By matloff
An almost-as-famous alternative to the famous Maximum Likelihood Estimation is the Method of Moments. MM has always been a favorite of mine because it often requires fewer distributional assumptions than MLE, and also because MM is much easier to explain than MLE to students and consulting clients. CRAN has a package gmm that does MM, actually the Generalized Method of Moments, and in this post I’ll explain how to use it (on the elementary level, at least).
Our data set will be bodyfat, which is included in the mfp package, with measurements on 252 men. The first column of this data frame, brozek, is the percentage of body fat, which when converted to a proportion is in (0,1). That makes it a candidate for fitting a beta distribution.
Denoting the parameters of that family by α and β, the mean and variance are α / (α + β) and α β / ((α + β)2 (α + β + 1)), respectively. MM is a model of simplicity — we match these to the sample mean and variance of our data, and then solve for α and β. Of course, the solution part may not be so simple, due to nonlinearities, but gmm worries about all that for us. Yet another tribute to the vast variety of packages available on CRAN!
In our elementary usage here, the call form is
gmm(data,momentftn,start)
where data is our data in matrix or vector form, momentftn specifies the moments, and start is our initial guess for the iterative solution process. Let’s specify momentftn:
g This function equates population moments to sample ones, by specifying expressions that gmm() is to set to 0. The argument th here (“theta”) will be the MM estimates (at any given iteration) of the population parameters, in this case of α and β.
The function is required to …read more
Source:: r-bloggers.com