Package 'ungroup' reference manual

Title:	Penalized Composite Link Model for Efficient Estimation of Smooth Distributions from Coarsely Binned Data
Description:	Versatile method for ungrouping histograms (binned count data) assuming that counts are Poisson distributed and that the underlying sequence on a fine grid to be estimated is smooth. The method is based on the composite link model and estimation is achieved by maximizing a penalized likelihood. Smooth detailed sequences of counts and rates are so estimated from the binned counts. Ungrouping binned data can be desirable for many reasons: Bins can be too coarse to allow for accurate analysis; comparisons can be hindered when different grouping approaches are used in different histograms; and the last interval is often wide and open-ended and, thus, covers a lot of information in the tail area. Age-at-death distributions grouped in age classes and abridged life tables are examples of binned data. Because of modest assumptions, the approach is suitable for many demographic and epidemiological applications. For a detailed description of the method and applications see Rizzi et al. (2015) <doi:10.1093/aje/kwv020>.
Authors:	Marius D. Pascariu [aut, cre] , Silvia Rizzi [aut], Jonas Schoeley [aut] , Maciej J. Danko [aut]
Maintainer:	Marius D. Pascariu <[email protected]>
License:	MIT + file LICENSE
Version:	1.4.4
Built:	2024-10-25 04:17:19 UTC
Source:	https://github.com/mpascariu/ungroup

Auxiliary for Controlling `pclm` Fitting

Description

Auxiliary for Controlling pclm Fitting

Usage

control.pclm(lambda     = NA,
             kr         = 2,
             deg        = 3,
             int.lambda = c(0.1, 1e+5),
             diff       = 2,
             opt.method = c("BIC", "AIC"),
             max.iter   = 1e+3,
             tol        = 1e-3)
control.pclm(lambda     = NA,
             kr         = 2,
             deg        = 3,
             int.lambda = c(0.1, 1e+5),
             diff       = 2,
             opt.method = c("BIC", "AIC"),
             max.iter   = 1e+3,
             tol        = 1e-3)

Arguments

`lambda`	Smoothing parameter to be used in pclm estimation. If `lambda = NA` an algorithm will find the optimal values.
`kr`	Knot ratio. Number of internal intervals used for defining 1 knot in B-spline basis construction. See `MortSmooth_bbase`.
`deg`	Degree of the splines needed to create equally-spaced B-splines basis over an abscissa of data.
`int.lambda`	If `lambda` is optimized an interval to be searched needs to be specified. Format: vector containing the end-points.
`diff`	An integer indicating the order of differences of the components of PCLM coefficients. Default value: 2.
`opt.method`	Selection criterion of the model. Possible values are `"AIC"` and `"BIC"`. Default: `"BIC"`.
`max.iter`	Maximal number of iterations used in fitting procedure.
`tol`	Relative tolerance in PCLM fitting procedure. Default: 0.1% i.e. the estimated aggregate bins should be in the 0.1% error margin.

Value

A list with exactly eight control parameters.

Examples

control.pclm()
control.pclm()

Auxiliary for Controlling `pclm2D` Fitting

Description

Auxiliary for Controlling pclm2D Fitting

Usage

control.pclm2D(lambda     = c(1, 1),
               kr         = 7,
               deg        = 3,
               int.lambda = c(0.1, 1e+3),
               diff       = 2,
               opt.method = c("BIC", "AIC"),
               max.iter   = 1e+3,
               tol        = 1e-3)
control.pclm2D(lambda     = c(1, 1),
               kr         = 7,
               deg        = 3,
               int.lambda = c(0.1, 1e+3),
               diff       = 2,
               opt.method = c("BIC", "AIC"),
               max.iter   = 1e+3,
               tol        = 1e-3)

Arguments

`lambda`	Smoothing parameter to be used in pclm estimation. If `lambda = NA` an algorithm will find the optimal values.
`kr`	Knot ratio. Number of internal intervals used for defining 1 knot in B-spline basis construction. See `MortSmooth_bbase`.
`deg`	Degree of the splines needed to create equally-spaced B-splines basis over an abscissa of data.
`int.lambda`	If `lambda` is optimized an interval to be searched needs to be specified. Format: vector containing the end-points.
`diff`	An integer indicating the order of differences of the components of PCLM coefficients. Default value: 2.
`opt.method`	Selection criterion of the model. Possible values are `"AIC"` and `"BIC"`. Default: `"BIC"`.
`max.iter`	Maximal number of iterations used in fitting procedure.
`tol`	Relative tolerance in PCLM fitting procedure. Default: 0.1% i.e. the estimated aggregate bins should be in the 0.1% error margin.

