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Table 1 Simulated data: Observed odds ratios (OR), associated 95% confidence intervals (CI) and SEM regression coefficients with corresponding standard errors (SE) obtained via ML estimation (N = 5000)

From: Beyond logistic regression: structural equations modelling for binary variables and its application to investigating unobserved confounders

 

Observed association

SEM-predicted effects

Parameter*

OR (95% CI) for the variable pairs

Correlation (Q) estimate

Regression estimate (SE) in Q-metric

Regression estimate (95% CI) in OR-metric**

a1 (BIN1→YBIN)

2.138 (1.887, 2.423)

0.3627

0.0281 (0.0039)

1.058 (1.042, 1.074)

a2 (BIN2→YBIN)

3.711 (3.255, 4.232)

0.5755

0.1036 (0.0044)

1.231 (1.210, 1.253)

a3 (BIN3→YBIN)

0.364 (0.321, 0.414)

-0.4660

-0.4979 (0.0033)

0.335 (0.329, 0.341)

a4 (MBIN→YBIN)

10.883 (9.411, 12.586)

0.8137

0.7760 (0.0050)

7.929 (7.554, 8.337)

b1 (BIN1→MBIN)

2.632 (2.304, 3.006)

0.4493

0.4479 (0.0093)

2.622 (2.507, 2.746)

b2 (BIN2→MBIN)

4.095 (3.561, 4.709)

0.6075

0.6070 (0.0093)

4.089 (3.863, 4.337)

b3 (BIN3→MBIN)

1.083 (0.955, 1.229)

0.0398

0.0276 (0.0093)

1.0568 (1.019, 1.096)

  1. * Arrows point to the dependent variables in the model (see Figure 2)
  2. ** Back-transformed from Q to OR by (1+Q)/(1-Q)