vitality.4p {vitality}

Fitting routine for the 2-process, 4-parameter vitality model (no childhood hook).

Description

This function provides the fitting routine for the 4-parameter 2-process vitality model. Intrinsic mortality is characterized by the mean (r) and variability (s) in the vitality loss rate. Extrinsic mortality is characterized by random challenges of frequency (lambda) and random magnitude (beta) exceeding the remaining average vitality. Model is appropriate to adult human mortality data (e.g. Li and Anderson 2013).

Usage

  vitality.4p(time = 0:(length(sdata)-1), sdata, init.params = FALSE, 
    lower = c(0, 0, 0, 0), upper = c(100,50,100,50),rc.data = FALSE, 
    se = FALSE, datatype = c("CUM", "INC"), ttol = 1e-06, pplot = TRUE,
    Iplot = FALSE, Mplot = FALSE, tlab = "years", silent = FALSE)

Arguments

time

Vector. Time component of data: Defaults to 0:(length(sdata)-1).

sdata

Required. Survival or mortality data. The default expects cumulative survival fraction. If providing incremental mortality fraction instead, use option: datatype = "INC". The default also expects the data to represent full mortality. Otherwise, use option: rc.data = T to indicate right censored data. If first element of sdata <1 data will be rescaled.

rc.data

Optional, Boolean. Specifies Right Censored data. If the data does not represent full mortality, it is probably right censored. The default is rc.data = F. A third option is rc.data = "TF". Use this case to add a near-term zero survival point to data which displays nearly full mortality ( <.01 survival at end). If rc.data = F but the data does not show full mortality, rc.data = "TF" will be invoked automatically.

se

Optional, Boolean. Calculates the standard errors for the MLE parameters. Default is FALSE. Set equal to the initial study population to compute standard errors.

datatype

Optional. Defaults to "CUM" for cumulative survival fraction data. Use "INC" - for incremental mortality fraction data.

ttol

Optional. Stopping criteria tolerance. Default is 1e-6. Specify as ttol = .0001. If one of the likelihood plots (esp. for "k") does not look optimal, try decreasing ttol. If the program crashes, try increasing ttol.

init.params

Optional. Please specify the initial param values. specify init.params = c(r, s, lambda, beta) in that order (e.g.. init.params = c(.1, .02, .3, 0.12)).

lower

vector of lower parameter bounds in order of c(r, s, lambda, beta). see nlminb

upper

vector of upper parameter bounds in order of c(r, s, lambda, beta). see nlminb

pplot

Optional, Boolean. Plots of cumulative survival for both data and fitted curves? Default TRUE. FALSE Produce no plots. A A third option: pplot = n (n >= 1) extends the time axis of the fitting plots (beyond the max time in data). For example: pplot = 1.2 extends the time axis by 20 Note: the incremental mortality plot is a continuous representation of the appropriately- binned histogram of incremental mortalities.

Iplot

Optional, Boolean. Incremental mortality for both data and fitted curves? Default: FALSE.

Mplot

Optional, Boolean. Plot fitted mortality curve? Default is FALSE. If TRUE 'observed' mortality rates for plotting are approximate and estimated from the input survival data. Depending on time (ages) and the change in mortality over age, these may be unrealistic but the fitted lines are derived from the parameter estimates themselves. For human data, the approximated mortality rates diverge at ages >80. pplot must be set to TRUE and Iplot=FALSE.

tlab

Optional, character. specifies units for x-axis of plots. Default is "days".

silent

Optional, Boolean. Stops all print and plot options (still get most warning and all error messages) Default is FALSE. A third option, "verbose" also enables the trace setting in the ms (minimum sum) S-Plus routine.

Value

vector of final MLE r, s, lambda, beta parameter estimates. standard errors of MLE parameter estimates (if se = <population> is specified).

References

D.H. Salinger, J.J. Anderson and O. Hamel (2003). "A parameter fitting routine for the vitality based survival model." Ecological Modeling 166(3): 287–294.

Li, T. and J.J. Anderson (2013). "Shaping human mortality patterns through intrinsic and extrinsic vitality processes." Demographic Research 28(12): 341-372.

Examples

data(swedish_females)
swe <- swedish_females
initial_age <- 20 # Could be adjusted
time <- initial_age:max(swedish_females$age)
survival_fraction <- swe$lx / swe$lx[1]
survival_fraction <- survival_fraction[time] # when first element <1 data is adjusted
sample_size <- swe$Lx[initial_age] #sample size

results.4par <- vitality.4p(time = time,
                            sdata = survival_fraction,
                            #init.params=FALSE,
                            init.params=c(0.012, 0.01, 0.1, 0.1),
                            lower = c(0, 0, 0, 0), upper = c(100,50,1,50),
                            rc.data = TRUE, 
                            se = sample_size, 
                            datatype = "CUM", 
                            ttol = 1e-06,
                            pplot = TRUE,
                            Iplot = TRUE,
                            Mplot = TRUE,
                            tlab = "years",
                            silent = FALSE)