**Submitted**

- Heck, D. W., Overstall, A., Gronau, Q. F., & Wagenmakers, E. (2017). Quantifying uncertainty in transdimensional Markov chain Monte Carlo using discrete Markov models. Manuscript Submitted for Publication.

[BibTeX] [https://arxiv.org/abs/1703.10364]`@unpublished{heck2017quantifying, location = {{Manuscript submitted for publication}}, title = {Quantifying Uncertainty in Transdimensional {{Markov}} Chain {{Monte Carlo}} Using Discrete {{Markov}} Models}, url = {https://arxiv.org/abs/1703.10364}, archivePrefix = {arXiv}, eprinttype = {arxiv}, eprint = {1703.10364}, type = {Manuscript Submitted for Publication}, howpublished = {Manuscript submitted for publication}, author = {Heck, Daniel W and Overstall, Antony and Gronau, Quentin F and Wagenmakers, Eric-Jan}, date = {2017}, owner = {Daniel} }`

- Heck, D. W., Hoffmann, A., & Moshagen, M. (2017). Detecting nonadherence without loss in efficiency: A simple extension of the crosswise model. .

[BibTeX]`@unpublished{heck2016detecting, location = {{Manuscript submitted for publication}}, title = {Detecting Nonadherence without Loss in Efficiency: {{A}} Simple Extension of the Crosswise Model}, author = {Heck, Daniel W and Hoffmann, Adrian and Moshagen, Morten}, date = {2017}, groups = {dwh} }`

**Peer-Reviewed Articles**

### 2017

- Heck, D. W., & Erdfelder, E. (in press). Linking process and measurement models of recognition-based decisions. Psychological Review. doi:10.1037/rev0000063

[BibTeX] [Abstract]

When making inferences about pairs of objects, one of which is recognized and the other is not, the recognition heuristic states that participants choose the recognized object in a noncompensatory way without considering any further knowledge. In contrast, information-integration theories such as parallel constraint satisfaction (PCS) assume that recognition is merely one of many cues that is integrated with further knowledge in a compensatory way. To test both process models against each other without manipulating recognition or further knowledge, we include response times into the r-model, a popular multinomial processing tree model for memory-based decisions. Essentially, this response-time-extended r-model allows to test a crucial prediction of PCS, namely, that the integration of recognition-congruent knowledge leads to faster decisions compared to the consideration of recognition only—even though more information is processed. In contrast, decisions due to recognition-heuristic use are predicted to be faster than decisions affected by any further knowledge. Using the classical German-cities example, simulations show that the novel measurement model discriminates between both process models based on choices, decision times, and recognition judgments only. In a reanalysis of 29 data sets including more than 400,000 individual trials, noncompensatory choices of the recognized option were estimated to be slower than choices due to recognition-congruent knowledge. This corroborates the parallel information-integration account of memory-based decisions, according to which decisions become faster when the coherence of the available information increases. (PsycINFO Database Record (c) 2017 APA, all rights reserved)

`@article{heck2017linking, title = {Linking Process and Measurement Models of Recognition-Based Decisions}, doi = {10.1037/rev0000063}, abstract = {When making inferences about pairs of objects, one of which is recognized and the other is not, the recognition heuristic states that participants choose the recognized object in a noncompensatory way without considering any further knowledge. In contrast, information-integration theories such as parallel constraint satisfaction (PCS) assume that recognition is merely one of many cues that is integrated with further knowledge in a compensatory way. To test both process models against each other without manipulating recognition or further knowledge, we include response times into the r-model, a popular multinomial processing tree model for memory-based decisions. Essentially, this response-time-extended r-model allows to test a crucial prediction of PCS, namely, that the integration of recognition-congruent knowledge leads to faster decisions compared to the consideration of recognition only—even though more information is processed. In contrast, decisions due to recognition-heuristic use are predicted to be faster than decisions affected by any further knowledge. Using the classical German-cities example, simulations show that the novel measurement model discriminates between both process models based on choices, decision times, and recognition judgments only. In a reanalysis of 29 data sets including more than 400,000 individual trials, noncompensatory choices of the recognized option were estimated to be slower than choices due to recognition-congruent knowledge. This corroborates the parallel information-integration account of memory-based decisions, according to which decisions become faster when the coherence of the available information increases. (PsycINFO Database Record (c) 2017 APA, all rights reserved)}, journaltitle = {Psychological Review}, author = {Heck, Daniel W and Erdfelder, Edgar}, urldate = {2017-04-04}, date = {2017}, keywords = {heckpaper}, pubstate = {inpress} }`

