lc_stan {StanMoMo}

Bayesian Lee-Carter with Stan

Description

Fit and Forecast Bayesian Lee-Carter model. The model can be fitted with a Poisson or Negative-Binomial distribution. The function outputs posteriors distributions for each parameter, predicted death rates and log-likelihoods.

Usage

lc_stan(
  death,
  exposure,
  forecast,
  validation = 0,
  family = c("poisson", "nb"),
  ...
)

Arguments

death

Matrix of deaths.

exposure

Matrix of exposures.

forecast

Number of years to forecast.

validation

Number of years for validation.

family

specifies the random component of the mortality model. "Poisson" assumes a Poisson model with log link and "nb" assumes a negative-binomial model with log link and overdispersion parameter \phi.

...

Arguments passed to rstan::sampling (e.g. iter, chains).

Details

The created model is either a log-Poisson or a log-Negative-Binomial version of the Lee-Carter model:

D_{x,t} \sim \mathcal{P}(\mu_{x,t} e_{x,t})

or

D_{x,t}\sim NB\left(\mu_{x,t} e_{x,t},\phi\right)

with

\log \mu_{xt} = \alpha_x + \beta_x\kappa_t.

To ensure the identifiability of th model, we impose

\sum_x\beta_x = 1,\kappa_1=0.

For the priors, the model chooses relatively wide priors:

\alpha_x \sim N(0,100),\beta_{x} \sim Dir(1,\dots,1),\frac{1}{\phi} \sim Half-N(0,1).

For the period term, we consider a first order autoregressive process (AR(1)) with linear trend:

\kappa_{t}=c+\kappa_{t-1}+\epsilon_{t},\epsilon_{t}\sim N(0,\sigma^2)

with c \sim N(0,10),\sigma \sim Exp(0.1).

Value

An object of class stanfit returned by rstan::sampling.

References

Lee, R. D., & Carter, L. R. (1992). Modeling and forecasting U.S. mortality. Journal of the American Statistical Association, 87(419), 659-671.

Examples

#10-year forecasts for French data for ages 50-90 and years 1970-2017 with a log-Poisson model
ages.fit<-50:90
years.fit<-1970:2017
deathFR<-FRMaleData$Dxt[formatC(ages.fit),formatC(years.fit)]
exposureFR<-FRMaleData$Ext[formatC(ages.fit),formatC(years.fit)]
iterations<-50 # Toy example, consider at least 2000 iterations
fitLC=lc_stan(death = deathFR,exposure=exposureFR, forecast = 10,
family = "poisson",iter=iterations,chains=1)