Value

A list with exactly eight control parameters.

Examples

control.pclm2D()
control.pclm2D()

Univariate Penalized Composite Link Model (PCLM)

Description

Fit univariate penalized composite link model (PCLM) to ungroup binned count data, e.g. age-at-death distributions grouped in age classes.

Usage

pclm(
  x,
  y,
  nlast,
  offset = NULL,
  out.step = 1,
  ci.level = 95,
  verbose = FALSE,
  control = list()
)
pclm(
  x,
  y,
  nlast,
  offset = NULL,
  out.step = 1,
  ci.level = 95,
  verbose = FALSE,
  control = list()
)

Arguments

`x`	Vector containing the starting values of the input intervals/bins. For example: if we have 3 bins `[0,5), [5,10) and [10, 15)`, `x` will be defined by the vector: `c(0, 5, 10)`.
`y`	Vector with counts to be ungrouped. It must have the same dimension as `x`.
`nlast`	Length of the last interval. In the example above `nlast` would be 5.
`offset`	Optional offset term to calculate smooth mortality rates. A vector of the same length as x and y. See Rizzi et al. (2015) for further details.
`out.step`	Length of estimated intervals in output. Values between 0.1 and 1 are accepted. Default: 1.
`ci.level`	Level of significance for computing confidence intervals. Default: `95`.
`verbose`	Logical value. Indicates whether a progress bar should be shown or not. Default: `FALSE`.
`control`	List with additional parameters: `lambda` – Smoothing parameter to be used in pclm estimation. If `lambda = NA` an algorithm will find the optimal values. kr – Knot ratio. Number of internal intervals used for defining 1 knot in B-spline basis construction. See `MortSmooth_bbase`. `deg` – Degree of the splines needed to create equally-spaced B-splines basis over an abscissa of data. `int.lambda` – If `lambda` is optimized an interval to be searched needs to be specified. Format: vector containing the end-points. `diff` – An integer indicating the order of differences of the components of PCLM coefficients. `opt.method` – Selection criterion of the model. Possible values are `"AIC"` and `"BIC"`. `max.iter` – Maximal number of iterations used in fitting procedure. `tol` – Relative tolerance in PCLM fitting procedure.

Details

The PCLM method is based on the composite link model, which extends standard generalized linear models. It implements the idea that the observed counts, interpreted as realizations from Poisson distributions, are indirect observations of a finer (ungrouped) but latent sequence. This latent sequence represents the distribution of expected means on a fine resolution and has to be estimated from the aggregated data. Estimates are obtained by maximizing a penalized likelihood. This maximization is performed efficiently by a version of the iteratively reweighted least-squares algorithm. Optimal values of the smoothing parameter are chosen by minimizing Bayesian or Akaike's Information Criterion.

Value

The output is a list with the following components:

`input`	A list with arguments provided in input. Saved for convenience.
`fitted`	The fitted values of the PCLM model.
`ci`	Confidence intervals around fitted values.
`goodness.of.fit`	A list containing goodness of fit measures: standard errors, AIC and BIC.
`smoothPar`	Estimated smoothing parameters: `lambda, kr` and `deg`.
`bins.definition`	Additional values to identify the bins limits and location in input and output objects.
`deep`	A list of objects created in the fitting process. Useful in diagnosis of possible issues.
`call`	An unevaluated function call, that is, an unevaluated expression which consists of the named function applied to the given arguments.

References

Rizzi S, Gampe J, Eilers PHC (2015). “Efficient Estimation of Smooth Distributions From Coarsely Grouped Data.” American Journal of Epidemiology, 182(2), 138-147. doi:10.1093/aje/kwv020.

