# gammaFit: Iteratively estimate variance model parameter gamma In PracTools: Tools for Designing and Weighting Survey Samples

### Description

Iteratively computes estimate of γ in a model with E_M(y)=x^Tβ and Var_M(y)=σ^2x^γ.

### Usage

 1 gammaFit(X, x, y, maxiter = 100, show.iter = FALSE, tol = 0.001) 

### Arguments

 X matrix of predictors in the linear model for y x vector of x's for individual units in the assumed specification of Var_M(y) y vector of dependent variables for individual units maxiter maximum number of iterations allowed show.iter should values of γ be printed of each iteration? TRUE or FALSE tol size of relative difference in \hat{γ}'s between consecutive iterations used to determine convergence. Algorithm terminates when relative difference is less than tol.

### Details

The function gammaFit estimates the power γ in a model where the variance of the errors is proportional to x^γ for some covariate x. Values of γ are typically in [0,2]. The function calls gamEst.

### Value

A list with the components:

 g.hat estimate of γ when iterative procedure stopped converged TRUE or FALSE depending on whether convergence was obtained steps number of steps used by the algorithm

### Author(s)

Richard Valliant, Jill A. Dever, Frauke Kreuter

### References

Valliant, R., Dever, J., Kreuter, F. (2013, chap. 3). Practical Tools for Designing and Weighting Survey Samples. New York: Springer.

gamEst
 1 2 3 4 5 6 data(hospital) x <- hospital$x y <- hospital$y X <- cbind(sqrt(x), x) gammaFit(X = X, x = x, y = y, maxiter=100, tol=0.001)