Item Response Theory (IRT) is a powerful statistical approach for evaluating test items and determining test taker abilities through response analysis. An IRT model that better fits the data leads to more accurate latent trait estimates. In this study, we present a new model for multiple choice data, the monotone multiple choice (MMC) model, which we fit using autoencoders. Using both simulated scenarios and real data from the Swedish Scholastic Aptitude Test, we demonstrate empirically that the MMC model outperforms the traditional nominal response IRT model in terms of fit. Furthermore, we illustrate how the latent trait scale from any fitted IRT model can be transformed into a ratio scale, aiding in score interpretation and making it easier to compare different types of IRT models. We refer to these new scales as bit scales. Bit scales are especially useful for models for which minimal or no assumptions are made for the latent trait scale distributions, such as for the autoencoder fitted models in this study.

Classification ensemble models are those composed by many models fitted to the same data, where the result for the classification can be the majority's vote, an average of the results, or the best performing model result. In Figure 1, there is an example of the voting classifier that we are going to build in this quick tutorial. Observe that there are three models fitted to the data. Two of them classified the data as 1, while one classified as 0. So, by the majority's vote, class 1 wins, and that is the result. In Scikit-Learn, a commonly used example of ensemble model is the Random Forest classifier.

Bayesian hierarchical models are well-suited to analyzing the often noisy data from electroencephalography experiments in cognitive neuroscience: these models provide an intuitive framework to account for structures and correlations in the data, and they allow a straightforward handling of uncertainty. In a typical neurolinguistic experiment, event-related potentials show only very small effect sizes and frequentist approaches to data analysis fail to establish the significance of some of these effects. Here, we present a Bayesian approach to analyzing event-related potentials using as an example data from an experiment which relates word surprisal and neural response. Our model is able to estimate the effect of word surprisal on most components of the event-related potential and provides a richer description of the data. The Bayesian framework also allows easier comparison between estimates based on surprisal values calculated using different language models.

Analyzing multi-way measurements with variations across one mode of the dataset is a challenge in various fields including data mining, neuroscience and chemometrics. For example, measurements may evolve over time or have unaligned time profiles. The PARAFAC2 model has been successfully used to analyze such data by allowing the underlying factor matrices in one mode (i.e., the evolving mode) to change across slices. The traditional approach to fit a PARAFAC2 model is to use an alternating least squares-based algorithm, which handles the constant cross-product constraint of the PARAFAC2 model by implicitly estimating the evolving factor matrices. This approach makes imposing regularization on these factor matrices challenging. There is currently no algorithm to flexibly impose such regularization with general penalty functions and hard constraints. In order to address this challenge and to avoid the implicit estimation, in this paper, we propose an algorithm for fitting PARAFAC2 based on alternating optimization with the alternating direction method of multipliers (AO-ADMM). With numerical experiments on simulated data, we show that the proposed PARAFAC2 AO-ADMM approach allows for flexible constraints, recovers the underlying patterns accurately, and is computationally efficient compared to the state-of-the-art. We also apply our model to a real-world chromatography dataset, and show that constraining the evolving mode improves the interpretability of the extracted patterns.

I am happy to introduce the package HCmodelSets, which is now available on CRAN. This package implements the methods proposed by Cox, D.R. and Battey, H.S. (2017). In particular it performs the reduction, exploratory and model selection phases given in the aforementioned reference. The software supports linear regression, likelihood-based fitting of generalized linear regression models and the proportional hazards model fitted by partial likelihood. The standard method described in the literature to deal with sparse regression is the LASSO proposed by Tibshirani (1996), which assumes sparsity of the effects.