# Research

## Our research topics

Our research is concerned with the development and validation of statistical methods for the analysis of complex psychological data. Specifically, we are interested in the development of regularized structural equation models and in the analysis of event-related potentials with structural equation models. In addition, the application of linear mixed models in the context of experimental psychology will be a research focus. In all research projects, we want to make newly developed methods available to other researchers and actively contribute to the development of open-source software.

## Regularized Structural Equation Models

Structural equation models are frequently used in psychology for cross-sectional and longitudinal data analysis because they can take into account measurement error and represent a range of assumed relationships between psychological constructs. However, when using structural equation models, many modeling decisions are required from the user and for which sufficient information is not always available. To mitigate this problem, structural equation models can be combined with regularizing estimation procedures, which in addition to optimizing model fit to the data can simultaneously produce models that are as parsimonious as possible. This combines the steps of estimation and model selection. Regularized structural equation models therefore allow a "semi-confirmatory" approach, where one can make modeling decisions for which little information is available in a data-driven manner. This is potentially useful for psychological research because existing knowledge can be optimally exploited without necessarily making all modeling decisions a priori.

In the project, the usefulness of regularized structural equation models for typical psychological applications will be (further) investigated (e.g., in the context of questionnaire development). Among other things, simulation studies will be conducted to investigate the performance in comparison to other established or proposed methods.

Relevant publications:

Scharf, F., & Nestler, S. (2019c). Should regularization replace simple structure rotation in exploratory factor analysis? Structural Equation Modeling: A Multidisciplinary Journal, 26, 576-590.

Scharf, F.*, Pförtner, J.*, & Nestler, S. (2021). Can ridge and elastic net structural equation modeling be used to stabilize parameter estimates when latent factors are correlated? Structural Equation Modeling: A Multidisciplinary Journal, 62, 928-940. (*shared first authorship).

## Analysis of Event-related Potentials with Structural Equation Models

In experimental psychology, event-related potentials (ERPs) are often used as dependent variables in empirical studies. These are characteristic voltage fluctuations in response to an event (e.g., a sound) that are measured at multiple electrode sites on the scalp of the participants. The analysis of ERP data is subject to a number of challenges, as the datasets contain a large number of measurement points per subject, which have complex spatial dependencies. To address these challenges, several analysis methods have been proposed. In this project, the mathematical relation between the different proposed approaches will be investigated in order to better define their advantages and disadvantages. In addition, we seek to lift some current limitations such as the assumption of equal time courses across subjects and conditions in order to increase the usefulness of the method for practical users.

Relevant publications:

Scharf, F., Widmann, A., Bonmassar, C. & Wetzel, N. (2022). A Tutorial on the Use of Temporal Principal Component Analysis in Developmental ERP Research - Opportunities and Challenges. Developmental Cognitive Neuroscience.

Scharf, F., & Nestler, S. (2019a). A comparison of simple structure rotation criteria in temporal exploratory factor analysis for event-related potential data. Methodology, 15, 43-60.

Scharf, F., & Nestler, S. (2019b). Exploratory structural equation modeling for event-related potential data - an all-in-one approach? Psychophysiology. DOI 10.1111/psyp.13303

Scharf, F., & Nestler, S. (2018). Principles behind variance misallocation in tem-poral exploratory factor analysis for ERP data: Insights from an inter-factor covariance decomposition. International Journal of Psychophysiology, 128, 119-136.

## Advanced linear mixed models in experimental psychology

In recent years, so-called linear mixed models have become popular in the analysis of data from experimental psychology (e.g., reaction times). An important advantage of these models over classical analyses of variance is that a participant's data from the experimental trials does not have to be aggregated. This enables researchers, for instance, to examine more complex temporal dynamics within an experimental session. In addition, the models can be used to generate estimates of individual subjects' experimental effects so that research questions can be investigated regarding interindividual differences (e.g., Do all subjects respond very similarly to the experimental manipulation? Are there characteristics of the subjects that can explain differences in experimental effects?). This is of particular interest for research which aims to bridge the research-applicatio gap, for example, when objective measures of cognitive ability are to be developed. The goal of this project is to explore and describe further possible applications of these models and to develop recommendations for their use.

Relevant publications:

Volkmer, S., Wetzel, N., Widmann, A., & Scharf, F. (2022). Attentional control in middle childhood is highly dynamic - Strong initial distraction is followed by advanced attention control. Developmental Science.

Wetzel, N., Widmann, A., & Scharf, F. (2021). Distraction of attention by novel sounds in children declines fast. Scientific Reports, 11(1), 5308.

Wetzel, N., Scharf, F., & Widmann, A. (2019). Can't Ignore-Distraction by Task-Irrelevant Sounds in Early and Middle Childhood. Child Development, 90(6), 454-464.

