Seemingly Unrelated Regressions Family Function
Fits a system of seemingly unrelated regressions.
SURff(mle.normal = FALSE,
divisor = c("n", "n-max(pj,pk)", "sqrt((n-pj)*(n-pk))"),
parallel = FALSE, Varcov = NULL, matrix.arg = FALSE)mle.normal |
Logical.
If |
divisor |
Character, partial matching allowed and the first choice is the default.
The divisor for the estimate of the covariances.
If |
parallel |
See
|
Varcov |
Numeric.
This may be assigned a variance-covariance of the errors.
If |
matrix.arg |
Logical. Of single length. |
Proposed by Zellner (1962), the basic seemingly unrelated regressions (SUR) model is a set of LMs (M > 1 of them) tied together at the error term level. Each LM's model matrix may potentially have its own set of predictor variables.
Zellner's efficient (ZEF) estimator (also known as
Zellner's two-stage Aitken estimator)
can be obtained by setting
maxit = 1
(and possibly divisor = "sqrt" or
divisor = "n-max").
The default value of maxit (in vglm.control)
probably means iterative GLS (IGLS) estimator is computed because
IRLS will probably iterate to convergence.
IGLS means, at each iteration, the residuals are used to estimate
the error variance-covariance matrix, and then the matrix is used
in the GLS.
The IGLS estimator is also known
as Zellner's iterative Aitken estimator, or IZEF.
An object of class "vglmff" (see vglmff-class).
The object is used by modelling functions such as
vglm and vgam.
The default convergence criterion may be a little loose.
Try setting epsilon = 1e-11, especially
with mle.normal = TRUE.
The fitted object has slot @extra$ncols.X.lm which is
a M vector with the number of parameters for each LM.
Also, @misc$values.divisor is the M-vector of
divisor values.
Constraint matrices are needed in order to specify which response
variables that each term on the RHS of the formula is a
regressor for.
See the constraints argument of vglm
for more information.
T. W. Yee.
Zellner, A. (1962). An Efficient Method of Estimating Seemingly Unrelated Regressions and Tests for Aggregation Bias. J. Amer. Statist. Assoc., 57(298), 348–368.
Kmenta, J. and Gilbert, R. F. (1968). Small Sample Properties of Alternative Estimators of Seemingly Unrelated Regressions. J. Amer. Statist. Assoc., 63(324), 1180–1200.
# Obtain some of the results of p.1199 of Kmenta and Gilbert (1968)
clist <- list("(Intercept)" = diag(2),
"capital.g" = rbind(1, 0),
"value.g" = rbind(1, 0),
"capital.w" = rbind(0, 1),
"value.w" = rbind(0, 1))
zef1 <- vglm(cbind(invest.g, invest.w) ~
capital.g + value.g + capital.w + value.w,
SURff(divisor = "sqrt"), maxit = 1,
data = gew, trace = TRUE, constraints = clist)
round(coef(zef1, matrix = TRUE), digits = 4) # ZEF
zef1@extra$ncols.X.lm
zef1@misc$divisor
zef1@misc$values.divisor
round(sqrt(diag(vcov(zef1))), digits = 4) # SEs
nobs(zef1, type = "lm")
df.residual(zef1, type = "lm")
mle1 <- vglm(cbind(invest.g, invest.w) ~
capital.g + value.g + capital.w + value.w,
SURff(mle.normal = TRUE),
epsilon = 1e-11,
data = gew, trace = TRUE, constraints = clist)
round(coef(mle1, matrix = TRUE), digits = 4) # MLE
round(sqrt(diag(vcov(mle1))), digits = 4) # SEsPlease choose more modern alternatives, such as Google Chrome or Mozilla Firefox.