Measuring Interactions in Categorical Datasets Using Multivariate Symmetrical Uncertainty

Interaction between variables is often found in statistical models, and it is usually expressed in the model as an additional term when the variables are numeric. However, when the variables are categorical (also known as nominal or qualitative) or mixed numerical-categorical, defining, detecting, and measuring interactions is not a simple task. In this work, based on an entropy-based correlation measure for n nominal variables (named as Multivariate Symmetrical Uncertainty (MSU)), we propose a formal and broader definition for the interaction of the variables. Two series of experiments are presented. In the first series, we observe that datasets where some record types or combinations of categories are absent, forming patterns of records, which often display interactions among their attributes. In the second series, the interaction/non-interaction behavior of a regression model (entirely built on continuous variables) gets successfully replicated under a discretized version of the dataset. It is shown that there is an interaction-wise correspondence between the continuous and the discretized versions of the dataset. Hence, we demonstrate that the proposed definition of interaction enabled by the MSU is a valuable tool for detecting and measuring interactions within linear and non-linear models.

Independent samples—more hypotheses testing

Two-way analysis of variance (ANOVA) without replication is called a factorial ANOVA with two factors. It is used to test if there is a significant difference between means of several sets of data (groups) dependable on two independent factors. It is applied when we have one measurement variable and two nominal variables (usually called ‘factors’ or ‘main effects’). In this chapter hypotheses and assumptions of the method are given. Then the example of the procedure of two-way analysis of variance (ANOVA) without replication is described in details. The two-way analysis of variance (ANOVA) with replication is utilized to simultaneously test the effects of varying two variables for a sample which consists of more than one respondent per a certain combination of variables. The example of the procedure of two-way analysis of variance (ANOVA) with replication is described in details in this chapter. For both procedures the easy to follow examples shows the procedure stepby-step. The practical part includes the guidance for SPSS and for Excel.

Predicting students’ academic performance using a modified kNN algorithm

The target (dependent) variable is often influenced not only by ratio scale variables, but also by qualitative (nominal scale) variables in classification analysis. Majority of machine learning techniques accept only numerical inputs. Hence, it is necessary to encode these categorical variables into numerical values using encoding techniques. If the variable does not have relation or order between its values, assigning numbers will mislead the machine learning techniques. This paper presents a modified k-nearest-neighbors algorithm that calculates the distances values of categorical (nominal) variables without encoding them. A student’s academic performance dataset is used for testing the enhanced algorithm. It shows that the proposed algorithm outperforms standard one that needs nominal variables encoding to calculate the distance between the nominal variables. The results show the proposed algorithm preforms 14% better than standard one in accuracy, and it is not sensitive to outliers.

Algorithmic correspondence and canonicity for possibility semantics

The present paper develops a unified correspondence treatment of the Sahlqvist theory for possibility semantics, extending the results in the work by Yamamoto (2016, Journal of Logic and Computation, 27, 2411–2430) from Sahlqvist formulas to the strictly larger class of inductive formulas and from the full possibility frames to filter-descriptive possibility frames. Specifically, we define the possibility semantics version of the algorithm Ackermann lemma based algorithm (ALBA) and an adapted interpretation of the expanded modal language used in the algorithm. One notable feature of the adaptation of ALBA to possibility frames setting is that the so-called nominal variables, which are interpreted as complete join-irreducibles in the standard setting, are interpreted as regular open closures of ‘singletons’ in the present setting, which is a novelty of the present paper. We prove the soundness of the algorithm with respect to both (the dual algebras of) full possibility frames and (the dual algebras of) filter-descriptive possibility frames, use the algorithm to give an alternative proof to the one in the work by Holliday (2016, Possibility frames and forcing for modal logic. UC Berkeley Working Paper in Logic and the Methodology of Science. URL. http://escholarship.org/uc/item/9v11r0dq) that the inductive formulas are constructively canonical and show that the algorithm succeeds on inductive formulas. We make some comparisons among different semantic settings in the design of the algorithms and fit possibility semantics into this broader picture.

