Public and scientific interest in why people believe in conspiracy theories (CT) surged in the past years. To come up with a theoretical explanation, researchers investigated relationships of CT belief with psychological factors such as political attitudes, emotions, or personality. However, recent studies have put the robustness of these relationships into question. In the present study, a prediction-based analysis approach and machine learning models are deployed to detect and remedy poor replicability of CT belief associations. The analysis of a representative dataset with 2025 UK citizens supports the assumption that the current simplicity of the field's analysis routine, exhibiting high sample-specificity and neglecting complex associations of psychological factors with CT belief, may obscure important relationships. The results further point towards key components of conspiratorial mindsets like general distrust and low socio-political control. Important implications for building a coherent theory of CT belief are derived.