new.apc.plot.fit: Plots of apc estimates

In apc: Age-Period-Cohort Analysis

Description

Functions to plot the apc estimates found by apc.fit.model. The function apc.plot.fit detects the type of model.design and model.family from the fit values and makes appropriate plots.

Depending on the model.design the plot has up to 9 sub plots. The type of these can be chosen using type

Model designs of any type. If type is "detrend" or "sum.sum" the canonical age period cohort parametrisation is used. This involves double differences of the time effects. The first row of plots are double differences of the time effects. The next two rows of plots illustrate the representation theorem depending on the choice of type. In both cases the sum of the plots add up to the predictor.

"detrend"

The last row of plots are double sums of double differences detrend so that that each series starts in zero and ends in zero. The corresponding level and (up to) two linear trends are shown in the middle row of plots. The linear trends are identified to be 0 for age, period or cohort equal to its smallest value. See note 2 below.

"sum.sum"

The last row of plots are double sums of double differences anchored as in the derivation of Nielsen (2014b). The corresponding level and (up to) two linear trends are shown in the middle row of plots. The linear trends are identified to be 0 for the anchoring point U of age, period or cohort as described in Nielsen (2014b). See note 1 below.

Model designs with 2 factors. If type is "dif" the canonical two factor parametrisation is used. This involves single differences. It is only implemented for model.design of "AC", "AP", "PC". It does not apply for model.design of "APC" because single differences are not identified. It does not apply for the drift models where model.design is "Ad", "Pd", "Cd", "t" because it is not clear which time scale the second linear trend should be attributed to. It is not implemented for model.design of "tA, "tP", "tC", "1". The first row of plots are single differences of the time effects. The next two rows of plots illustrate the representation theorem. In the second row the level is given and in the third row plots of single sums of single differences are given, normalised to start in zero.

Appearance may vary. Note, the plots "detrend" and "dif" can give very different appearance of the time effects. The "dif" plots are dominated by linear trends. They can therefore be more difficult to interpret than the "detrend" plots, where linear trends are set aside.

Standard deviations. All plots include plots of 1 and 2 standard deviations. The only exception is the intercept in the case model.family is "poisson.response" as this uses a multinomial sampling scheme, where the intercept is set to increase in the asymptotic experiment. The default is to plot standard deviations around zero, so that they represent a test for zero values of the parameters. Using the argument sdv.at.zero the standard deviations can be centered around the estimates. This can give a very complicated appearance.

Values of coefficients. These can be found using apc.identify.

Usage

new.apc.plot.fit(apc.fit.model,scale=FALSE,
					sdv.at.zero=TRUE,type="detrend",
					include.linear.plane=TRUE,
					include.double.differences=TRUE,
					sub.plot=NULL,main.outer=NULL,main.sub=NULL,
					cex=NULL,cex.axis=NULL,cex.lab=NULL,cex.main=NULL,
					cex.main.outer=1.2,
					line.main=0.5,line.main.outer=NULL,
					mar=NULL,oma=NULL,mgp=c(2,1,0))

Arguments

apc.fit.model	List. See apc.fit.model for a description of the format.
scale	Optional. Logical. If (TRUE) FALSE use scale of (inverse) link function. Default is FALSE.
sdv.at.zero	Optional. Logical. If FALSE/TRUE standard deviations are plotted around estimates/zero. Default is TRUE.
type	Optional. Character. If "detrend" double sums start and end in zero. If "sum.sum" double sums anchored as discussed in Nielsen (??). Default is "detrend".
include.linear.plane	Optional. Logical. If true include plots of linear plane. Default TRUE
include.double.differences	Optional. Logical. If true include plots of double differences. Default TRUE
sub.plot	Optional. Character: "a","b",...,"i". Only the indicated sub plot is plotted. Default is NULL so all plots shown.
main.outer	Optional. Character. Main title in outer margin. Default is generated internally.
main.sub	Optional. Vector of 9 characters. Main titles for individual plots. Default is generated internally, see note 3 below.
cex	Optional. Plot parameter, see par. Controls size of text. Default is NULL so that R default is used.
cex.axis	Optional. Plot parameter, see par. Controls magnification of axis annotations. Default is NULL so that R default is used.
cex.lab	Optional. Plot parameter, see par. Controls magnification of axis labels. Default is NULL so that R default is used.
cex.main	Optional. Plot parameter, see par. Controls magnification of main title. Default is NULL so that R default is used.
cex.main.outer	Optional. Controls magnification of outer main title if an array of plots is shown. Default is 1.2 (same as cex.main).
line.main	Optional. Specifies the line position of main title in individual plots. Default is 0.5.
line.main.outer	Optional. Specifies the line position of outer main title if an array of plots is shown. Default is NULL so that R default is used.
mar	Optional. Gives the number of lines of margin to be specified on the four sides of the plot. Default: c(4,3,2,0) for array of plots, c(4,4,3,1) for a single plot.
oma	Optional. Gives the size of the outer margins in lines of text. Default: c(0,0,5,1) for array of plots, c(0,0,0,0) for a single plot.
mgp	Optional. Plot parameter, see par. The margin line for the axis title, axis label and axis line. Defauls is c(2,1,0), different from R default.