- Heck, D. W., Arnold, N. R., & Arnold, D. (in press). TreeBUGS: An R package for hierarchical multinomial-processing-tree modeling. Behavior Research Methods. doi:10.3758/s13428-017-0869-7

[BibTeX] [Abstract]

Multinomial processing tree (MPT) models are a class of measurement models that account for categorical data by assuming a finite number of underlying cognitive processes. Traditionally, data are aggregated across participants and analyzed under the assumption of independently and identically distributed observations. Hierarchical Bayesian extensions of MPT models explicitly account for participant heterogeneity by assuming that the individual parameters follow a continuous hierarchical distribution. We provide an accessible introduction to hierarchical MPT modeling and present the user-friendly and comprehensive R package TreeBUGS, which implements the two most important hierarchical MPT approaches for participant heterogeneity—the beta-MPT approach (Smith & Batchelder, Journal of Mathematical Psychology 54:167-183, 2010) and the latent-trait MPT approach (Klauer, Psychometrika 75:70-98, 2010). TreeBUGS reads standard MPT model files and obtains Markov-chain Monte Carlo samples that approximate the posterior distribution. The functionality and output are tailored to the specific needs of MPT modelers and provide tests for the homogeneity of items and participants, individual and group parameter estimates, fit statistics, and within- and between-subjects comparisons, as well as goodness-of-fit and summary plots. We also propose and implement novel statistical extensions to include continuous and discrete predictors (as either fixed or random effects) in the latent-trait MPT model.

`@article{heck2017treebugs, title = {{{TreeBUGS}}: {{An R}} Package for Hierarchical Multinomial-Processing-Tree Modeling}, doi = {10.3758/s13428-017-0869-7}, shorttitle = {{{TreeBUGS}}}, abstract = {Multinomial processing tree (MPT) models are a class of measurement models that account for categorical data by assuming a finite number of underlying cognitive processes. Traditionally, data are aggregated across participants and analyzed under the assumption of independently and identically distributed observations. Hierarchical Bayesian extensions of MPT models explicitly account for participant heterogeneity by assuming that the individual parameters follow a continuous hierarchical distribution. We provide an accessible introduction to hierarchical MPT modeling and present the user-friendly and comprehensive R package TreeBUGS, which implements the two most important hierarchical MPT approaches for participant heterogeneity—the beta-MPT approach (Smith \& Batchelder, Journal of Mathematical Psychology 54:167-183, 2010) and the latent-trait MPT approach (Klauer, Psychometrika 75:70-98, 2010). TreeBUGS reads standard MPT model files and obtains Markov-chain Monte Carlo samples that approximate the posterior distribution. The functionality and output are tailored to the specific needs of MPT modelers and provide tests for the homogeneity of items and participants, individual and group parameter estimates, fit statistics, and within- and between-subjects comparisons, as well as goodness-of-fit and summary plots. We also propose and implement novel statistical extensions to include continuous and discrete predictors (as either fixed or random effects) in the latent-trait MPT model.}, langid = {english}, journaltitle = {Behavior Research Methods}, shortjournal = {Behav Res}, author = {Heck, Daniel W and Arnold, Nina R. and Arnold, Denis}, urldate = {2017-04-04}, date = {2017}, keywords = {heckpaper}, pubstate = {inpress} }`

- Heck, D. W., Hilbig, B. E., & Moshagen, M. (2017). From information processing to decisions: Formalizing and comparing probabilistic choice models. Cognitive Psychology, 96, 26-40. doi:10.1016/j.cogpsych.2017.05.003

[BibTeX]`@article{heck2017information, title = {From Information Processing to Decisions: {{Formalizing}} and Comparing Probabilistic Choice Models}, volume = {96}, doi = {10.1016/j.cogpsych.2017.05.003}, journaltitle = {Cognitive Psychology}, author = {Heck, Daniel W and Hilbig, Benjamin E and Moshagen, Morten}, date = {2017}, pages = {26--40} }`

- Heck, D. W., & Moshagen, M. (in press). RRreg: An R package for correlation and regression analyses of randomized response data. Journal of Statistical Software.