Examples

# Data  
x <- c(0, 1, seq(5, 85, by = 5))
y <- c(294, 66, 32, 44, 170, 284, 287, 293, 361, 600, 998, 
       1572, 2529, 4637, 6161, 7369, 10481, 15293, 39016)
offset <- c(114, 440, 509, 492, 628, 618, 576, 580, 634, 657, 
            631, 584, 573, 619, 530, 384, 303, 245, 249) * 1000
nlast <- 26 # the size of the last interval

# Example 1 ----------------------
M1 <- pclm(x, y, nlast)
ls(M1)
summary(M1)
fitted(M1)
plot(M1)

# Example 2 ----------------------
# ungroup even in smaller intervals
M2 <- pclm(x, y, nlast, out.step = 0.5)
head(fitted(M1))
plot(M1, type = "s")
# Note, in example 1 we are estimating intervals of length 1. In example 2 
# we are estimating intervals of length 0.5 using the same aggregate data.

# Example 3 ----------------------
# Do not optimise smoothing parameters; choose your own. Faster.
M3 <- pclm(x, y, nlast, out.step = 0.5, 
           control = list(lambda = 100, kr = 10, deg = 10))
plot(M3)

summary(M2)
summary(M3) # not the smallest BIC here, but sometimes is not important.

# Example 4 -----------------------
# Grouped x & grouped offset (estimate death rates)
M4 <- pclm(x, y, nlast, offset)
plot(M4, type = "s")

# Example 5 -----------------------
# Grouped x & ungrouped offset (estimate death rates)

ungroupped_Ex <- pclm(x, y = offset, nlast, offset = NULL)$fitted # ungroupped offset data

M5 <- pclm(x, y, nlast, offset = ungroupped_Ex)
# Data  
x <- c(0, 1, seq(5, 85, by = 5))
y <- c(294, 66, 32, 44, 170, 284, 287, 293, 361, 600, 998, 
       1572, 2529, 4637, 6161, 7369, 10481, 15293, 39016)
offset <- c(114, 440, 509, 492, 628, 618, 576, 580, 634, 657, 
            631, 584, 573, 619, 530, 384, 303, 245, 249) * 1000
nlast <- 26 # the size of the last interval

# Example 1 ----------------------
M1 <- pclm(x, y, nlast)
ls(M1)
summary(M1)
fitted(M1)
plot(M1)

# Example 2 ----------------------
# ungroup even in smaller intervals
M2 <- pclm(x, y, nlast, out.step = 0.5)
head(fitted(M1))
plot(M1, type = "s")
# Note, in example 1 we are estimating intervals of length 1. In example 2 
# we are estimating intervals of length 0.5 using the same aggregate data.

# Example 3 ----------------------
# Do not optimise smoothing parameters; choose your own. Faster.
M3 <- pclm(x, y, nlast, out.step = 0.5, 
           control = list(lambda = 100, kr = 10, deg = 10))
plot(M3)

summary(M2)
summary(M3) # not the smallest BIC here, but sometimes is not important.

# Example 4 -----------------------
# Grouped x & grouped offset (estimate death rates)
M4 <- pclm(x, y, nlast, offset)
plot(M4, type = "s")

# Example 5 -----------------------
# Grouped x & ungrouped offset (estimate death rates)

ungroupped_Ex <- pclm(x, y = offset, nlast, offset = NULL)$fitted # ungroupped offset data

M5 <- pclm(x, y, nlast, offset = ungroupped_Ex)

Two-Dimensional Penalized Composite Link Model (PCLM-2D)

Description

Fit two-dimensional penalized composite link model (PCLM-2D), e.g. simultaneous ungrouping of age-at-death distributions grouped in age classes for adjacent years. The PCLM can be extended to a two-dimensional regression problem. This is particularly suitable for mortality analysis when mortality surfaces are to be estimated to capture both age-specific trajectories of coarsely grouped distributions and time trends (Rizzi et al. 2019).

