Statistical Models in Psychology (2): application

In order to mathematically quantify a contingency between two binary variables, their joint frequencies need to be considered. For a long time, research has presupposed that individuals infer contingencies in a similar way, by taking the frequency of the variables’ joint occurrences into account. Yet, a wide range of studies demonstrated that individuals’ contingency inferences are biased and deviate from mathematical quantifications like the Δp measure or φ coefficient of contingency. Instead, contingency judgments are based on more aggregate information in terms of skewed marginal frequencies: According to the Pseudocontingency account, individuals heuristically associate frequent categories with each other as well as infrequent categories. Illusory Correlations occur when individuals infer a contingency when there is no association at all (e.g., Hamilton & Gifford, 1976), while research on Pseudocontingencies showed that such inferences can even override existing true contingencies (e.g., Fiedler, Freytag, & Meiser, 2009). Hence, illusory correlations and pseudocontingencies are often discussed as being irrational or illogical. Recently, however, a normative account of illusory correlations has been proposed by Costello and Watts (2019) who argue that illusory correlations follow probability theory and are the “rational” consequence of applying Laplace’s Rule of Succession. Even though we discuss several limitations of the Rule of Succession, we propose an alternative normative account which succeeds not only in producing illusory correlations, too, but also in producing pseudocontingencies and in accounting for qualitative patterns found in published data which the Rule of Succession fails to do.

People can rely on two qualitatively different types of processes to make judgments and decisions: Rule-based processes and exemplar-based processes. Methods to measure the dominant process are often based on the assumption that individuals would only use one process at a time. As a consequence, data is aggregated across participants or they are classified as using either exemplar-based or rule-based processing according to the best fitting model. However, more recent research suggests that both kinds of processes might operate together or in parallel. Hence, Bröder and Colleagues (2017) proposed the measurement model RuleEx-J which combines both processing modes by quantifying their relative contributions in a numerical judgment task via an α parameter. Improving on the RuleEx-J model, we used a Bayesian approach which offers a principled foundation for statistical inference while simultaneously affording creative freedom and modelling flexibility. In a simulation study we tested different parameterizations of the RuleEx-J model, different priors and simulation conditions. First simulation results suggest that the Bayesian RuleEx-J model shows a good parameter recovery and provides less biased parameter estimates than the original version. The reanalysis of existing data as well as new data provided first evidence for parameter validity of the Bayesian model.

Multinomial processing tree (MPT) models are measurement models to estimate the probabilities of latent cognitive processes. Using MPT models, we analyze data from two experiments to test theoretical assumptions regarding the underlying cognitive mechanisms of the sleep benefit in episodic memory. First, we tested different explanations of the sleep benefit by applying the Encoding-Maintenance-Retrieval model (Küpper-Tetzel & Erdfelder, 2012). This model is tailored to a free then cued recall paradigm. It allows us to disentangle encoding, storage, and retrieval contributions by providing separate measures for successful encoding of word-pair associations (e), maintaining encoded associations across the retention interval (m), and retrieving stored associations (r) in free recall. Second, we tested whether there is a sleep benefit also in source memory. For a fine-graded analysis of the underlying cognitive processes, we applied a variant of the Multidimensional Source Recognition MPT model (Boywitt & Meiser, 2012; Meiser, 2014). This model makes use of the remember-know recognition task in combination with a source monitoring test. It provides parameters for both dependent and independent retrieval of multiple source features. Based on our findings we show that MPT models are powerful tools to disentangle the cognitive processes that produce the sleep benefit in episodic memory. Implications for theories of the sleep benefit in episodic memory will be discussed.

The diffusion model (Ratcliff, 1978) is a mathematical model for the analysis of response time distributions and accuracy rates in simple binary decision tasks. The three main parameters estimated when applying the diffusion model are the speed of information uptake (drift rate), conservatism of the decision criterion (boundary separation), and non-decision time, which encompasses all non-decisional processes contributing to response times. Stemming from the roots of the model in cognitive research, the sample sizes in most studies utilizing the diffusion model have been relatively low when to compared to the usual Ns found in individual differences research. We present findings on the nomological network of the main diffusion model parameters based on large sample (N>4,000,000) of Implicit Association Test data. In order to fit the model to these data, we had to adjust the model to provide two different forms of non-decision time for correct and error responses. To handle the great number of participants, we also used a new parameter estimation procedure based on machine learning, that yields valid results in a very short amount of time. We report findings on the relationships of the model parameters to demographic and personality measures.

Investigations on attitudes and behaviour of humans with respect to acceptance of novel technologies have yielded various competing models, each with different determinants. We want to extend already established psychological models of action control and technology acceptance, such as the Unified theory of acceptance and use of technology (UTAUT; Venkatesh et al., 2003) by affective factors. To this end, we adapt the method of Cognitive Affective Mapping (CAM, Thagard, 2010), with which complex concepts and their affective connotations can be represented. Subjects design their own cognitive-affective representation on a given topic in a kind of mind-map, which visualizes not only cognitive but also affective structures. This representation of coherent concepts reflects how the human brain functions and helps to better conceptualize mental processes, which are crucial to understand the determinants of acceptance and decision-making processes. Currently, the CAM method is used for data collection and analysed on an individual level. Extending this aim, we will discuss methods to aggregate the data to be able to make predictions for acceptance and decision-making processes.