predict.Mort1Dsmooth: Predict Method for 1D P-splines Fits
In MortalitySmooth: Smoothing and Forecasting Poisson Counts with P-Splines

Description Usage Arguments Details Value Author(s) References See Also Examples

Obtains predictions, forecasts and optionally estimated standard errors of those predictions from a fitted Mort1Dsmooth object.

## S3 method for class 'Mort1Dsmooth'
predict(object, newdata = NULL, 
        type = c("link", "response"), 
        se.fit = FALSE, ...)

`object`	an object of class "Mort1Dsmooth", usually, a result of a call to `Mort1Dsmooth`.
`newdata`	optionally, a vector in which to look for x 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.

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.

Forecast is possible, therefore newdata can include values out of the range of the original x. See example below.

Interpolation is also feasible. See example below.

It is noteworthy to point out that when interpolating the B-spline coefficients form a polynomial sequence of degree 2*pord-1, and for extrapolation/forecasting the degree is pord-1. For the default order of differences in Mort1Dsmooth which is pord=2, one has a cubic interpolation and a linear extrapolation.

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

`fit`	predictions.
`se.fit`	estimated standard errors.

Carlo G Camarda

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/.

Mort1Dsmooth for computing Mort1Dsmooth.object.

## forecasting example
## selected data
years <- 1950:2006
death <- selectHMDdata("Denmark", "Deaths", "Females",
                       ages = 70, years = years)
exposure <- selectHMDdata("Denmark", "Exposures", "Females",
                          ages = 70, years = years)
## fit
fit <- Mort1Dsmooth(x=years, y=death,
                    offset=log(exposure))
## extrapolation
years.new <- 1950:2025
pred <- predict(fit, newdata=years.new,
                type="link", se.fit=TRUE) 
## plotting actual and fitted log-rates
## and 95% confidence interval
plot(years, log(death/exposure),
     xlim=range(years.new), ylim=range(pred$fit))
lines(years.new, pred$fit, lwd=2, col=2)
lines(years.new, pred$fit + 2*pred$se.fit, lty=2, col=2)
lines(years.new, pred$fit - 2*pred$se.fit, lty=2, col=2)

## interpolation+extrapolating example over years
## selected+summed data
years0 <- 1860:2004
death0 <- selectHMDdata("Sweden", "Deaths",
                        "Females", 50, years0)
death <- c(rowsum(death0, gl(length(death0),
                             5, length(death0))))
exposure0 <- selectHMDdata("Sweden", "Exposures",
                           "Females", 50, years0)
exposure <- c(rowsum(exposure0, gl(length(exposure0),
                                   5, length(exposure0))))
years <- seq(1862, 2002, 5)
## fit
fit <- Mort1Dsmooth(x=years, y=death, offset=log(exposure))
## predict the model for each year
pre <- predict(fit, newdata=years0,
               se.fit=TRUE)
## plot log-rates 
plot(years, log(death/exposure))
## add fitted log-rates from fit
## (every fifth year)
points(years, log(fit$fitted/exposure),
       pch=16, col=2)
## add to the plot fit and 95% confidence interval
## (every single year)
points(years0, pre$fit, col=4)
lines(years0, pre$fit + 2*pre$se, col=4)
lines(years0, pre$fit - 2*pre$se, col=4)

## interpolation+extrapolating example over ages
## selected+summed data
year <- 1965
death1.4 <- sum(selectHMDdata("Swi", "Deaths",
                              "Males", 1:4, year))
death5.99 <- colSums(matrix(selectHMDdata("Swi",
                                          "Deaths",
                                          "Males",
                                          5:99, year),
                            nrow=5))
death <- c(death1.4, death5.99)
exposure1.4 <- sum(selectHMDdata("Swi", "Exposures",
                                 "Males", 1:4, year))
exposure5.99 <- colSums(matrix(selectHMDdata("Swi",
                                             "Exposures",
                                             "Males",
                                             5:99, year),
                               nrow=5))
exposure <- c(exposure1.4, exposure5.99)
ages <- c(2.5, seq(7, 97, 5))

## fit
fit <- Mort1Dsmooth(x=ages, y=death, offset=log(exposure),
                    ndx=10)
## since the aim is to interpolate FEW data-points
## we use a large number of B-splines allows a precise,
## but not parsimonius, description

## predict the model for each age
newages <- 1:100
pre <- predict(fit, newdata=newages,
               se.fit=TRUE)
## plot log-rates 
plot(ages, log(death/exposure), pch=16)
## add fitted log-rates from fit
## (every fifth age)
points(ages, log(fit$fitted/exposure),
       pch=16, col=2)
## add to the plot fit and 95% confidence interval
## (every single year)
points(newages, pre$fit, col=4, t="o")
lines(newages, pre$fit + 2*pre$se, col=4)
lines(newages, pre$fit - 2*pre$se, col=4)