Usage

pclm2D(
  x,
  y,
  nlast,
  offset = NULL,
  out.step = 1,
  ci.level = 95,
  verbose = TRUE,
  control = list()
)
pclm2D(
  x,
  y,
  nlast,
  offset = NULL,
  out.step = 1,
  ci.level = 95,
  verbose = TRUE,
  control = list()
)

Arguments

`x`	Vector containing the starting values of the input intervals/bins. For example: if we have 3 bins `[0,5), [5,10) and [10, 15)`, `x` will be defined by the vector: `c(0, 5, 10)`.
`y`	`data.frame` with counts to be ungrouped. The number of rows should be equal with the length of `x`.
`nlast`	Length of the last interval. In the example above `nlast` would be 5.
`offset`	Optional offset term to calculate smooth mortality rates. A vector of the same length as x and y. See Rizzi et al. (2015) for further details.
`out.step`	Length of estimated intervals in output. Values between 0.1 and 1 are accepted. Default: 1.
`ci.level`	Level of significance for computing confidence intervals. Default: `95`.
`verbose`	Logical value. Indicates whether a progress bar should be shown or not. Default: `TRUE`.
`control`	List with additional parameters: `lambda` – Smoothing parameter to be used in pclm estimation. If `lambda = NA` an algorithm will find the optimal values. kr – Knot ratio. Number of internal intervals used for defining 1 knot in B-spline basis construction. See `MortSmooth_bbase`. `deg` – Degree of the splines needed to create equally-spaced B-splines basis over an abscissa of data. `int.lambda` – If `lambda` is optimized an interval to be searched needs to be specified. Format: vector containing the end-points. `diff` – An integer indicating the order of differences of the components of PCLM coefficients. `opt.method` – Selection criterion of the model. Possible values are `"AIC"` and `"BIC"`. `max.iter` – Maximal number of iterations used in fitting procedure. `tol` – Relative tolerance in PCLM fitting procedure.

Value

The output is a list with the following components:

`input`	A list with arguments provided in input. Saved for convenience.
`fitted`	The fitted values of the PCLM model.
`ci`	Confidence intervals around fitted values.
`goodness.of.fit`	A list containing goodness of fit measures: standard errors, AIC and BIC.
`smoothPar`	Estimated smoothing parameters: `lambda, kr` and `deg`.
`bins.definition`	Additional values to identify the bins limits and location in input and output objects.
`deep`	A list of objects created in the fitting process. Useful in diagnosis of possible issues.
`call`	An unevaluated function call, that is, an unevaluated expression which consists of the named function applied to the given arguments.

References

Rizzi S, Gampe J, Eilers PHC (2015). “Efficient Estimation of Smooth Distributions From Coarsely Grouped Data.” American Journal of Epidemiology, 182(2), 138-147. doi:10.1093/aje/kwv020.

Rizzi S, Halekoh U, Thinggaard M, Engholm G, Christensen N, Johannesen TB, Lindahl-Jacobsen R (2019). “How to estimate mortality trends from grouped vital statistics.” International Journal of Epidemiology, 48(2), 571–582. doi:10.1093/ije/dyy183.

Examples

# Input data
Dx <- ungroup.data$Dx
Ex <- ungroup.data$Ex

# Aggregate data to be ungrouped in the examples below
# Select a 10y data frame
x      <- c(0, 1, seq(5, 85, by = 5))
nlast  <- 26
n      <- c(diff(x), nlast)
group  <- rep(x, n)
y      <- aggregate(Dx, by = list(group), FUN = "sum")[, 2:10]
offset <- aggregate(Ex, by = list(group), FUN = "sum")[, 2:10]

# Example 1 ---------------------- 
# Fit model and ungroup data using PCLM-2D
P1 <- pclm2D(x, y, nlast)
summary(P1)

# Plot fitted values
plot(P1)

# Plot input data
plot(P1, "observed")

# NOTE: pclm2D does not search for optimal smoothing parameters by default
# (like pclm does) because it is more time consuming. If optimization is 
# required set lambda = c(NA, NA):

P1 <- pclm2D(x, y, nlast, control = list(lambda = c(NA, NA)))

