Methods & Models

In many applications, one is interested in estimating standard errors for maximum likelihood estimates but it is typically assumed that such standard errors are not valid if the covariance matrix of the maximum likelihood estimates is singular. Such a situation can arise, for example, if there are more parameters than data points in the model. In this talk, we show how it is sometimes possible to estimate standard errors for maximum likelihood estimates in the simultaneous presence of parameter redundancy and possible model misspecification. The essential idea is that even if the covariance matrix of the maximum likelihood estimates is singular, it may still be possible to show that certain linear combinations of the maximum likelihood estimates have a legitimate asymptotic Gaussian distribution. The theory is applicable to a broad class of smooth nonlinear finite-dimensional parametric probability models including exponential family models and latent variable models. After sketching the main theorem, a practical algorithm is developed and applied to the analysis of standard error estimation for a Deterministic Input Noisy And (DINA) Cognitive Diagnostic Model (CDM) fit to an extract of the Tatsuoka (1983) Fraction-Subtraction data set. Simulation studies are also reported to help evaluate the validity of the asymptotic approximation.

The Lexical Decision Task (LDT) is a fundamental tool for understanding how the human brain processes and recognizes words, offering insight into the complex mechanisms of language comprehension. Human lexical decision-making, the process of distinguishing words from non-words, is influenced by various factors such as word frequency, length, and semantic priming. Existing decision-making models like the drift-diffusion model capture response time and accuracy effectively but lack the biological plausibility to explicitly represent these lexical properties. This research proposes a novel joint model that combines the strengths of spiking neural networks (SNNs) and the reflecting boundary race diffusion Model (RBRDM), a neurally-inspired evidence accumulation, to overcome the mentioned limitation. The SNN component simulates neural activity in brain regions involved in lexical processing, encoding information through spike timing and count. This allows for the explicit representation of lexical properties, such as word frequency, via variations in spike patterns. The RBRDM, drawing inspiration from biological decision-making processes, accumulates evidence for and against a word decision with non-negative firing rates (known as Reflecting Boundary) and employs separate accumulators for each option (Independent Accumulators). Our findings demonstrate a strong correlation between firing rates and the frequency of the associated word in context. This potential link may reflect participants' confidence levels (higher drift rate, lower response time). However, further research is crucial to establish causality. Importantly, neural activity and spiking patterns predicted participants' response times and inferred confidence levels (drift rates). This provides a bridge between these neural phenomena and the parameters of the sequential sampling model (drift rate and threshold). Regarding morphological similarity, our trained SNN showed selectivity, suggesting potential modulation of participants' confidence levels. However, further investigation is needed to elucidate the precise nature of this influence. Word perception remains a highly complex cognitive process, encompassing multiple lexical properties and neural mechanisms. This study specifically investigated the effect of word frequency on accuracy and response time, laying the groundwork for future research to delve deeper into the multifaceted nature of this process.

The interest in underlying mechanisms of psychological phenomena promotes the widespread application of mediation models in psychological research. Researchers in psychology usually employ regression-based approaches (such as Baron and Kenny’s criteria, Sobel test and SEM) to explore causal relationships between independent variables, mediators, and outcome variables. However, regression-based approaches are restrictive due to their strong assumptions about the causal relationship between variables and the limitations in commonly used experiment designs. Previous literature has cautioned researchers about this restriction, but misuses of regression-based approaches persist when the assumptions are not satisfied. The reasons for such misuse can be complex. In addition to researchers potentially not paying attention to the assumptions, they may encounter various challenges in assessing the causal relationship between variables, especially when using psychological states as mediators. These challenges include but are not limited to: (1) Psychological states are latent variables; (2) Some psychological processes are nearly instantaneous; (3) Potential unknown confounders; (4) Common method bias; (5) Bad control problem; and (6) Potential causal heterogeneity. This presentation discusses the limitations of regression-based approaches in exploring a causal relationship and analyzes the challenges in assessing a causal mediation relationship with psychological states as mediators. In addition, it introduces several advanced approaches from the counterfactual framework of causality to address these challenges.

“Better safe than sorry” summarises the principle that strong responses to rare events may be appropriate if the outcome is important enough. The calculation of optimal bias in signal detection theory (McMillan & Creelman, 1991) formalises this idea and is often used to explain the evolution of response biases. However, signal detection theory assumes that payoffs are stable over time. Trimmer et al. (2017) showed that when payoffs change across trials, the optimal bias may have the opposite sign compared to the case of invariant payoffs. Here, we show that the same can happen when payoffs change within trials. We argue that such changes over time are plausible for evolutionary scenarios to which signal detection theory has been applied, and that conclusions drawn from signal detection theory are not always valid when the assumption of time-invariant payoffs is violated.