[BibTeX] [Abstract]

The randomized-response (RR) technique was developed to improve the validity of measures assessing attitudes, behaviors, and attributes threatened by social desirability bias. The RR removes any direct link between individual responses and the sensitive attribute to maximize the anonymity of respondents and, in turn, to elicit more honest responding. Since multivariate analyses are no longer feasible using standard methods, we present the R package RRreg that allows for multivariate analyses of RR data in a user-friendly way. We show how to compute bivariate correlations, how to predict an RR variable in an adapted logistic regression framework (with or without random effects), and how to use RR predictors in a modified linear regression. In addition, the package allows for power-analysis and robustness simulations. To facilitate the application of these methods, we illustrate the benefits of multivariate methods for RR variables using an empirical example.

`@article{heck2017rrreg, title = {{{RRreg}}: {{An R}} Package for Correlation and Regression Analyses of Randomized Response Data}, abstract = {The randomized-response (RR) technique was developed to improve the validity of measures assessing attitudes, behaviors, and attributes threatened by social desirability bias. The RR removes any direct link between individual responses and the sensitive attribute to maximize the anonymity of respondents and, in turn, to elicit more honest responding. Since multivariate analyses are no longer feasible using standard methods, we present the R package RRreg that allows for multivariate analyses of RR data in a user-friendly way. We show how to compute bivariate correlations, how to predict an RR variable in an adapted logistic regression framework (with or without random effects), and how to use RR predictors in a modified linear regression. In addition, the package allows for power-analysis and robustness simulations. To facilitate the application of these methods, we illustrate the benefits of multivariate methods for RR variables using an empirical example.}, journaltitle = {Journal of Statistical Software}, author = {Heck, Daniel W and Moshagen, Morten}, date = {2017}, pubstate = {inpress} }`

- Klein, S. A., Hilbig, B. E., & Heck, D. W. (in press). Which is the greater good? A social dilemma approach for disentangling environmentalism and cooperation. Journal of Environmental Psychology. doi:10.1016/j.jenvp.2017.06.001

[BibTeX]`@article{klein2017which, title = {Which Is the Greater Good? {{A}} Social Dilemma Approach for Disentangling Environmentalism and Cooperation}, doi = {10.1016/j.jenvp.2017.06.001}, journaltitle = {Journal of Environmental Psychology}, author = {Klein, Sina A and Hilbig, Benjamin E and Heck, Daniel W}, date = {2017}, pubstate = {inpress} }`

- Miller, R., Scherbaum, S., Heck, D. W., Goschke, T., & Enge, S. (in press). On the relation between the (censored) shifted Wald and the Wiener distribution as measurement models for choice response times. Applied Psychological Measurement.

[BibTeX]`@article{miller2017relation, title = {On the Relation between the (Censored) Shifted {{Wald}} and the {{Wiener}} Distribution as Measurement Models for Choice Response Times}, journaltitle = {Applied Psychological Measurement}, author = {Miller, Robert and Scherbaum, S and Heck, Daniel W and Goschke, Thomas and Enge, Soeren}, date = {2017}, pubstate = {inpress} }`

### 2016

- Heck, D. W., & Erdfelder, E. (2016). Extending multinomial processing tree models to measure the relative speed of cognitive processes. Psychonomic Bulletin & Review, 23, 1440-1465. doi:10.3758/s13423-016-1025-6

[BibTeX] [Abstract]

Multinomial processing tree (MPT) models account for observed categorical responses by assuming a finite number of underlying cognitive processes. We propose a general method that allows for the inclusion of response times (RTs) into any kind of MPT model to measure the relative speed of the hypothesized processes. The approach relies on the fundamental assumption that observed RT distributions emerge as mixtures of latent RT distributions that correspond to different underlying processing paths. To avoid auxiliary assumptions about the shape of these latent RT distributions, we account for RTs in a distribution-free way by splitting each observed category into several bins from fast to slow responses, separately for each individual. Given these data, latent RT distributions are parameterized by probability parameters for these RT bins, and an extended MPT model is obtained. Hence, all of the statistical results and software available for MPT models can easily be used to fit, test, and compare RT-extended MPT models. We demonstrate the proposed method by applying it to the two-high-threshold model of recognition memory.

