A class of generalised Lee-Carter models
A purpose-built regression routine to fit any of the six variants of the class of Lee-Carter model structures using an iterative Newton-Raphson fitting method.
lca.rh(dat, year = dat$year, age = dat$age, series = 1, max.age = 100,
dec.conv = 6, clip = 3, error = c("poisson", "gaussian"),
model = c("m", "h0", "h1", "h2", "ac", "lc"),
restype = c("logrates", "rates", "deaths", "deviance"), scale = F,
interpolate = F, verbose = T, spar = NULL)dat |
source data object of |
year |
vector of years to be included in the regression (all available years by default) |
age |
vector of ages to be included in the regression (all available ages by default) |
series |
numerical index corresponding to the target series to be used from the source data |
max.age |
highest age to be used in the regression |
dec.conv |
number of decimal places used to achieve convergence. The lower the value the faster the convergence of the fitting algorithm. |
clip |
number of marginal birth cohorts to exclude from the regression (i.e., give 0 weights). It is only applicable to the first 5 models (see below) |
error |
type of error structure of the model choice (Poisson distribution of the errors by default) |
model |
a character (see usage) or a numeric value (1-6) to specify the model choice |
restype |
types of residuals, which also controls the type of the fitted value.
Thus, in the cases of |
scale |
logical, if TRUE, re-scale the interaction parameters so that the k_t has drift parameter equal to 1 (see also |
interpolate |
logical, if TRUE, replace before regression all zero or missing values in the mortality rates of |
verbose |
logical, if TRUE, the program prints out the updated deviance values along with the starting and final parameter estimates |
spar |
numerical smoothing spline parameter in the interval (0,1] (with a recommended value of 0.6). If it is not NULL, the interaction effects (i.e. β_x^{(0,1)}) are smoothed out after the initial regression. Consequently, the period and/or cohort effects are adjusted (smoothed out) accordingly. |
Implements the modelling approach proposed in Renshaw and Haberman (2006), which extends the basic Lee-Carter model within the GLM framework. The function makes use of tailored iterative Newton-Raphson fitting algorithms to estimate the graduation parameters of the six variants within this class of extended Lee-Carter models.
A Lee-Carter type fitted object with the following components:
label |
data label |
age |
vector of fitted ages |
year |
vector of fitted fitted years |
<series> |
matrix of observed (source) mortality rates used for fitting. It is named the same way as the chosen series |
ax |
parameter estimates of (mean) age-specific mortality rates across the entire fitting period |
bx |
parameter estimates of age-specific interaction effect between age and period |
kt |
parameter estimates of year-specific period trend of mortality rates |
df |
degree of freedom of the fitted GLM model |
residuals |
residuals of the fitted model in the form of a functional time series object |
fitted |
fitted values of the fitted model in the form of a functional time series object |
varprop |
percent of variance |
y |
source mortality data in the form of a functional time series object |
mdev |
mean deviance of total and base lack of fit (see also |
model |
string expression of the fitted model |
adjust |
type of error structure (e.g. "poisson" or "gaussian") |
call |
copy of the R call to the model |
conv.iter |
number of iterations used to reach convergence |
bx0 |
parameter estimates of age-specific interaction effect between age and cohort (only applies to the age-period-cohort model) |
itx |
parameter estimates of year-specific cohort trend of mortality rates (only applies to the age-period-cohort model) |
Zoltan Butt, Steven Haberman and Han Lin Shang
Renshaw, A. E. and Haberman, S. (2003a), “Lee-Carter mortality forecasting: a parallel generalised linear modelling approach for England and Wales mortality projections", Journal of the Royal Statistical Society, Series C, 52(1), 119-137.
Renshaw, A. E. and Haberman, S. (2003b), “Lee-Carter mortality forecasting with age specific enhancement", Insurance: Mathematics and Economics, 33, 255-272.
Renshaw, A. E. and Haberman, S. (2006), “A cohort-based extension to the Lee-Carter model for mortality reduction factors", Insurance: Mathematics and Economics, 38, 556-570.
Renshaw, A. E. and Haberman, S. (2008), “On simulation-based approaches to risk measurement in mortality with specific reference to Poisson Lee-Carter modelling", Insurance: Mathematics and Economics, 42(2), 797-816.
Renshaw, A. E. and Haberman, S. (2009), “On age-period-cohort parametric mortality rate projections", Insurance: Mathematics and Economics, 45(2), 255-270.
# standard LC model with Gaussian errors (corresponding to SVD graduation): # correct 0 or missing mortality rates before graduation mod6g <- lca.rh(dd.cmi.pens, mod='lc', error='gauss', max=110, interpolate=TRUE) # AP LC model with Poisson errors mod6p <- lca.rh(dd.cmi.pens, mod='lc', error='pois', interpolate=TRUE) # Model Summary, Coefficients and Plotting: mod6p; coef(mod6p); plot(mod6p) # Comparison with standard fitting method # Standard LC model (with Gaussian errors) - SVD fit (demography package) modlc <- lca(dd.cmi.pens, interp=TRUE, adjust='none') # Gaussian (SVD) - Gaussian (iterative) round(modlc$ax-mod6g$ax, 4) round(modlc$bx-mod6g$bx, 4) round(modlc$kt-mod6g$kt, 4) # -------------------------------------------------- # # APC LC model fitted to restricted age range with 'deviance' residuals # the remaining 0/NA values reestimated: # WARNING: for proper fit recommend dec=6, but it can lead to slow convergence! mod1 <- lca.rh(dd.cmi.pens, age=60:100, mod='m', interpolate=TRUE, res='dev', dec=1)
Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.