Table 4 Fit indices for Nuclear Twin and Family Design models.

From: Conventional twin studies overestimate the environmental differences between families relevant to educational attainment

Ref #

Model name

Fixed parameters

-2LL

df

AIC

BIC

Against

Δ df

Δ -2LL

p-value

Full

Saturated

 

8,981.36

0

9,064.84

9,129.90

    

PA-1

ASTPE

N = 0

9,006.71

3570

9028.98

9047.56

Full

39

25.35

0.96

PA-1.1

ASTPE (no rGE)

N = rGE = 0

9,006.71

3571

9026.93

9043.84

PA-1

1

0.00

0.96

PA-1.2

ASTE

N = P = 0

9,006.71

3573

9022.86

9036.42

PA-1

3

0.00

1.00

PA-2

ANTPE

S = 0

9,010.47

3570

9032.75

9051.32

Full

39

29.12

0.88

PA-2.1

ANTPE (no rGE)

S = rGE = 0

9,010.56

3571

9030.79

9047.70

PA-2

1

0.09

0.77

PA-2.2

ATPE

S = N = 0

9,010.63

3571

9030.86

9047.77

PA-2

1

0.16

0.69

PA-2.3

ATPE (no rGE)

S = N = rGE = 0

9,010.63

3572

9028.82

9044.05

PA-2

2

0.16

0.92

PA-2.4

ANTE

S = P = 0

9,010.56

3573

9026.71

9040.27

PA-2

3

0.09

0.99

PA-2.5

ATE

S = N = P = 0

9,010.63

3574

9024.75

9036.63

PA-2

4

0.16

1.00

PA-3

ANSTE

P = 0

9,006.71

3570

9028.98

9047.56

Full

39

25.35

0.96

PA-3.1

ASTE

P = N = 0

9,006.71

3573

9022.86

9036.42

PA-3

3

0.00

1.00

SH-1

ASTPE

N = 0

9,006.71

3570

9028.98

9047.56

Full

39

25.35

0.96

SH-2

ANTPE

S = 0

9,011.19

3570

9033.46

9052.03

Full

39

29.83

0.85

SH-2.1

ATPE

S = N = 0

9,011.19

3571

9031.41

9048.32

SH-2

1

0.00

1.00

SH-3

ANSTE

P = 0

9,034.37

3570

9056.64

9075.21

Full

39

53.01

0.07

SH-3.1

ASTE

P = N = 0

9,034.36

3573

9050.51

9064.07

SH-3

3

0.00

1.00

SH-3.2

ANSE

P = T = 0

9,034.95

3573

9051.10

9064.66

SH-3

3

0.58

0.90

SH-3.3

ASE

P = N = T = 0

9,034.95

3574

9049.06

9060.94

SH-3

4

0.58

0.96

  1. PA Phenotypic Assortment model, SH Social Homogamy model, A Additive genetic influence, N non-additive genetic influence (dominance), S environmental influences shared by all siblings, T environmental influences shared by twins only, P phenotypic transmission, E nonshared environment, rGE passive gene-environment correlation, -2LL negative 2 log likelihood, df degrees of freedom, AIC Akaike’s Information Criterion, BIC Bayesian Information Criterion, Δ difference.
  2. Non-additive genetic influences, sibling shared environmental influences, and phenotypic transmission effects were respectively set to zero in three baseline Phenotypic Assortment models and three baseline Social Homogamy models (top row of each section). These were compared with a saturated model (top row). For baseline models which did not show a significant reduction in fit (α = 0.05), non-significant paths were iteratively dropped to see if nested sub-models showed a significant reduction in fit relative to baseline. Our best-fitting model (ASTE) is in boldface and appears twice under PA-1.2 and PA-3.1. Our best-fitting SH model (ASTPE) is in italics. Alternative model-fitting results where non-additive genetic influences were characterised as epistasis rather than dominance are provided in Supplementary Table 3, but differences were negligible. For our P = 0 baseline models only one path is dropped (m) but for all P = 0 submodels three paths have been dropped (m, x, and w). This is because the value of x and w automatically fall to zero when m is dropped (see path diagram in Fig. 3) and parameter estimates remained the same whether one, two, or three paths were dropped. We have omitted redundant P = 0 submodels that were less parsimonious.
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