`@article{heck2016extending, title = {Extending Multinomial Processing Tree Models to Measure the Relative Speed of Cognitive Processes}, volume = {23}, doi = {10.3758/s13423-016-1025-6}, abstract = {Multinomial processing tree (MPT) models account for observed categorical responses by assuming a finite number of underlying cognitive processes. We propose a general method that allows for the inclusion of response times (RTs) into any kind of MPT model to measure the relative speed of the hypothesized processes. The approach relies on the fundamental assumption that observed RT distributions emerge as mixtures of latent RT distributions that correspond to different underlying processing paths. To avoid auxiliary assumptions about the shape of these latent RT distributions, we account for RTs in a distribution-free way by splitting each observed category into several bins from fast to slow responses, separately for each individual. Given these data, latent RT distributions are parameterized by probability parameters for these RT bins, and an extended MPT model is obtained. Hence, all of the statistical results and software available for MPT models can easily be used to fit, test, and compare RT-extended MPT models. We demonstrate the proposed method by applying it to the two-high-threshold model of recognition memory.}, number = {5}, journaltitle = {Psychonomic Bulletin \& Review}, author = {Heck, Daniel W and Erdfelder, Edgar}, date = {2016}, pages = {1440--1465}, keywords = {heckpaper}, owner = {Daniel} }`

- Heck, D. W., & Wagenmakers, E. (2016). Adjusted priors for Bayes factors involving reparameterized order constraints. Journal of Mathematical Psychology, 73, 110-116. doi:10.1016/j.jmp.2016.05.004

[BibTeX] [Abstract]

Many psychological theories that are instantiated as statistical models imply order constraints on the model parameters. To fit and test such restrictions, order constraints of the form theta_i $<$ theta_j can be reparameterized with auxiliary parameters eta in [0,1] to replace the original parameters by theta_i = eta*theta_j. This approach is especially common in multinomial processing tree (MPT) modeling because the reparameterized, less complex model also belongs to the MPT class. Here, we discuss the importance of adjusting the prior distributions for the auxiliary parameters of a reparameterized model. This adjustment is important for computing the Bayes factor, a model selection criterion that measures the evidence in favor of an order constraint by trading off model fit and complexity. We show that uniform priors for the auxiliary parameters result in a Bayes factor that differs from the one that is obtained using a multivariate uniform prior on the order-constrained original parameters. As a remedy, we derive the adjusted priors for the auxiliary parameters of the reparameterized model. The practical relevance of the problem is underscored with a concrete example using the multi-trial pair-clustering model.

`@article{heck2016adjusted, title = {Adjusted Priors for {{Bayes}} Factors Involving Reparameterized Order Constraints}, volume = {73}, doi = {10.1016/j.jmp.2016.05.004}, abstract = {Many psychological theories that are instantiated as statistical models imply order constraints on the model parameters. To fit and test such restrictions, order constraints of the form theta\_i $<$ theta\_j can be reparameterized with auxiliary parameters eta in [0,1] to replace the original parameters by theta\_i = eta*theta\_j. This approach is especially common in multinomial processing tree (MPT) modeling because the reparameterized, less complex model also belongs to the MPT class. Here, we discuss the importance of adjusting the prior distributions for the auxiliary parameters of a reparameterized model. This adjustment is important for computing the Bayes factor, a model selection criterion that measures the evidence in favor of an order constraint by trading off model fit and complexity. We show that uniform priors for the auxiliary parameters result in a Bayes factor that differs from the one that is obtained using a multivariate uniform prior on the order-constrained original parameters. As a remedy, we derive the adjusted priors for the auxiliary parameters of the reparameterized model. The practical relevance of the problem is underscored with a concrete example using the multi-trial pair-clustering model.}, journaltitle = {Journal of Mathematical Psychology}, author = {Heck, Daniel W and Wagenmakers, Eric-Jan}, date = {2016}, pages = {110--116} }`

- Thielmann, I., Heck, D. W., & Hilbig, B. E. (2016). Anonymity and incentives: An investigation of techniques to reduce socially desirable responding in the Trust Game. Judgment and Decision Making, 11, 527-536.

