Model comparison is the cornerstone of theoretical progress in psychological research. Common practice overwhelmingly relies on tools that evaluate competing models by balancing in-sample descriptive adequacy against model flexibility, with modern approaches advocating the use of marginal likelihood for hierarchical cognitive models. Cross-validation is another popular approach but its implementation has remained out of reach for cognitive models evaluated in a Bayesian hierarchical framework, with the major hurdle being prohibitive computational cost. To address this issue, we develop novel algorithms that make variational Bayes (VB) inference for hierarchical models feasible and computationally efficient for complex cognitive models of substantive theoretical interest. It is well known that VB produces good estimates of the first moments of the parameters which gives good predictive densities estimates. We thus develop a novel VB algorithm with Bayesian prediction as a tool to perform model comparison by cross-validation, which we refer to as CVVB. In particular, the CVVB can be used as a model screening device that quickly identifies bad models. We demonstrate the utility of CVVB by revisiting a classic question in decision making research: what latent components of processing drive the ubiquitous speed-accuracy tradeoff? We demonstrate that CVVB strongly agrees with model comparison via marginal likelihood yet achieves the outcome in much less time. Our approach brings cross-validation within reach of theoretically important psychological models, and makes it feasible to compare much larger families of hierarchically specified cognitive models than has previously been possible.
翻译:模式比较是心理研究理论进步的基石。 常见做法压倒性地依赖一些工具,这些工具通过在模拟描述性充分性与模型灵活性之间取得平衡,来评价相互竞争的模式,同时采用现代方法,倡导使用等级认知模型的边缘可能性。交叉校验是另一种受欢迎的方法,但在巴伊西亚等级框架内评价的认知模型方面,其实施仍然遥遥无期,主要障碍是令人难以接受的计算成本。为了解决这一问题,我们开发了新的算法,使等级模型的变换性贝耶斯(VB)推论变得可行,而且对于具有实质性理论兴趣的复杂认知模型而言具有计算效率。众所周知,VB对参数的最初时刻提出了良好的估计,这些参数提供了良好的预测性密度估计。因此,我们开发了一种新的VB算法,将巴耶西亚预测作为一种工具,用来进行相互比较模型比较,我们称之为CVVB。 特别是,CVVB可以用作一种快速识别坏模式的模型。我们通过重新审视一个典型的决策研究问题,表明CVB的效用是:处理中的隐性组成部分如何推动我们通过边际速度分析结果,而我们不太容易地取得一致。