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. Author manuscript; available in PMC: 2017 Nov 1.
Published in final edited form as: Soc Sci Res. 2016 May 18;60:148–162. doi: 10.1016/j.ssresearch.2016.05.001

Table 5.

Results of Log-Multiplicative Layer Models: Robust Analysis

Observed Data
d.f. L2 BIC AIC Δ ϕk across Cohorts
1980–1983 1984–1986 1987–1989
(6) WC, HC 48 986.88 647.65 890.88 0.35
(7) WC, HC, M, constant ϕk over C 43 364.91 61.01 278.91 0.16
(8) WC, HC, M, varying ϕk over C 41 360.99 71.23 278.99 0.15 1 1.05 1.20
(9) Model 2 + D 40 38.17 −244.52 −41.83 0.05
(10) Model 3 + D 32 31.97 −194.18 −32.03 0.03 1 0.92 1.81
Counterfactual based on IPF
d.f. L2 BIC AIC Δ ϕk across Cohorts
1980–1983 1984–1986 1987–1989
(6) WC, HC 48 1337.49 984.30 1241.49 0.36
(7) WC, HC, M, constant ϕk over C 43 525.07 208.67 439.07 0.16
(8) WC, HC, M, varying ϕk over C 41 519.54 217.85 437.54 0.16 1 0.99 1.18
(9) Model 2 + D 40 67.03 −227.30 −12.97 0.05
(10) Model 3 + D 32 56.69 −178.77 −7.31 0.04 1 0.48 1.65

Data Source: the Shanghai Post-’80 Generation Survey

Note: W=wife’s education; H=husband’s education; C=cohorts; M=main diagonal; D=distance from the main diagonal; d.f. = degree of freedom; L2=the log likelihood ratio chi-square statistic; BIC= Bayesian information criterion; AIC= Akaike information criterion; Δ=the dissimilarity index between observed and predicted frequencies. N=1173.