MFDM: Multilevel functional data method

In ftsa: Functional Time Series Analysis

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

mort_female	Female mortality (p by n matrix), where p denotes the dimension and n denotes the sample size.
mort_male	Male mortality (p by n matrix).
mort_ave	Total mortality (p by n matrix).
percent_1	Cumulative percentage used for determining the number of common functional principal components.
percent_2	Cumulative percentage used for determining the number of sex-specific functional principal components.
fh	Forecast horizon.
level	Nominal coverage probability of a prediction interval.
alpha	1 - Nominal coverage probability.
MCMCiter	Number of MCMC iterations.
fmethod	Univariate time-series forecasting method.
BC	If Box-Cox transformation is performed.
lambda	If BC = TRUE, specify a Box-Cox transformation parameter.

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.

Value

first_percent	Percentage of total variation explained by the first common functional principal component.
female_percent	Percentage of total variation explained by the first female functional principal component in the residual.
male_percent	Percentage of total variation explained by the first male functional principal component in the residual.
mort_female_fore	Forecast female mortality in the original scale.
mort_male_fore	Forecast male mortality in the original scale.

Note

It can be quite time consuming, especially when MCMCiter is large.

Author(s)

Han Lin Shang

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.

V. Zipunnikov and B. Caffo and D. M. Yousem and C. Davatzikos and B. S. Schwartz and C. Crainiceanu (2015) "Multilevel functional principal component analysis for high-dimensional data", Journal of Computational and Graphical Statistics, 20, 852-873.

H. L. Shang, P. W. F. Smith, J. Bijak, A. Wisniowski (2016) "A multilevel functional data method for forecasting population, with an application to the United Kingdom", International Journal of Forecasting, 32(3), 629-649.

See Also

ftsm, forecast.ftsm, fplsr, forecastfplsr

ftsa documentation built on Sept. 11, 2023, 5:09 p.m.