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Table 3 Small sample (N = 100) parameter estimates and their standard errors (SE) for SEM using Q-statistic input (correlations estimated via Yule's transformation)

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)

1.600 (0.669, 3.824)

0.2308

0.0068 (0.0410)

1.014 (0.863, 1.191)

a2 (BIN2→YBIN)

3.881 (1.561, 9.650)

0.5902

0.4354 (0.0485)

2.542 (2.032, 3.259)

a3 (BIN3→YBIN)

0.233 (0.092, 0.594)

-0.6220

-0.5604 (0.0403)

0.282 0.220, 0.350)

a4 (MBIN→YBIN)

8.037 (2.700, 23.925)

0.7787

0.3387 (0.0568)

2.173 (1.589, 2.636)

b1 (BIN1→MBIN)

2.581 (0.856, 7.782)

0.4415

0.3697 (0.0625)

2.173 (1.657, 2.939)

b2 (BIN2→MBIN)

3.857 (1.278, 11.638)

0.5882

0.5854 (0.0625)

3.8239 (2.724, 5.847)

b3 (BIN3→MBIN)

0.512 (0.185, 1.418)

-0.3230

-0.3441 (0.0624)

0.4880 (0.364, 0.637)

  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)