
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)
An object of class "vglmff"
(see vglmff-class
).
The object is used by modelling functions such as
vglm
and vgam
.
Logical.
If TRUE
then the MLE, assuming multivariate normal errors,
is computed;
the effect is just to add a loglikelihood
slot to the
returned object.
Then it results in the maximum likelihood estimator.
Character, partial matching allowed and the first choice is the default.
The divisor for the estimate of the covariances.
If "n"
then the estimate will be biased.
If the others then the estimate will be unbiased for some elements.
If mle.normal = TRUE
and this argument is not "n"
then
a warning or an error will result.
See
CommonVGAMffArguments
.
If parallel = TRUE
then the constraint applies to
the intercept too.
Numeric.
This may be assigned a variance-covariance of the errors.
If matrix.arg
then this is a !matrix.arg
then this is a M*(M+1)/2
elements).
Logical. Of single length.
T. W. Yee.
The default convergence criterion may be a little loose.
Try setting epsilon = 1e-11
, especially
with mle.normal = TRUE
.
Proposed by Zellner (1962), the basic
seemingly unrelated regressions (SUR)
model is a set of LMs (
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.
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.
uninormal
,
gew
.
# 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) # SEs
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