apc.plot.fit: Plots of apc estimates

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

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,
					las=NULL,mar=NULL,oma=NULL,mgp=c(2,1,0),
					vec.xlab=NULL)

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.
las: Optional. Plot parameter, see par. Numeric. The style of axis labels. 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.
vec.xlab: Optional. Controls title for xaxis. Should be a 9-vector of characters for an array of plots and a character for a single plot. As R recycles entries if a vector is too short, then vec.xlab="" will remove titles on x-axis. Default: NULL.

Author

Bent Nielsen <bent.nielsen@nuffield.ox.ac.uk> & Zoe Fannon 28 September 2020 (12 Apr 2015).

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: tools:::Rd_expr_doi("https://doi.org/10.1093/biomet/asn026"); Earlier version Nuffield DP.

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

Examples

Run this code

#####################
#	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")
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")
apc.plot.fit(fit.ac)

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

#	to get only a sub plot and playing with titles
#	main.outer not used with individual plot
apc.plot.fit(fit.ac,sub.plot="a",main.outer="My outer title",main.sub="My sub title")
#	to play with
#		titles (main.outer/main.sub),
#		label orientation (las),
#		axis titles (vec.xlab)
apc.plot.fit(fit.ac,main.outer="My outer title",
				main.sub=c("1","2","3","4","5","6","7","8","9"),
				las=1,
				vec.xlab=c("a","b","c","d","e","f","g","h","i"))

Run the code above in your browser using DataLab