vitality.6p {vitality}

Fitting routine for the 2-process, 6-parameter vitality model (with childhood hook).

Description

This function provides the fitting routine for the 6-parameter 2-process vitality model. Intrinsic mortality is characterized by the mean (r) and variability (s) in the vitality loss rate. Adult extrinsic mortality is characterized by random challenges of frequency (lambda) and random magnitude (beta) exceeding the remaining average vitality. Child extrinsic mortality is characterized by childhood challenges of frequency (gamma) exceeding childhood vitality development rate (alpha). Model is appropriate to full lifespan of human mortality data (e.g. Anderson and Li 2015).

Usage

  vitality.6p(time = 0:(length(sdata)-1), sdata, init.params = FALSE, 
    lower = c(0, 0, 0, 0, 0, 0),upper = c(100,50,100,50,50,10), 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). Typically this refers to ages.

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.

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, gamma, alpha) in that order (e.g.. init.params = c(.1, .02, .3, 0.12, 0.1, 1)).

lower

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

upper

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

pplot

Optional, Boolean. Plots of cumulative survival for both data and fitted curves? Default: TRUE. FALSE produces no plots. 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 total, intrinsic, extrinsic (child), and extrinsic (adult) mortality curves? Default: 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, the approximated, plotted mortality rates may be inaccurate (e.g. For human mortality data, mortality rates at the oldest ages are underestimated because nax is assumed to be half the length of the age interval but the true nax is likely larger). This caveat applies only to the plotted mortality rates (black circles in plot). The plotted, fitted lines are calculated with the parameter estimates themselves and are unaffected by the estimation of the mortality rates for this plot. pplot must be set to TRUE and Iplot=FALSE.

tlab

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

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, gamma and alpha 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.

Anderson, J.J. and T. Li. (2015). "A two-process mortality model with extensions to juvenile mortality, populations and evolution." Population Association of America Annual Meeting 2015 http://paa2015.princeton.edu/abstracts/153144

Examples

data(swedish_females)
swe <- swedish_females
initial_age <- 0 
time <- swedish_females$age
survival_fraction <- swe$lx / swe$lx[1]
sample_size <- swe$Lx[1] #sample size

results.6par <- vitality.6p(time = time,
                            sdata = survival_fraction,
                            #init.params=FALSE,
                            init.params=c(0.012, 0.01, 0.1, 0.1, 0.1, 1),
                            lower = c(0, 0, 0, 0, 0, 0), upper = c(100,50,1,50,50,50),
                            rc.data = TRUE, 
                            se=FALSE,
                            #se = sample_size, 
                            datatype = "CUM", 
                            ttol = 1e-06,
                            pplot = TRUE,
                            Iplot = TRUE,
                            Mplot = TRUE,
                            tlab = "years",
                            silent = FALSE)