tram-methods: Methods for Stratified Linear Transformation Models

Description

Methods for objects inheriting from class tram

Usage

# S3 method for tram
as.mlt(object)
# S3 method for tram
model.frame(formula, ...)
# S3 method for tram
model.matrix(object, data = object$data, with_baseline = FALSE, ...) 
# S3 method for tram
coef(object, with_baseline = FALSE, ...) 
# S3 method for Lm
coef(object, as.lm = FALSE, ...)
# S3 method for Survreg
coef(object, as.survreg = FALSE, ...)
# S3 method for tram
vcov(object, with_baseline = FALSE, complete = FALSE, ...) 
# S3 method for tram
logLik(object, parm = coef(as.mlt(object), fixed = FALSE), ...)
# S3 method for tram
estfun(object, parm = coef(as.mlt(object), fixed = FALSE), ...)
# S3 method for tram
predict(object, newdata = model.frame(object), 
        type = c("lp", "trafo", "distribution", "survivor", "density", 
                    "logdensity", "hazard", "loghazard", "cumhazard", "quantile"), 
           ...)
# S3 method for tram
plot(x, newdata = model.frame(x), 
     which = c("QQ-PIT", "baseline only", "distribution"), 
     confidence = c("none", "interval", "band"), level = 0.95, 
     K = 50, cheat = K, col = "black", fill = "lightgrey", lwd = 1, ...)

Arguments

object, formula, x

a fitted stratified linear transformation model inheriting from class tram.

data

an optional data frame.

with_baseline

logical, if TRUE all model parameters are returned, otherwise parameters describing the baseline transformation are ignored.

as.lm

logical, return parameters in the lm parameterisation if TRUE.

as.survreg

logical, return parameters in the survreg parameterisation in TRUE.

parm

model parameters, including baseline parameters.

complete

currently ignored

newdata

an optional data frame of new observations.

type

type of prediction, current options include linear predictors ("lp", of x variables in the formula y | s ~ x), transformation functions ("trafo") or distribution functions on the scale of the cdf ("distribution"), survivor function, density function, log-density function, hazard function, log-hazard function, cumulative hazard function or quantile function.

which

type of plot, either a QQ plot of the probability-integral transformed observations ("QQ-PIT"), of the baseline transformation of the whole distribution.

confidence

type of uncertainty assessment.

level

confidence level.

number of grid points in the response, see plot.ctm.

cheat

reduced number of grid points for the computation of confidence bands, see confband.

col

line color.

fill

fill color.

lwd

line width.

…

additional arguments to the underlying methods for class mlt, see mlt-methods.

Details

coef can be used to get (and set) model parameters, logLik evaluates the log-likelihood (also for parameters other than the maximum likelihood estimate); vcov returns the estimated variance-covariance matrix (possibly taking cluster into account) and and estfun gives the score contribution by each observation. predict and plot can be used to inspect the model on different scales.

References

Torsten Hothorn, Lisa Moest, Peter Buehlmann (2018), Most Likely Transformations, Scandinavian Journal of Statistics, 45(1), 110--134, 10.1111/sjos.12291.

Examples

Run this code

# NOT RUN {
    data("BostonHousing2", package = "mlbench")

    ### fit non-normal Box-Cox type linear model with two
    ### baseline functions (for houses near and off Charles River)
    BC_BH_2 <- BoxCox(cmedv | 0 + chas ~ crim + zn + indus + nox + 
                      rm + age + dis + rad + tax + ptratio + b + lstat,
                      data = BostonHousing2)
    logLik(BC_BH_2)

    ### classical likelihood inference
    summary(BC_BH_2)

    ### coefficients of the linear predictor
    coef(BC_BH_2)

    ### plot linear predictor (mean of _transformed_ response) 
    ### vs. observed values
    plot(predict(BC_BH_2, type = "lp"), BostonHousing2$cmedv)

    ### all coefficients
    coef(BC_BH_2, with_baseline = TRUE)

    ### compute predicted median along with 10% and 90% quantile for the first
    ### observations
    predict(BC_BH_2, newdata = BostonHousing2[1:3,], type = "quantile",
            prob = c(.1, .5, .9))

    ### plot the predicted density for these observations
    plot(BC_BH_2, newdata = BostonHousing2[1:3, -1],
         which = "distribution", type = "density", K = 1000)

    ### evaluate the two baseline transformations, with confidence intervals
    nd <- model.frame(BC_BH_2)[1:2, -1]
    nd$chas <- factor(c("0", "1"))
    library("colorspace")
    col <- diverge_hcl(2, h = c(246, 40), c = 96, l = c(65, 90))
    fill <- diverge_hcl(2, h = c(246, 40), c = 96, l = c(65, 90), alpha = .3)
    plot(BC_BH_2, which = "baseline only", newdata = nd, col = col,
         confidence = "interval", fill = fill, lwd = 2,
         xlab = "Median Value", ylab = expression(h[Y]))
    legend("bottomright", lty = 1, col = col, 
            title = "Near Charles River", legend = c("no", "yes"), bty = "n")

# }