# Example 2 ---------------------- 
# Ungroup and build a mortality surface
P2 <- pclm2D(x, y, nlast, offset)
summary(P2)

plot(P2, type = "observed")
plot(P2, type = "fitted")
plot(P2, type = "fitted", colors = c("blue", "red"))
# Input data
Dx <- ungroup.data$Dx
Ex <- ungroup.data$Ex

# Aggregate data to be ungrouped in the examples below
# Select a 10y data frame
x      <- c(0, 1, seq(5, 85, by = 5))
nlast  <- 26
n      <- c(diff(x), nlast)
group  <- rep(x, n)
y      <- aggregate(Dx, by = list(group), FUN = "sum")[, 2:10]
offset <- aggregate(Ex, by = list(group), FUN = "sum")[, 2:10]

# Example 1 ---------------------- 
# Fit model and ungroup data using PCLM-2D
P1 <- pclm2D(x, y, nlast)
summary(P1)

# Plot fitted values
plot(P1)

# Plot input data
plot(P1, "observed")

# NOTE: pclm2D does not search for optimal smoothing parameters by default
# (like pclm does) because it is more time consuming. If optimization is 
# required set lambda = c(NA, NA):

P1 <- pclm2D(x, y, nlast, control = list(lambda = c(NA, NA)))

# Example 2 ---------------------- 
# Ungroup and build a mortality surface
P2 <- pclm2D(x, y, nlast, offset)
summary(P2)

plot(P2, type = "observed")
plot(P2, type = "fitted")
plot(P2, type = "fitted", colors = c("blue", "red"))

Generic Plot for pclm Class

Description

Generic Plot for pclm Class

Usage

## S3 method for class 'pclm'
plot(x, xlab, ylab, ylim, type, lwd, col, legend, legend.position, ...)
## S3 method for class 'pclm'
plot(x, xlab, ylab, ylim, type, lwd, col, legend, legend.position, ...)

Arguments

`x`	An object of class `pclm`
`xlab`	a label for the x axis, defaults to a description of `x`.
`ylab`	a label for the y axis, defaults to a description of `y`.
`ylim`	the y limits of the plot.
`type`	1-character string giving the type of plot desired. The following values are possible, for details, see plot: "p" for points, "l" for lines, "b" for both points and lines, "c" for empty points joined by lines, "o" for overplotted points and lines, "s" and "S" for stair steps and "h" for histogram-like vertical lines. Finally, "n" does not produce any points or lines.
`lwd`	Line width, a positive number, defaulting to 2.
`col`	Three colours to be used in the plot for observed values, fitted values and confidence intervals.
`legend`	a character or expression vector of length $\ge 1$ to appear in the legend. Other objects will be coerced by `as.graphicsAnnot`.
`legend.position`	Legend position, or the x and y co-ordinates to be used to position the legend.
`...`	other graphical parameters (see par for more details).

Examples

# See complete examples in pclm help page
# See complete examples in pclm help page

Generic Plot for pclm2D Class

Description

The generic plot for a pclm2D object is constructed using persp method.

Usage

## S3 method for class 'pclm2D'
plot(
  x,
  type = c("fitted", "observed"),
  colors = c("#b6e3db", "#e5d9c2", "#b5ba61", "#725428"),
  nbcol = 25,
  xlab = "x",
  ylab = "y",
  zlab = "values",
  phi = 30,
  theta = 210,
  border = "grey50",
  ticktype = "simple",
  ...
)
## S3 method for class 'pclm2D'
plot(
  x,
  type = c("fitted", "observed"),
  colors = c("#b6e3db", "#e5d9c2", "#b5ba61", "#725428"),
  nbcol = 25,
  xlab = "x",
  ylab = "y",
  zlab = "values",
  phi = 30,
  theta = 210,
  border = "grey50",
  ticktype = "simple",
  ...
)

