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 #>