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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 3.

Results of Log-Multiplicative Layer Models

Observed Data
d.f. L2 BIC AIC Δ ϕk across Cohorts
1980–1983 1984–1986 1987–1989
(1) WC, HC 48 1000.86 661.63 904.86 0.35
(2) WC, HC, M, constant ϕk over C 43 374.05 70.16 288.05 0.16
(3) WC, HC, M, varying ϕk over C 41 372.46 82.70 290.46 0.16 1 1.06 1.15
(4) Model 2 + D 40 47.27 −235.42 −32.72 0.05
(5) Model 3 + D 32 39.51 −186.64 −24.49 0.04 1 0.56 2.43
Counterfactual based on IPF
d.f. L2 BIC AIC Δ ϕk across Cohorts
1980–1983 1984–1986 1987–1989
(1) WC, HC 48 1779.68 1416.35 1683.68 0.37
(2) WC, HC, M, constant ϕk over C 43 660.61 335.12 574.61 0.16
(3) WC, HC, M, varying ϕk over C 41 656.33 345.99 574.33 0.16 1 1.05 1.16
(4) Model 2 + D 40 94.39 −193.65 29.13 0.05
(5) Model 3 + D 32 88.79 −153.43 24.79 0.04 1 0.81 2.28

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.