Marginal MLEs for the Fay-Herriot model

Marginal MLEs for the Fay-Herriot random effects model where the covariance matrix for the sampling model is known to scale.

mmleFH(y, X, V, ss0 = 0, df0 = 0)

Arguments

y	direct data following normal model \(y\sim N(\theta,V\sigma^2)\)
X	linking model predictors \( \theta\sim N(X\beta,\tau^2 I)\)
V	covariance matrix to scale
ss0	prior sum of squares for estimate of \(\sigma^2\)
df0	prior degrees of freedom for estimate of \(\sigma^2\)

Value

a list of parameter estimates including

1. beta, the estimated regression coefficients

2. t2, the estimate of \(\tau^2\)

3. s2, the estimate of \(\sigma^2\)

Author

Peter Hoff

Examples

 
n<-30 ; p<-3 
X<-matrix(rnorm(n*p),n,p)  
beta<-rnorm(p) 
theta<-X%*%beta + rnorm(n)  
V<-diag(n) 
y<-theta+rnorm(n) 
mmleFH(y,X,V) 
#> $beta
#>        Xd1        Xd2        Xd3 
#> -0.4974420  0.7214477  0.1429494 
#> 
#> $t2
#> [1] 0.9667798
#> 
#> $s2
#> [1] 1.169488
#>