Arguments

`x`	an object of class `pclm2D`.
`type`	chart type. Defines which data are plotted, `"fitted"` values or `"observed"` input data. Default: `"fitted"`.
`colors`	colors to interpolate; must be a valid argument to `col2rgb()`.
`nbcol`	dimension of the color palette. Number of colors. Default: 25.
`xlab`, `ylab`, `zlab`	titles for the axes. N.B. These must be character strings; expressions are not accepted. Numbers will be coerced to character strings.
`theta`, `phi`	angles defining the viewing direction. `theta` gives the azimuthal direction and `phi` the colatitude.
`border`	the color of the line drawn around the surface facets. The default, `NULL`, corresponds to `par("fg")`. A value of `NA` will disable the drawing of borders: this is sometimes useful when the surface is shaded.
`ticktype`	character: `"simple"` draws just an arrow parallel to the axis to indicate direction of increase; `"detailed"` draws normal ticks as per 2D plots.
`...`	any other argument to be passed to `persp`.

Examples

# See complete examples in pclm2D help page
# See complete examples in pclm2D help page

Extract PCLM Deviance Residuals

Description

Extract PCLM Deviance Residuals

Usage

## S3 method for class 'pclm'
residuals(object, ...)
## S3 method for class 'pclm'
residuals(object, ...)

Arguments

`object`	an object for which the extraction of model residuals is meaningful.
`...`	other arguments.

Value

Residuals extracted from the object object.

Examples

x <- c(0, 1, seq(5, 85, by = 5))
y <- c(294, 66, 32, 44, 170, 284, 287, 293, 361, 600, 998, 
       1572, 2529, 4637, 6161, 7369, 10481, 15293, 39016)
M1 <- pclm(x, y, nlast = 26)

residuals(M1)
x <- c(0, 1, seq(5, 85, by = 5))
y <- c(294, 66, 32, 44, 170, 284, 287, 293, 361, 600, 998, 
       1572, 2529, 4637, 6161, 7369, 10481, 15293, 39016)
M1 <- pclm(x, y, nlast = 26)

residuals(M1)

Extract PCLM-2D Deviance Residuals

Description

Extract PCLM-2D Deviance Residuals

Usage

## S3 method for class 'pclm2D'
residuals(object, ...)
## S3 method for class 'pclm2D'
residuals(object, ...)

Arguments

`object`	an object for which the extraction of model residuals is meaningful.
`...`	other arguments.

Value

Residuals extracted from the object object.

Examples


Dx <- ungroup.data$Dx
Ex <- ungroup.data$Ex

# Aggregate data to ungroup it in the example below
x      <- c(0, 1, seq(5, 85, by = 5))
nlast  <- 26
n      <- c(diff(x), nlast)
group  <- rep(x, n)
y      <- aggregate(Dx, by = list(group), FUN = "sum")[, -1]

# Example
P1 <- pclm2D(x, y, nlast)

residuals(P1)
Dx <- ungroup.data$Dx
Ex <- ungroup.data$Ex

# Aggregate data to ungroup it in the example below
x      <- c(0, 1, seq(5, 85, by = 5))
nlast  <- 26
n      <- c(diff(x), nlast)
group  <- rep(x, n)
y      <- aggregate(Dx, by = list(group), FUN = "sum")[, -1]

# Example
P1 <- pclm2D(x, y, nlast)

residuals(P1)

ungroup: Penalized Composite Link Model for Efficient Estimation of Smooth Distributions from Coarsely Binned Data

Description

Versatile method for ungrouping histograms (binned count data) assuming that counts are Poisson distributed and that the underlying sequence on a fine grid to be estimated is smooth. The method is based on the composite link model and estimation is achieved by maximizing a penalized likelihood. Smooth detailed sequences of counts and rates are so estimated from the binned counts. Ungrouping binned data can be desirable for many reasons: Bins can be too coarse to allow for accurate analysis; comparisons can be hindered when different grouping approaches are used in different histograms; and the last interval is often wide and open-ended and, thus, covers a lot of information in the tail area. Age-at-death distributions grouped in age classes and abridged life tables are examples of binned data. Because of modest assumptions, the approach is suitable for many demographic and epidemiological applications. For a detailed description of the method and applications see Rizzi et al. (2015) doi:10.1093/aje/kwv020.