[BibTeX] [Abstract] [http://journal.sjdm.org/16/16613/jdm16613.html]

Economic games offer a convenient approach for the study of prosocial behavior. As an advantage, they allow for straightforward implementation of different techniques to reduce socially desirable responding. We investigated the effectiveness of the most prominent of these techniques, namely providing behavior-contingent incentives and maximizing anonymity in three versions of the Trust Game: (i) a hypothetical version without monetary incentives and with a typical level of anonymity, (ii) an incentivized version with monetary incentives and the same (typical) level of anonymity, and (iii) an indirect questioning version without incentives but with a maximum level of anonymity, rendering responses inconclusive due to adding random noise via the Randomized Response Technique. Results from a large (N = 1,267) and heterogeneous sample showed comparable levels of trust for the hypothetical and incentivized versions using direct questioning. However, levels of trust decreased when maximizing the inconclusiveness of responses through indirect questioning. This implies that levels of trust might be particularly sensitive to changes in individuals’ anonymity but not necessarily to monetary incentives.

`@article{thielmann2016anonymity, title = {Anonymity and Incentives: {{An}} Investigation of Techniques to Reduce Socially Desirable Responding in the {{Trust Game}}}, volume = {11}, url = {http://journal.sjdm.org/16/16613/jdm16613.html}, abstract = {Economic games offer a convenient approach for the study of prosocial behavior. As an advantage, they allow for straightforward implementation of different techniques to reduce socially desirable responding. We investigated the effectiveness of the most prominent of these techniques, namely providing behavior-contingent incentives and maximizing anonymity in three versions of the Trust Game: (i) a hypothetical version without monetary incentives and with a typical level of anonymity, (ii) an incentivized version with monetary incentives and the same (typical) level of anonymity, and (iii) an indirect questioning version without incentives but with a maximum level of anonymity, rendering responses inconclusive due to adding random noise via the Randomized Response Technique. Results from a large (N = 1,267) and heterogeneous sample showed comparable levels of trust for the hypothetical and incentivized versions using direct questioning. However, levels of trust decreased when maximizing the inconclusiveness of responses through indirect questioning. This implies that levels of trust might be particularly sensitive to changes in individuals’ anonymity but not necessarily to monetary incentives.}, number = {5}, journaltitle = {Judgment and Decision Making}, author = {Thielmann, Isabell and Heck, Daniel W and Hilbig, Benjamin E}, date = {2016}, pages = {527--536} }`

### 2015

- Erdfelder, E., Castela, M., Michalkiewicz, M., & Heck, D. W. (2015). The advantages of model fitting compared to model simulation in research on preference construction. Frontiers in Psychology, 6, 140. doi:10.3389/fpsyg.2015.00140

[BibTeX]`@article{erdfelder2015advantages, title = {The Advantages of Model Fitting Compared to Model Simulation in Research on Preference Construction}, volume = {6}, doi = {10.3389/fpsyg.2015.00140}, journaltitle = {Frontiers in Psychology}, author = {Erdfelder, Edgar and Castela, Marta and Michalkiewicz, Martha and Heck, Daniel W}, date = {2015}, pages = {140} }`

- Heck, D. W., Wagenmakers, E., & Morey, R. D. (2015). Testing order constraints: Qualitative differences between Bayes factors and normalized maximum likelihood. Statistics & Probability Letters, 105, 157-162. doi:10.1016/j.spl.2015.06.014

[BibTeX] [Abstract]

We compared Bayes factors to normalized maximum likelihood for the simple case of selecting between an order-constrained versus a full binomial model. This comparison revealed two qualitative differences in testing order constraints regarding data dependence and model preference.

`@article{heck2015testing, title = {Testing Order Constraints: {{Qualitative}} Differences between {{Bayes}} Factors and Normalized Maximum Likelihood}, volume = {105}, doi = {10.1016/j.spl.2015.06.014}, shorttitle = {Testing Order Constraints}, abstract = {We compared Bayes factors to normalized maximum likelihood for the simple case of selecting between an order-constrained versus a full binomial model. This comparison revealed two qualitative differences in testing order constraints regarding data dependence and model preference.}, journaltitle = {Statistics \& Probability Letters}, shortjournal = {Statistics \& Probability Letters}, author = {Heck, Daniel W and Wagenmakers, Eric-Jan and Morey, Richard D.}, date = {2015}, pages = {157--162}, keywords = {Inequality constraint,Minimum description length,model,Model complexity,model selection,Model selection,selection} }`

