tobit {VGAM} | R Documentation |
Fits a Tobit model to a univariate response.
tobit(Lower = 0, Upper = Inf, lmu="identity", lsd="loge", emu=list(), esd=list(), imethod=1, zero=2)
Lower |
Numeric of length 1, it is the value L described below.
Any value of the linear model
x_i^T beta that
is less than this value is assigned this value.
Hence this should be the smallest possible value in the response variable.
|
Upper |
Numeric of length 1, it is the value U described below.
Any value of the linear model
x_i^T beta that
is greater than this value is assigned this value.
Hence this should be the largest possible value in the response variable.
|
lmu, lsd |
Parameter link functions applied to the mean and
standard deviation parameters.
See Links for more choices.
The standard deviation is a positive quantity, therefore a log link
is its default.
|
emu, esd |
List. Extra argument for each of the links.
See earg in Links for general information.
|
imethod |
Initialization method. Either 1 or 2, this specifies
two methods for obtaining initial values for the parameters.
|
zero |
An integer vector, containing the value 1 or 2. If so,
the mean or standard deviation respectively are modelled as an intercept only.
Setting zero=NULL means both linear/additive predictors
are modelled as functions of the explanatory variables.
|
The Tobit model can be written
y_i^* = x_i^T beta + e_i
where the e_i ~ N(0,sigma^2) independently and i=1,...,n. However, we measure y_i = y_i^* only if y_i^* > L and y_i^* < U for some cutpoints L and U. Otherwise we let y_i=L or y_i=U, whatever is closer. The Tobit model is thus a multiple linear regression but with censored responses if it is below or above certain cutpoints.
The defaults for Lower
and Upper
correspond to the
classical Tobit model. By default, the mean x_i^T
beta is the first linear/additive predictor, and the log of the
standard deviation is the second linear/additive predictor. The Fisher
information matrix for uncensored data is diagonal.
The fitted values are the estimates of x_i^T beta.
An object of class "vglmff"
(see vglmff-class
).
The object is used by modelling functions such as vglm
,
and vgam
.
The response must be univariate. If there is no censoring then
normal1
is recommended instead. Any value of the
response less than Lower
or greater than Upper
will
be assigned the value Lower
and Upper
respectively,
and a warning will be issued.
The fitted object has components censoredL
and censoredU
in the extra
slot which specifies whether observations
are censored in that direction.
Thomas W. Yee
Tobin, J. (1958) Estimation of relationships for limited dependent variables. Econometrica 26, 24–36.
n = 1000 x = seq(-1, 1, len=n) f = function(x) 1 + 4*x ystar = f(x) + rnorm(n) Lower = 1 Upper = 4 y = pmax(ystar, Lower) y = pmin(y, Upper) table(y==Lower | y==Upper) # How many censored values? fit = vglm(y ~ x, tobit(Lower=Lower, Upper=Upper), trace=TRUE) table(fit@extra$censoredL) table(fit@extra$censoredU) coef(fit, matrix=TRUE) summary(fit) ## Not run: plot(x, y, main="Tobit model", las=1) legend(-0.9, 3, c("Truth", "Estimate"), col=c("Blue", "Red"), lwd=2) lines(x, f(x), col="blue", lwd=2) # The truth lines(x, fitted(fit), col="red", lwd=2, lty="dashed") # The estimate ## End(Not run)