Censored Normal Distribution

Maximum likelihood estimation for the normal distribution with left and right censoring.

cens.normal(lmu = "identitylink", lsd = "loglink", imethod = 1,
            zero = "sd")

Arguments

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 the default.

imethod

Initialization method. Either 1 or 2, this specifies two methods for obtaining initial values for the parameters.

zero

A vector, e.g., 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. See CommonVGAMffArguments for more information.

Details

This function is like uninormal but handles observations that are left-censored (so that the true value would be less than the observed value) else right-censored (so that the true value would be greater than the observed value). To indicate which type of censoring, input extra = list(leftcensored = vec1, rightcensored = vec2) where vec1 and vec2 are logical vectors the same length as the response. If the two components of this list are missing then the logical values are taken to be FALSE. The fitted object has these two components stored in the extra slot.

Value

An object of class "vglmff" (see vglmff-class). The object is used by modelling functions such as vglm, and vgam.

Author

T. W. Yee

Note

This function, which is an alternative to tobit, cannot handle a matrix response and uses different working weights. If there are no censored observations then uninormal is recommended instead.

See also

tobit, uninormal, double.cens.normal.

Examples

if (FALSE) { # \dontrun{
cdata <- data.frame(x2 = runif(nn <- 1000))  # ystar are true values
cdata <- transform(cdata, ystar = rnorm(nn, m = 100 + 15 * x2, sd = exp(3)))
with(cdata, hist(ystar))
cdata <- transform(cdata, L = runif(nn,  80,  90),  # Lower censoring points
                          U = runif(nn, 130, 140))  # Upper censoring points
cdata <- transform(cdata, y = pmax(L, ystar))  # Left  censored
cdata <- transform(cdata, y = pmin(U, y))      # Right censored
with(cdata, hist(y))
Extra <- list(leftcensored  = with(cdata, ystar < L),
              rightcensored = with(cdata, ystar > U))
fit1 <- vglm(y ~ x2, cens.normal, data = cdata, crit = "c", extra = Extra)
fit2 <- vglm(y ~ x2, tobit(Lower = with(cdata, L), Upper = with(cdata, U)),
            data = cdata, crit = "c", trace = TRUE)
coef(fit1, matrix = TRUE)
max(abs(coef(fit1, matrix = TRUE) -
        coef(fit2, matrix = TRUE)))  # Should be 0
names(fit1@extra)
} # }