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Table 2 Results of the simulation study

From: Spurious interaction as a result of categorization

 

Normal

Uniform

Chi-square

80th percentile

ρ = 0.7 β1 = 1,  β2 = 0

\( {\widehat{\overset{\sim }{\beta}}}_1 \)

1.65 (0.16)

0.50 (0.05)

3.35 (0.35)

\( {\widehat{\overset{\sim }{\beta}}}_2 \)

0.70 (0.18)

0.24 (0.05)

0.99 (0.35)

\( {\widehat{\overset{\sim }{\beta}}}_3 \)

−0.40 (0.26)

− 0.20 (0.08)

0.29 (0.55)

80th percentile

ρ = 0.7

βi = 2, i = 1, 2

\( {\widehat{\overset{\sim }{\beta}}}_1 \)

4.72 (0.17)

1.48 (0.05)

8.69 (0.36)

\( {\widehat{\overset{\sim }{\beta}}}_2 \)

4.72 (0.18)

1.48 (0.05)

8.68 (0.37)

\( {\widehat{\overset{\sim }{\beta}}}_3 \)

−1.63 (0.27)

− 0.79 (0.08)

1.16 (0.61)

  1. The table gives estimated regression coefficients with corresponding empirical standard errors in parentheses