gamEst {PracTools}

Estimate variance model parameter \gamma

Description

Regresses a y on a set of covariates X where Var_M(y)=\sigma^2x^\gamma and then regresses the squared residuals on log(x) to estimate \gamma.

Usage

gamEst(X1, x1, y1, v1)

Arguments

X1

matrix of predictors in the linear model for y1

x1

vector of x's for individual units in the assumed specification of Var_M(y)

y1

vector of dependent variables for individual units

v1

vector proportional to Var_M(y)

Details

The function gamEst estimates the power \gamma in a model where the variance of the errors is proportional to x^\gamma for some covariate x. Values of \gamma are typically in [0,2]. The function is iteratively called by gammaFit, which is normally the function that an analyst should use.

Value

The estimate of \gamma.

Author(s)

Richard Valliant, Jill A. Dever, Frauke Kreuter

References

Valliant, R., Dever, J., Kreuter, F. (2018, chap. 3). Practical Tools for Designing and Weighting Survey Samples, 2nd edition. New York: Springer.

See Also

gammaFit

Examples

data(hospital)
x <- hospital$x
y <- hospital$y

X <- cbind(sqrt(x), x)
gamEst(X1 = X, x1 = x, y1 = y, v1 = x)