### 2014

- Heck, D. W., Moshagen, M., & Erdfelder, E. (2014). Model selection by minimum description length: Lower-bound sample sizes for the Fisher information approximation. Journal of Mathematical Psychology, 60, 29-34. doi:10.1016/j.jmp.2014.06.002

[BibTeX] [Abstract]

The Fisher information approximation (FIA) is an implementation of the minimum description length principle for model selection. Unlike information criteria such as AIC or BIC, it has the advantage of taking the functional form of a model into account. Unfortunately, FIA can be misleading in finite samples, resulting in an inversion of the correct rank order of complexity terms for competing models in the worst case. As a remedy, we propose a lower-bound N‘ for the sample size that suffices to preclude such errors. We illustrate the approach using three examples from the family of multinomial processing tree models.

`@article{heck2014model, title = {Model Selection by Minimum Description Length: {{Lower}}-Bound Sample Sizes for the {{Fisher}} Information Approximation}, volume = {60}, doi = {10.1016/j.jmp.2014.06.002}, abstract = {The Fisher information approximation (FIA) is an implementation of the minimum description length principle for model selection. Unlike information criteria such as AIC or BIC, it has the advantage of taking the functional form of a model into account. Unfortunately, FIA can be misleading in finite samples, resulting in an inversion of the correct rank order of complexity terms for competing models in the worst case. As a remedy, we propose a lower-bound N' for the sample size that suffices to preclude such errors. We illustrate the approach using three examples from the family of multinomial processing tree models.}, journaltitle = {Journal of Mathematical Psychology}, author = {Heck, Daniel W and Moshagen, Morten and Erdfelder, Edgar}, date = {2014}, pages = {29--34} }`

- Platzer, C., Bröder, A., & Heck, D. W. (2014). Deciding with the eye: How the visually manipulated accessibility of information in memory influences decision behavior. Memory & Cognition, 42, 595-608. doi:10.3758/s13421-013-0380-z

[BibTeX] [Abstract]

Decision situations are typically characterized by uncertainty: Individuals do not know the values of different options on a criterion dimension. For example, consumers do not know which is the healthiest of several products. To make a decision, individuals can use information about cues that are probabilistically related to the criterion dimension, such as sugar content or the concentration of natural vitamins. In two experiments, we investigated how the accessibility of cue information in memory affects which decision strategy individuals rely on. The accessibility of cue information was manipulated by means of a newly developed paradigm, the spatial-memory-cueing paradigm, which is based on a combination of the looking-at-nothing phenomenon and the spatial-cueing paradigm. The results indicated that people use different decision strategies, depending on the validity of easily accessible information. If the easily accessible information is valid, people stop information search and decide according to a simple take-the-best heuristic. If, however, information that comes to mind easily has a low predictive validity, people are more likely to integrate all available cue information in a compensatory manner.

`@article{platzer2014deciding, title = {Deciding with the Eye: {{How}} the Visually Manipulated Accessibility of Information in Memory Influences Decision Behavior}, volume = {42}, doi = {10.3758/s13421-013-0380-z}, abstract = {Decision situations are typically characterized by uncertainty: Individuals do not know the values of different options on a criterion dimension. For example, consumers do not know which is the healthiest of several products. To make a decision, individuals can use information about cues that are probabilistically related to the criterion dimension, such as sugar content or the concentration of natural vitamins. In two experiments, we investigated how the accessibility of cue information in memory affects which decision strategy individuals rely on. The accessibility of cue information was manipulated by means of a newly developed paradigm, the spatial-memory-cueing paradigm, which is based on a combination of the looking-at-nothing phenomenon and the spatial-cueing paradigm. The results indicated that people use different decision strategies, depending on the validity of easily accessible information. If the easily accessible information is valid, people stop information search and decide according to a simple take-the-best heuristic. If, however, information that comes to mind easily has a low predictive validity, people are more likely to integrate all available cue information in a compensatory manner.}, number = {4}, journaltitle = {Memory \& Cognition}, author = {Platzer, Christine and Bröder, Arndt and Heck, Daniel W}, date = {2014}, pages = {595--608}, keywords = {Accessibility,Decision Making,memory,Spatial attention,Visual salience} }`