Details

To learn more about the package, start with the vignettes: browseVignettes(package = "ungroup")

Author(s)

Maintainer: Marius D. Pascariu [email protected] (ORCID)

Authors:

Silvia Rizzi [email protected]
Jonas Schoeley (ORCID)
Maciej J. Danko [email protected] (ORCID)

References

Currie ID, Durban M, Eilers PH (2004). “Smoothing and forecasting mortality rates.” Statistical modelling, 4(4), 279–298.

Eilers PH (2007). “Ill-posed problems with counts, the composite link model and penalized likelihood.” Statistical Modelling, 7(3), 239-254. doi:10.1177/1471082X0700700302.

Hastie TJ, Tibshirani RJ (1990). “Generalized additive models.” Monographs on Statistics and Applied Probability, 43.

Human Mortality Database (2018). “University of California, Berkeley (USA), and Max Planck Institute for Demographic Research (Germany). Data downloaded on 17/01/2018.” https://www.mortality.org.

Pascariu MD (2018). MortalityLaws: Parametric Mortality Models, Life Tables and HMD. R package version 1.6.0, https://github.com/mpascariu/MortalityLaws.

Rizzi S, Gampe J, Eilers PHC (2015). “Efficient Estimation of Smooth Distributions From Coarsely Grouped Data.” American Journal of Epidemiology, 182(2), 138-147. doi:10.1093/aje/kwv020.

Rizzi S, Halekoh U, Thinggaard M, Engholm G, Christensen N, Johannesen TB, Lindahl-Jacobsen R (2019). “How to estimate mortality trends from grouped vital statistics.” International Journal of Epidemiology, 48(2), 571–582. doi:10.1093/ije/dyy183.

Rizzi S, Thinggaard M, Engholm G, Christensen N, Johannesen TB, Vaupel JW, Lindahl-Jacobsen R (2016). “Comparison of non-parametric methods for ungrouping coarsely aggregated data.” BMC medical research methodology, 16(1), 59. doi:10.1186/s12874-016-0157-8.

Thompson R, Baker RJ (1981). “Composite link functions in generalized linear models.” Applied Statistics, 125–131.

Test Dataset in the Package

Description

Dataset containing death counts (Dx) and exposures (Ex) by age for a certain population between 1980 and 2014. The data-set is provided for testing purposes only and might be altered and outdated. Download actual demographic data free of charge from Human Mortality Database (2018). Once a username and a password is created on the website the MortalityLaws R package can be used to extract data in R format.

Usage

ungroup.data
ungroup.data

Format

An object of class ungroup.data of length 2.

Source

Human Mortality Database

References

Human Mortality Database (2018). “University of California, Berkeley (USA), and Max Planck Institute for Demographic Research (Germany). Data downloaded on 17/01/2018.” https://www.mortality.org.

Pascariu MD (2018). MortalityLaws: Parametric Mortality Models, Life Tables and HMD. R package version 1.6.0, https://github.com/mpascariu/MortalityLaws.

Package 'ungroup'

Help Index

Auxiliary for Controlling pclm Fitting

Description

Usage

Arguments

Value

See Also

Examples

Auxiliary for Controlling pclm2D Fitting

Description

Usage

Arguments

Value

See Also

Examples

Univariate Penalized Composite Link Model (PCLM)

Description

Usage

Arguments

Details

Value

References

See Also

Examples

Two-Dimensional Penalized Composite Link Model (PCLM-2D)

Description

Usage

Arguments

Value

References

See Also

Examples

Generic Plot for pclm Class

Description

Usage

Arguments

See Also

Examples

Generic Plot for pclm2D Class

Description

Usage

Arguments

See Also

Examples

Extract PCLM Deviance Residuals

Description

Usage

Arguments

Value

Examples

Extract PCLM-2D Deviance Residuals

Description

Usage

Arguments

Value

Examples

ungroup: Penalized Composite Link Model for Efficient Estimation of Smooth Distributions from Coarsely Binned Data

Description

Details

Author(s)

References

See Also

Test Dataset in the Package

Description

Usage

Format

Source

References

See Also

Auxiliary for Controlling `pclm` Fitting

Auxiliary for Controlling `pclm2D` Fitting