coherent forecasting of multiple-decrement life tables ......max planck institute for demographic...
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Max Planck Institute for Demographic Research
Institut national d’études démographiques
Coherent forecasting of multiple-decrement lifetables: compositional models for French cause ofdeath data, 1925–2008.
Jim Oeppen 1 Carlo Giovanni Camarda 2
1Max Planck Institute for Demographic Research2Institut national d’études démographiques
CoDa
Compositional Data Analysis.
I Appropriate for proportions e.g. ndx or nd ix
I Relative, not absolute, information
I The Simplex is the appropriate space for analysis
Key Reference:Aitchison, J. (1986)The Statistical Analysis of Compositional Data.London: Chapman and Hall.
Oeppen & Camarda (MPIDR & INED) CoDa Rome 2013 2 / 14
Model Structure
Lee-Carter Single Decrement Model Structure.
lnmx ,t = ax +bxkt + εx ,t
kt = kt−1 +d +et
AgesD
N
Periods=
Rank-1 Singular Value Decomposition.
X X
a(x)
b(x)
k(t)
Oeppen & Camarda (MPIDR & INED) CoDa Rome 2013 3 / 14
Model Structure
Multiple Decrement Model Structure.
K D
N
N
K x D
Rank-1 SVD
=
X X
Oeppen & Camarda (MPIDR & INED) CoDa Rome 2013 4 / 14
Data
0.0
0.1
0.2
0.3
0.4
1960 1970 1980 1990 2000 2010
Pro
port
ion
GroupCardio−VascularNeoplasmsOther diseasesRespiratoryInjury & PoisonDigestiveInfectious
Deaths by Group of Causes: France, female
Oeppen & Camarda (MPIDR & INED) CoDa Rome 2013 5 / 14
Data
Cardio−Vascular Neoplasms Other diseases Respiratory Injury & Poison Digestive Infectious
0.000
0.025
0.050
0.075
0.100
0 20 40 60 80 1000 20 40 60 80 1000 20 40 60 80 1000 20 40 60 80 1000 20 40 60 80 1000 20 40 60 80 1000 20 40 60 80 100
Geometric Mean d(x)
Oeppen & Camarda (MPIDR & INED) CoDa Rome 2013 6 / 14
Model Estimates
Rank 1: 82% Rank 2: 7% Rank 3: 3% Rank 4: 1% (not used)
−0.25
0.00
0.25
0.50
0.75
1975 2000 2025 2050 1975 2000 2025 2050 1975 2000 2025 2050 1975 2000 2025 2050
Year
Effe
cts
(sca
led)
VectorFcstObs
Singular Vectors
Oeppen & Camarda (MPIDR & INED) CoDa Rome 2013 7 / 14
Model Estimates
Cardio−Vascular Neoplasms Other diseases Respiratory Injury & Poison Digestive Infectious
−0.2
−0.1
0.0
0.1
0.2
−0.2
−0.1
0.0
0.1
0.2
−0.2
−0.1
0.0
0.1
0.2
Rank 1: 82%
Rank 2: 7%
Rank 3: 3%
0 20 40 60 80 1000 20 40 60 80 1000 20 40 60 80 1000 20 40 60 80 1000 20 40 60 80 1000 20 40 60 80 1000 20 40 60 80 100
Age
Effe
cts
(sca
led)
France, 1955−2008, female: scaled singular vectors v
Oeppen & Camarda (MPIDR & INED) CoDa Rome 2013 8 / 14
Forecast
0.0
0.1
0.2
0.3
0.4
0.5
1960 1970 1980 1990 2000 2010 2020 2030 2040 2050
Pro
port
ion
GroupCardio−VascularNeoplasmsOther diseasesRespiratoryInjury & PoisonDigestiveInfectious
TypeDataEstFcst
Deaths by Group of Causes: France, female
Oeppen & Camarda (MPIDR & INED) CoDa Rome 2013 9 / 14
Forecast
Fitted
Forecast75
80
85
90
1960 1970 1980 1990 2000 2010 2020 2030 2040 2050
Year
s
DataObs
ModelCoDa Rank 1CoDa Rank 3Lee−C Rank 1
DecrementSingleMultiple
Life Expectancy at Birth: female
Oeppen & Camarda (MPIDR & INED) CoDa Rome 2013 10 / 14
Group Correlations
Cardio−
Vascular .64
Neoplasms
.81
.87
Other
diseases
.71
.50
.64
Injury &
Poison
.59
.81
.70
.54
Respiratory
.80
.67
.75
.71
.61
Digestive
.76
.71
.84
.66
.55
.70
Infectious
0
25
50
75
100Age
Centred data: clr transform
Oeppen & Camarda (MPIDR & INED) CoDa Rome 2013 11 / 14
Group Correlations
Cardio−
Vascular .69
Neoplasms
.86
.91
Other
diseases
.79
.55
.69
Injury &
Poison
.63
.85
.72
.60
Respiratory
.89
.73
.81
.81
.66
Digestive
.82
.76
.89
.73
.58
.76
Infectious
0
25
50
75
100Age
Fitted Centred data: clr transform
Oeppen & Camarda (MPIDR & INED) CoDa Rome 2013 12 / 14
Group Correlations
Cardio−
Vascular.08
Neoplasms
.03
.12
Other
diseases
.01
−.02
.05
Injury &
Poison
.06
0
.10
−.10
Respiratory
.02
.03
.04
−.01
0
Digestive
.03
−.08
−.02
.01
−.03
.11
Infectious
0
25
50
75
100Age
Compositional residuals: clr transform
Oeppen & Camarda (MPIDR & INED) CoDa Rome 2013 13 / 14
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