MFDM: Multilevel functional data method

Description Usage Arguments Details Value Note Author(s) References See Also

View source: R/MFDM.R

Description

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

Usage

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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 Jan. 13, 2021, 6:21 p.m.