Semiparametric Regression for Dual Population Mortality

Figures & data

FIGure 1. Semiparametric Fits to Warsaw Apartment Data.

FIGURE 2. Cumulative Trends by Age Group.

TABLE 1 Excerpt of Design Matrix

Cohort	Year	Age	Deaths	r[2]	r[3]	r[4]	q[2]	q[3]	q[4]
1920	1970	50	305	0	0	0	37	36	35
1919	1970	51	306	1	0	0	36	35	34
1918	1970	52	344	2	1	0	35	34	33
1917	1970	53	359	3	2	1	34	33	32
1916	1970	54	384	4	3	2	33	32	31
1915	1970	55	417	5	4	3	32	31	30
1914	1970	56	496	6	5	4	31	30	29
1913	1970	57	570	7	6	5	30	29	28
1912	1970	58	569	8	7	6	29	28	27
1911	1970	59	605	9	8	7	28	27	26
1910	1970	60	732	10	9	8	27	26	25
1909	1970	61	781	11	10	9	26	25	24
1908	1970	62	793	12	11	10	25	24	23
1907	1970	63	854	13	12	11	24	23	22
1906	1970	64	953	14	13	12	23	22	21
1905	1970	65	943	15	14	13	22	21	20
1904	1970	66	1,003	16	15	14	21	20	19
1903	1970	67	1,092	17	16	15	20	19	18
1902	1970	68	1,156	18	17	16	19	18	17
1901	1970	69	1,192	19	18	17	18	17	16
1900	1970	70	1,266	20	19	18	17	16	15
1899	1970	71	1,237	21	20	19	16	15	14
1898	1970	72	1,324	22	21	20	15	14	13
1897	1970	73	1,338	23	22	21	14	13	12
1896	1970	74	1,414	24	23	22	13	12	11
1895	1970	75	1,317	25	24	23	12	11	10
1894	1970	76	1,481	26	25	24	11	10	9
1893	1970	77	1,363	27	26	25	10	9	8
1892	1970	78	1,323	28	27	26	9	8	7
1891	1970	79	1,311	29	28	27	8	7	6
1890	1970	80	1,294	30	29	28	7	6	5
1889	1970	81	1,262	31	30	29	6	5	4
1888	1970	82	1,187	32	31	30	5	4	3
1887	1970	83	1,189	33	32	31	4	3	2
1886	1970	84	1,075	34	33	32	3	2	1
1885	1970	85	1,024	35	34	33	2	1	0
1884	1970	86	842	36	35	34	1	0	0
1883	1970	87	764	37	36	35	0	0	0
1921	1971	50	334	0	0	0	38	37	36
1920	1971	51	352	1	0	0	37	36	35
1919	1971	52	330	2	1	0	36	35	34
1918	1971	53	363	3	2	1	35	34	33

TABLE 2 Summary of Goodness-of-Fit Measures

	Parameters	Loo	Penalty	NLL
APC (Poisson with Laplace shrinkage)	54	22,159	77	22,082
Renshaw-Haberman (Poisson with Laplace shrinkage)	118	20,726	81	20,645
Renshaw-Haberman (Poisson with $\nu =2$ shrinkage)	116	20,723	79	20,644
Renshaw-Haberman (Negative. Binomial. with $\nu =2$ shrinkage)	116	20,648	59	20,589

TABLE 3 Parameter Count and Sum of Absolute Values for Negative Binomial Model

	Age	Cohort	Trend	Weight
Sweden count	10	15	5	34
Denmark count	3	9	4	33
Sweden sum |$\beta$|	0.126	0.062	0.054	0.363
Denmark sum |$\beta$|	0.022	0.041	0.093	0.189

FIGURE 3. Trend Factors.

FIGURE 4. Trend Age Weights.

FIGURE 5. Age Factors.

FIGURE 6. Cohort Factors.

FIGURE 7. Actual vs. Fitted Age by Cohort.

FIGURE 8. Actual vs. Fitted Age by Year.