Note

(1) The type "sum.sum" (same as "ss.dd") gives double sums anchored to be zero in the three points where age=cohort=U, age=U+1,cohort=U age=U,cohort=U+1 with apc.fit.model$U and where U is the integer value of (per.zero+3)/2 This corresponds to the representation in Nielsen (2014b). The linear plane is parametrised in terms of a level, which is the value of the predictor at age=cohort=U; an age slope, which is the difference of the values of the predictor at age=U+1,cohort=U and age=cohort=U; an cohort slope, which is the difference of the values of the predictor at age=U,cohort=U+1 and age=cohort=U.

(2) The type "detrend" gives double sums that start in zero and end in zero. The linear plane is parametrised in terms of a level, which is the value of the predictor at age=cohort=1, which is usually outside the index set for the data; while age and cohort slopes are adjusted for the ad hoc identification of the time effects.

(3) The default of the titles main.sub are generated internally depending on model specification. In the case of model.design="APC" and a dose-response model family the default value is c(expression(paste("(a) ",Delta^2,alpha)), expression(paste("(b) ",Delta^2,beta)), expression(paste("(c) ",Delta^2,gamma)), "(d) first linear trend", "(e) level", "(f) second linear trend", expression(paste("(g) detrended ",Sigma^2,Delta^2,alpha)), expression(paste("(h) detrended ",Sigma^2,Delta^2,beta)), expression(paste("(i) detrended ",Sigma^2,Delta^2,gamma)))

(4) Default values of parameters changed (25 Sep 2020). The old appearance can be reproduced by setting cex.lab=1.5. For example:

data.list <- data.Italian.bladder.cancer()

fit.apc <- apc.fit.model(data.list,"poisson.dose.response","APC")

apc.plot.fit(fit.apc,cex.lab=1.5)

Author(s)

Bent Nielsen <[e-mail]> 12 Apr 2015 updated 24 September 2020 vs 2.0.0. Subsumes var.apc.plot.fit by Zoe Fannon.

References

Kuang, D., Nielsen, B. and Nielsen, J.P. (2008a) Identification of the age-period-cohort model and the extended chain ladder model. Biometrika 95, 979-986. Download: Article; Earlier version Nuffield DP.

Nielsen, B. (2014b) Deviance analysis of age-period-cohort models. Work in progress.

See Also

data.asbestos and data.Italian.bladder.cancer for information on the data used in the example.

Values of coefficients can be found using apc.identify.

Further information on the identification in the vignette Identification.pdf, Identification.R on Vignettes.

Examples

#####################
#	Example with Italian bladder cancer data
#	Note that the model.design "AC" cannot be rejected against "APC"
#		so there is little difference between the two plots of those fits.

data.list	<- data.Italian.bladder.cancer()
apc.fit.table(data.list,"poisson.dose.response")
fit.apc		<- apc.fit.model(data.list,"poisson.dose.response","APC")
new.apc.plot.fit(fit.apc)
#	now try an AC model
#	can use dev.new() to see both
fit.ac		<- apc.fit.model(data.list,"poisson.dose.response","AC")
new.apc.plot.fit(fit.ac)

#	to check the numerical values for the last two rows of plots use
new.apc.identify(fit.ac)$coefficients.detrend

#	to get only a sub plot and playing with titles
#	main.outer not used with individual plot
new.apc.plot.fit(fit.ac,sub.plot="a",main.outer="My outer title",main.sub="My sub title")
#	to get only a all plots and playing with titles
new.apc.plot.fit(fit.ac,main.outer="My outer title",main.sub=c("1","2","3","4","5","6","7","8","9"))

apc documentation built on Oct. 23, 2020, 6:17 p.m.