l / 2 pi x^3)^(1/2) exp((-l (x - m)^2 / 2 m^2 x)).
muvar(varlist1) and lambdavar(varlist2) allow the user to specify each parameter as a function of the covariates specified in the respective variable list. A constant term is always included in each equation.
robust specifies that the Huber/White/sandwich estimator of variance is to be used in place of the traditional calculation; see [U] 20.14 Obtaining robust variance estimates. robust combined with cluster() allows observations which are not independent within cluster (although they must be independent between clusters).
cluster(clustervar) specifies that the observations are independent across groups (clusters) but not necessarily within groups. clustervar specifies to which group each observation belongs; e.g., cluster(personid) in data with repeated observations on individuals. See [U] 20.14 Obtaining robust variance estimates. Specifying cluster() implies robust.
level(#) specifies the confidence level, in percent, for the confidence intervals of the coefficients; see help level.
nolog suppresses the iteration log.
maximize_options control the maximization process; see help maximize. If you are seeing many "(not concave)" messages in the log, using the difficult option may help convergence.
The inverse Gaussian appears in various guises in other Stata model fit commands, but none is identical to that here. glm with identity link and inverse Gaussian family is similar except that the parameterisation is different; the scale parameter is there treated as ancillary, and thus the definition of likelihood is quite different; and glm does not allow the scale parameter to depend on covariates. Various programs by Joseph Hilbe (Hilbe 2000 and later work on SSC accessible using findit and ssc) wire in log link functions. Finally, the use of inverse Gaussian as one way of modelling frailty in streg differs yet again. Note, however, that the program geninvgauss by Roberto Gutierrez in his gendist package (accessible using findit) that produces random deviates from an inverse Gaussian uses the same parameterisation, and the same names mu and lambda, as that here.
In addition to the usual results saved after ml, invgaussfit also saves the following, if no covariates have been specified:
e(mu) and e(lambda) are the estimated inverse Gaussian parameters.
The following results are saved regardless of whether covariates have been specified:
e(b_mu) and e(b_lambda) are row vectors containing the parameter estimates from each equation.
e(length_b_mu) and e(length_b_lambda) contain the lengths of these vectors. If no covariates are specified in an equation, the corresponding vector has length equal to 1 (the constant term); otherwise, the length is one plus the number of covariates.
. invgaussfit mpg
Nicholas J. Cox, Durham University firstname.lastname@example.org
Stephen P. Jenkins, University of Essex email@example.com
Evans, M., Hastings, N. and Peacock, B. 2000. Statistical distributions. New York: John Wiley.
Hilbe, J. 2000. Two-parameter log-gamma and log-inverse Gaussian models. Stata Technical Bulletin 53: 31-32 (STB Reprints 9: 273-275).
Johnson, N.L., Kotz, S. and Balakrishnan, N. 1994. Continuous univariate distributions: Volume 1. New York: John Wiley.
Online: help for pinvgauss (if installed), qinvgauss (if installed) invgausscf (if installed)