MFDM: Multilevel functional data method

Description

Fit a multilevel functional principal component model. The function uses two-step functional principal component decompositions.

Usage

MFDM(mort_female, mort_male, mort_ave, percent_1 = 0.95, percent_2 = 0.95, fh, 
	level = 80, alpha = 0.2, MCMCiter = 100, fmethod = c("auto_arima", "ets"), 
		BC = c(FALSE, TRUE), lambda)

Arguments

Value

first_percentPercentage of total variation explained by the first common functional principal componentfemale_percentPercentage of total variation explained by the first female functional principal component in the residualmale_percentPercentage of total variation explained by the first male functional principal component in the residualmort_female_foreForecast female mortality in the original scalemort_male_foreForecast male mortality in the original scale

Details

The basic idea of multilevel functional data method is to decompose functions from different sub-populations into an aggregated average, a sex-specific deviation from the aggregated average, a common trend, a sex-specific trend and measurement error. The common and sex-specific trends are modelled by projecting them onto the eigenvectors of covariance operators of the aggregated and sex-specific centred stochastic process, respectively.

References

C. M. Crainiceanu and J. Goldsmith (2010) "Bayesian functional data analysis using WinBUGS", Journal of Statistical Software, 32(11).

C-Z. Di and C. M. Crainiceanu and B. S. Caffo and N. M. Punjabi (2009) "Multilevel functional principal component analysis", The Annals of Applied Statistics, 3(1), 458-488.