Description Usage Arguments Details Value Author(s) References See Also Examples
The PCLM method is based on the composite link model, with a penalty added to ensure the smoothness of the target distribution. Estimates are obtained by maximizing a penalized likelihood. This maximization is performed efficiently by a version of the iteratively reweighted leastsquares algorithm. Optimal values of the smoothing parameter are chosen by minimizing Bayesian or Akaike<e2><80><99> s Information Criterion [From Rizzi et al. 2015 abstract].
1 2 3 
object 
A 
population.size 
Population size. If it is not given then it will be retrieved from the pash object (if possible). You may want to set it to a high value (e.g. 10000) if the data has no information about population number. 
out.step 
Age interval length in output aggregated lifetable. If set to 
to.pash 
A way how the

last_open 
Logical determining if to construct 
nax.method 
A way of calculating nax in 
control 
List with additional parameters. See 
The function read pash
object and run pclm.general
function. The new pash
object is constructed from pclm.general
output.
Use pclm.general
for more flexible and direct PCLM fitting.
An object of classes "pclm"
and "pash"
with PCLMbased lifetable and $pclm
component.
The function updates a pash
object by fitting PCLM.
The new object inherits source
and time_unit
attributes from the original pash
object as well as class "pash"
.
The pash lifetable (component $lt
) contains the lifetable based on the fitted PCLM (aggregated or nonaggregated depending on to.pash
parameter).
The newly constructed pash
object contains extra $pclm
component needed to run summary
and plot
functions.
List of $pclm
subcomponents:

Lifetable based on aggregated PCLM fit defined by 

Lifetable based on original (raw) PCLMfit. 

PCLM fit used to construct lifetables. 

List with warnings. 

