Does this indicate a lack of causal relationship?

[f174937]

I have a question regarding the results I obtained using your methodology. The p-value for the CAUSE model exceeds 0.05. Does this indicate a lack of causal relationship?

model1  model2 delta_elpd se_delta_elpd          z

1    null sharing  0.2030073     0.1568134  1.2945782 2    null  causal -0.9606224     1.2914358 -0.7438406 3 sharing  causal -1.1636296     1.1884105 -0.9791479 p-value testing that causal model is a better fit:  0.16 Posterior medians and  95 % credible intervals: model     gamma            eta                   q [1,] "Sharing" NA               "0.04 (-0.52, 0.49)"  "0.05 (0, 0.27)" [2,] "Causal"  "0.04 (0, 0.08)" "-0.02 (-0.56, 0.49)" "0.04 (0, 0.24)"

[jean997]

I think this case is a little borderline personally. I think it is ok to make inference based on the 95\% credible interval for gamma, though in the paper we use the model comparison p-value. The model comparison p-value is more conservative. Basically this is telling you that when you fit the model with a causal effect, most of the posterior is positive. The causal model also fits better than the non-causal (sharing only model). However, the causal model doesn't fit overwhelmingly better than the sharing model. So I think this is weak evidence of a causal effect.