MortalitySmooth (version 2.3.4)

predict.Mort2Dsmooth: Predict Method for 2D P-splines Fits

Description

Obtains predictions, forecasts and optionally estimated standard errors of those predictions from a fitted Mort2Dsmooth object.

Usage

"predict"(object, newdata = NULL,  type = c("link", "response"),  se.fit = FALSE, ...)

Arguments

object

an object of class "Mort2Dsmooth", usually, a result of a call to Mort2Dsmooth.

newdata

optionally, a list in which to look for x and/or y with which to predict. If omitted, the fitted linear predictors are used.

type

the type of prediction required. The default ("link") is on the scale of the linear predictors; the alternative "response" is on the scale of the response variable.

se.fit

logical switch indicating if standard errors are required. Default: FALSE.

...

other predict parameters to passed to predict. Not in used.

Value

If se.fit = FALSE, a matrix of predictions. If se.fit = TRUE, a list with components:

fit

a matrix of predictions.

se.fit

a matrix of estimated standard errors.

Details

If newdata is omitted the predictions are based on the data used for the fit. Note that, in common with other prediction functions, any offset supplied as an argument is always ignored when predicting, unlike offsets specified in modelling. The user can provide also a single predictor (either x or y) within the argument newdata. The name within the list newdata must be named x and y. Forecast is possible, therefore newdata can include values out of the range of the original x and y. See example below.

Interpolation is also feasible. See example below.

References

Camarda, C. G. (2012). MortalitySmooth: An R Package for Smoothing Poisson Counts with P-Splines. Journal of Statistical Software. 50, 1-24. http://www.jstatsoft.org/v50/i01/.

Currie, I. D., M. Durban, and P. H. C. Eilers (2004). Smoothing and forecasting mortality rates. Statistical Modelling. 4, 279-298.

See Also

Mort2Dsmooth for computing Mort2Dsmooth.object.

Examples

## computing confidence intervals
## selected data
years <- 1980:2006
ages <- 80:100
death <- selectHMDdata("Denmark", "Deaths", "Females",
                       ages = ages, years = years)
exposure <- selectHMDdata("Denmark", "Exposures", "Females",
                          ages = ages, years = years)
## fit
fit <- Mort2Dsmooth(x=ages, y=years, Z=death,
                    offset=log(exposure),
                    method=3, lambdas=c(100,500))

## predict and computing standard errors
pre <- predict(fit, se.fit=TRUE)

## plotting over ages and years 95% confidence intervals 
## !hard to distinguish between upper
## and lower confidence bounds
grid. <- expand.grid(x = ages, y = years, gr = 1:2)
grid.$lmx <- c(c(pre$fit - 2*pre$se.fit),
               c(pre$fit + 2*pre$se.fit))
wireframe(lmx ~ x * y, data = grid., groups = gr,
          scales = list(arrows = FALSE),
          drape = TRUE, colorkey = TRUE)

## plotting age 80 (first row)
plot(years, log(death[1,] / exposure[1,]),
     main="Mortality rates, log-scale.
           Danish females, age 80, 1980:2006")
lines(years, pre$fit[1,], lwd=2, col=2)
lines(years, pre$fit[1,] + 2*pre$se.fit[1,],
      lwd=2, col=2, lty=2)
lines(years, pre$fit[1,] - 2*pre$se.fit[1,],
      lwd=2, col=2, lty=2)

## forecasting example
newyears <- 1980:2020
newdata <- list(x=ages, y=newyears) 
pre.for <- predict(fit, newdata=newdata, se.fit=TRUE)

## plot fitted+forecast log-rates for all ages over years
matplot(years, t(log(death/exposure)), pch=1, cex=0.5,
        col=rainbow(length(ages)),
        xlim=range(newyears),
        ylim=range(pre.for$fit),
        ylab="log-mortality")
matlines(newyears, t(pre.for$fit), lty=1, lwd=2,
        col=rainbow(length(ages)))

## plot selected ages over years, with 95% confidence intervals
whiA <- c(1,6,11)
matplot(years, t(log(death[whiA,]/exposure[whiA,])),
        pch=1,
        xlim=range(newyears),
        ylim=c(-3.3, -1.5),
        ylab="log-mortality")
matlines(newyears, t(pre.for$fit[whiA,]), lty=1, lwd=2)
matlines(newyears, t(pre.for$fit[whiA,]+
                     2*pre.for$se.fit[whiA,]), lty=2)
matlines(newyears, t(pre.for$fit[whiA,]-
                     2*pre.for$se.fit[whiA,]), lty=2)


## interpolation example
## compute log-death rates for
## each calendar month and calendar ages
newyears12 <- seq(1990, 2000, length=11*11)
newages12 <- seq(90, 100, length=11*11)
newdata12 <- list(x=newages12, y=newyears12)
pre12 <- predict(fit, newdata=newdata12, se.fit=TRUE)

## death rates in June 1995 at age 95.5
which.age <- which(newages12==95.5)
which.year <- which(newyears12==1995.5)
exp(pre12$fit[which.age, which.year] +
    c(-2*pre12$se.fit[which.age, which.year],
      0, 2*pre12$se.fit[which.age, which.year]))