Interval multiple, see 

Value of 

Interval length of aggregated lifetable, see 
Maciej J. Danko <[email protected]> <[email protected]>
Rizzi S, Gampe J, Eilers PHC. Efficient estimation of smooth distributions from coarsely grouped data. Am J Epidemiol. 2015;182:138?47.
Rizzi S, Thinggaard M, Engholm G, et al. Comparison of nonparametric methods for ungrouping coarsely aggregated data. BMC Medical Research Methodology. 2016;16:59. doi:10.1186/s1287401601578.
pclm.control
, plot.pclm
, summary.pclm
, pash
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# *******************************************************************
# Usage of PCLM methods for simple cases
# *******************************************************************
# *** Create pash objects with different interval lengths
AU1 < Inputlx(x = australia_1y$x, lx = australia_1y$lx,
nax = australia_1y$nax, nx = australia_1y$nx, last_open = TRUE)
AU10 < Inputlx(x = australia_10y$x, lx = australia_10y$lx,
nax = australia_10y$nax, nx = australia_10y$nx, last_open = TRUE)
# *** Use PCLM
# Ungroup AU10 with out.step equal minimal interval length
min(AU10$lt$nx[13])
AU10p.1a < pclm.fit(AU10)
print(AU10p.1a)
plot(AU10p.1a)
# Ungroup AU10 with out.step equal minimal interval length
# and get good estimates of nax
AU10p.1b < pclm.fit(AU10, control = list(x.div = 10))
print(AU10p.1b)
plot(AU10p.1b)
# This time number of internal (raw) PCLM classes was high
# and automatically Psplines were used to prevent long computations
# This number can be estimated before performing
# PCLM calclualtions:
pclm.nclasses(AU10$lt$x, control = list(x.div = 10))
# which is the same as in the fitted model
length(AU10p.1b$pclm$raw$x)
# whereas number of classes in the pash lifetable
# depends on out.step
length(AU10p.1b$lt$x)
length(AU10p.1b$pclm$grouped$x) # equivalently
# To speedup computations we can decrease the number of Psline knots
AU10p.1c < pclm.fit(AU10, control = list(x.div = 10,
bs.use = TRUE, bs.df.max = 100))
# We can also use raw (nonaggregated) PCLM lifetable
# as the default pash lifetable:
AU10p.1d < pclm.fit(AU10, control = list(x.div = 10),
to.pash = "nonaggregated")
print(AU10p.1d)
length(AU10p.1d$lt$x) # the number of raw PCLM classes =
# = number of pash lifetable classes
# *** Pace measures sorted (ascending order) by
# potential precision of computation
GetPace(AU10)
GetPace(AU10p.1a)
GetPace(AU10p.1b)
GetPace(AU10p.1c)
GetPace(AU10p.1d)
GetPace(AU1)
# The same for shappe
GetShape(AU10)
GetShape(AU10p.1a)
GetShape(AU10p.1b)
GetShape(AU10p.1c)
GetShape(AU10p.1d)
GetShape(AU1)
# *** Diagnostic plots for fitted PCLM model
# Aggregated PCLM fit:
plot(AU10p.1b, type = 'aggregated')
# Raw PCLM fit before aggregation:
plot(AU10p.1b, type = 'nonaggregated')
# In this PCLM fit aggregated lifetable is identical
# with nonaggregated
plot(AU10p.1a, type = 'aggregated')
plot(AU10p.1a, type = 'nonaggregated')
# *** Combined summary of pash and pclm objects
summary(AU10p.1a)
summary(AU10p.1b)
summary(AU10p.1c)
summary(AU10p.1d)
# Summary if pclm object is not present
summary(AU10)
# *** Smooth and aggregate data into 12year interval
AU10p.2 < pclm.fit(AU10, out.step = 12)
print(AU10p.2)
print(AU10p.2, type = 'aggregated') # grouped PCLM lifetable
print(AU10p.2, type = 'nonaggregated') # raw PCLM lifetable
plot(AU10p.2)
# *** Effect of the smaller sample size on the estimate.
# Forced change of population size.
AU10p.3 < pclm.fit(AU10, population.size = 20, out.step = 1,
control = list(x.div = 1))
plot(AU10p.3)
# *** Plotting mortality
AU10p.4a < pclm.fit(AU10, population.size=1e6, control = list(x.div = 5))
plot(AU10p.4a$lt$x, log10(AU10p.4a$lt$nmx), type='l', lwd = 2,
xlim=c(0,130), xlab='Age', ylab='log_10 mortality', col = 2)
lines(AU1$lt$x, log10(AU1$lt$nmx), type = 'p')
tail(AU10p.4a, n = 10)
#note that lx has standardized values
# Improving the plot to cover more age classes
AU10p.4b < pclm.fit(AU10, control = list(zero.class.end = 150,
x.div = 4))
plot(AU10p.4b$lt$x, log10(AU10p.4b$lt$nmx), type='l', lwd = 2,
xlim=c(0,130), xlab='Age', ylab='log_10 mortality', col = 2)
lines(AU1$lt$x, log10(AU1$lt$nmx), type = 'p')
print(AU10p.4b$lt[111:120,])
# The change of the order of the difference in pclm algorithm may
# affect hte interpretation of the tail.
# But try to check also pclm.deg = 4 and 5.
AU10p.4c < pclm.fit(AU10, control = list(zero.class.end = 150,
x.div = 4, pclm.deg = 4))
plot(AU10p.4c$lt$x, log10(AU10p.4c$lt$nmx), type='l', lwd = 2,
xlim=c(0,130), xlab='Age', ylab='log_10 mortality', col = 2)
lines(AU1$lt$x, log10(AU1$lt$nmx), type = 'p')
# *******************************************************************
# Usage of PCLM methods for more complicated dataset
#  understanding the out.step, x.div, and interval multiple
# *******************************************************************
# *** Generate a dataset with varying and fractional interval lengths
x < c(0, 0.6, 1, 1.4, 3, 5.2, 6.4, 8.6, 11, 15,
17.2, 19, 20.8, 23, 25, 30)
ndx < ceiling(10000*diff(pgamma(x, shape = 3.8, rate = .4)))
barplot(ndx/diff(x), width = c(diff(x), 2)) # preview
# *** Create pash object
(B < Inputlx(x = x, lx = 10000c(0, cumsum(ndx)), last_open = TRUE))
# *** Fit PCLM with automatic out.step
Bp1 < pclm.fit(B)
# Output interval length (out.step) is automatically set to 0.4
# which is the minimal interval length in original data.
min(B$lt$nx, na.rm = T)
summary(Bp1) #new out.step can be also read from summary
plot(Bp1)
# *** Setting manually out.step
Bp2 < pclm.fit(B, out.step = 1)
plot(Bp2, type = 'aggregated') # The fit with out.step = 1
plot(Bp2, type = 'nonaggregated') # It is clear that
# PCLM extended internal interval length even without changing x.div
# It was done because of the fractional parts in x vector.
# This is also a case for Bp1
summary(Bp2) #PCLM interval length = 0.2
Bp2$pclm$raw$n[1:10]
# *** Setting manually out.step to a smaller value than
# the smallest original interval length
Bp3 < pclm.fit(B, out.step = 0.1)
summary(Bp3)
# We got a warning as out.step cannot be smaller than
# smallest age class if x.div = 1
# We can change x.div to make it possible
Bp3 < pclm.fit(B, out.step = 0.1, control = list(x.div = 2))
#0.1 is two times smaller than minimal interval length
summary(Bp3) # We were able to change the interval
plot(Bp3)
# NOTE: In this case x.div has not sufficient value to
# get good axn estimates
Bp3$pclm$grouped$ax[1:10]
Bp3$lt$nax[1:10] #equivalently
# This can be changed by the further increase of x.div
Bp4 < pclm.fit(B, out.step = 0.1, control = list(x.div = 20))
Bp4$pclm$grouped$ax[1:10]
# NOTE: This time Pspline approximation was used because
# the composition matrix was huge
# Finally, we were able to get our assumed out.step
Bp4$pclm$grouped$n[1:10]
Bp4$lt$nx[1:10] #equivalently
In the fitted model the interval multiple (m) is 5.
(m < pclm.interval.multiple(B$lt$x, control = list(x.div = 20)))
summary(Bp4)
# Interval multiple determines
# the maximal interval length in raw PCLM lifetable,
(K < 1 / m)
# which is further divided by x.div.
K / 20
# Simply: 1 / (m * x.div) = 1 / (5 * 20) = 0.01
# The interval in the raw PCLM lifetable is 10 times shorter than
# in the grouped lifetable
#interval length in aggregated PCLM lifetable:
Bp4$pclm$grouped$n[1:10]/ # divided by
# interval length in nonaggregated PCLM lifetable:
Bp4$pclm$raw$n[1:10]
# REMEBER: The interval for the raw PCLM lifetable depends
# on original interval, m, and x.div,
# whereas the grouped PCLM interval length is set by out.step,
# which could be eventually increased if out.step < raw PCLM
# interval length.
# *** Setting nonaggregated PCLM lifetable as pash lifetable #2
Bp5 < pclm.fit(B, out.step = 0.1, control = list(x.div = 20),
to.pash = "nonaggregated", nax.method = "cfm")
# NOTE: For the very small interval length the "cfm" method
# may not give realistic nax values
Bp5
Bp4
GetShape(Bp4)
GetShape(Bp5)
# **** See more examples in the help for pclm.nclasses() function.
## End(Not run)

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