### Our research topics

Our research is concerned with the development and validation of statistical methods for the analysis of complex psychological data. Specifically, we are interested in the development of regularized structural equation models and in the analysis of event-related potentials with structural equation models. In addition, the application of linear mixed models in the context of experimental psychology will be a research focus. In all research projects, we want to make newly developed methods available to other researchers and actively contribute to the development of open-source software.

### Regularized Structural Equation Models

Structural equation models are frequently used in psychology for cross-sectional and longitudinal data analysis because they can take into account measurement error and represent a range of assumed relationships between psychological constructs. However, when using structural equation models, many modeling decisions are required from the user and for which sufficient information is not always available. To mitigate this problem, structural equation models can be combined with regularizing estimation procedures, which in addition to optimizing model fit to the data can simultaneously produce models that are as parsimonious as possible. This combines the steps of estimation and model selection. Regularized structural equation models therefore allow a "semi-confirmatory" approach, where one can make modeling decisions for which little information is available in a data-driven manner. This is potentially useful for psychological research because existing knowledge can be optimally exploited without necessarily making all modeling decisions a priori.

In the project, the usefulness of regularized structural equation models for typical psychological applications will be (further) investigated (e.g., in the context of questionnaire development). Among other things, simulation studies will be conducted to investigate the performance in comparison to other established or proposed methods.

Relevant publications:

Scharf, F., & Nestler, S. (2019c). Should regularization replace simple structure rotation in exploratory factor analysis? Structural Equation Modeling: A Multidisciplinary Journal, 26, 576-590.

Scharf, F.*, Pförtner, J.*, & Nestler, S. (2021). Can ridge and elastic net structural equation modeling be used to stabilize parameter estimates when latent factors are correlated? Structural Equation Modeling: A Multidisciplinary Journal, 62, 928-940. (*shared first authorship).

### Analysis of Event-related Potentials with Structural Equation Models

In experimental psychology, event-related potentials (ERPs) are often used as dependent variables in empirical studies. These are characteristic voltage fluctuations in response to an event (e.g., a sound) that are measured at multiple electrode sites on the scalp of the participants. The analysis of ERP data is subject to a number of challenges, as the datasets contain a large number of measurement points per subject, which have complex spatial dependencies. To address these challenges, several analysis methods have been proposed. In this project, the mathematical relation between the different proposed approaches will be investigated in order to better define their advantages and disadvantages. In addition, we seek to lift some current limitations such as the assumption of equal time courses across subjects and conditions in order to increase the usefulness of the method for practical users.

Relevant publications:

Scharf, F., Widmann, A., Bonmassar, C. & Wetzel, N. (2022). A Tutorial on the Use of Temporal Principal Component Analysis in Developmental ERP Research - Opportunities and Challenges. Developmental Cognitive Neuroscience.

Scharf, F., & Nestler, S. (2019a). A comparison of simple structure rotation criteria in temporal exploratory factor analysis for event-related potential data. Methodology, 15, 43-60.

Scharf, F., & Nestler, S. (2019b). Exploratory structural equation modeling for event-related potential data - an all-in-one approach? Psychophysiology. DOI 10.1111/psyp.13303

Scharf, F., & Nestler, S. (2018). Principles behind variance misallocation in tem-poral exploratory factor analysis for ERP data: Insights from an inter-factor covariance decomposition. International Journal of Psychophysiology, 128, 119-136.

### Advanced linear mixed models in experimental psychology

In recent years, so-called linear mixed models have become popular in the analysis of data from experimental psychology (e.g., reaction times). An important advantage of these models over classical analyses of variance is that a participant's data from the experimental trials does not have to be aggregated. This enables researchers, for instance, to examine more complex temporal dynamics within an experimental session. In addition, the models can be used to generate estimates of individual subjects' experimental effects so that research questions can be investigated regarding interindividual differences (e.g., Do all subjects respond very similarly to the experimental manipulation? Are there characteristics of the subjects that can explain differences in experimental effects?). This is of particular interest for research which aims to bridge the research-applicatio gap, for example, when objective measures of cognitive ability are to be developed. The goal of this project is to explore and describe further possible applications of these models and to develop recommendations for their use.

Relevant publications:

Volkmer, S., Wetzel, N., Widmann, A., & Scharf, F. (2022). Attentional control in middle childhood is highly dynamic - Strong initial distraction is followed by advanced attention control. Developmental Science.

Wetzel, N., Widmann, A., & Scharf, F. (2021). Distraction of attention by novel sounds in children declines fast. Scientific Reports, 11(1), 5308.

Wetzel, N., Scharf, F., & Widmann, A. (2019). Can't Ignore-Distraction by Task-Irrelevant Sounds in Early and Middle Childhood. Child Development, 90(6), 454-464.