Efficient Decomposition of Bayesian Networks With Non-graded Variables

Elicitation, estimation and exact inference in Bayesian Networks (BNs) are often difficult because the dimension of each Conditional Probability Table (CPT) grows exponentially with the increase in the number of parent variables. The Noisy-MAX decomposition has been proposed to break down a large CPT into several smaller CPTs exploiting the assumption of causal independence, i.e., absence of causal interaction among parent variables. In this way, the number of conditional probabilities to be elicited or estimated and the computational burden of the joint tree algorithm for exact inference are reduced. Unfortunately, the Noisy-MAX decomposition is suited to graded variables only, i.e., ordinal variables with the lowest state as reference, but real-world applications of BNs may also involve a number of non-graded variables, like the ones with reference state in the middle of the sample space (double-graded variables) and with two or more unordered non-reference states (multi-valued nominal variables). In this paper, we propose the causal independence decomposition, which includes the Noisy-MAX and two generalizations suited to double-graded and multi-valued nominal variables. While the general definition of BN implicitly assumes the presence of all the possible causal interactions, our proposal is based on causal independence, and causal interaction is a feature that can be added upon need. The impact of our proposal is investigated on a published BN for the diagnosis of acute cardiopulmonary diseases.

Three methods of coding nominal variables in regression analysis

The paper compares three methods of coding nominal variables in regression analysis: coding of each level as a separate variable, coding with binary code, numbering of factor levels. Although these methods have existed for a long time and even have a theoretical justification (except for encoding with binary code), there were no recommendations and comparisons for their practical application. The features of the application of each method and the existing limitations are analyzed. In the article, there are considered two examples that provide a detailed comparison of these three methods. Comparative analysis has been carried out in the following areas: the presence of restrictions in use; statistical properties of plans; labour intensity and difficulty of obtaining mathematical models and the final result of their building; convenience of semantic analysis and use. Additionally, there have been made comparisons with models based on Chebyshev orthogonal polynomials. It has been established that different methods of coding nominal variables, when used correctly, lead to regression models that are approximately identical in their properties. Moreover, the method of encoding each level as a separate variable is possible only if there are experiments in which there is no nominal variable as an influence effect. The binary coding method is inconvenient to use with a large number of levels of variation of the nominal variable and inconvenient to analyze. When coding by level numbering, it is necessary that the average response values, according to the dispersion diagram of this factor, are sorted by value in accordance with the assigned numbers. With this encoding method, a natural number of factors is preserved. Sharply distinguishable best results are achieved with this coding method using Chebyshev orthogonal polynomials. The highest accuracy and uniformity of approximation are ensured.

Immersive Virtual Tasks With Motor and Cognitive Components: A Feasibility Study With Young and Older Adults

Objective: To analyze the feasibility, safety, and acceptability of immersive virtual tasks. Methods: The authors recruited 11 young adults and 10 older adults. The participants performed three virtual reaching tasks while walking on a virtual path. The descriptive analysis and comparison between participants were performed using the Mann–Whitney U test and chi-square test for nonparametric and nominal variables, respectively. The authors also used analysis of variance for a between-groups comparison for normal variables. Results: Twenty percent of older adults and 81.8% of young adults completed all three tasks (chi-square test; p = .005). Both groups reported minor symptoms, with no significant differences. The older adults were more motivated to practice the tasks (Mann–Whitney U test; p = .015) and would be more likely to suggest them to others (chi-square test; p = .034). Conclusion: All three tasks were feasible for young adults. All participants, except for one, had cybersickness. The symptoms were mostly mild and subsided once the interaction was complete.

Inclusive Special School Teachers’ Self-Assessment of their Diagnostic and Therapeutic Knowledge and Skills

Anna Borzęcka, Inclusive Special School Teachers’ Self-Assessment of their Diagnostic and Therapeutic Knowledge and Skills. Interdisciplinary Contexts of Special Pedagogy, no. 27, Poznań 2019. Pp. 181–195. Adam Mickiewicz University Press. ISSN 2300-391X. e-ISSN 2658-283X. DOI: https://doi.org/10.14746/ikps.2019.27.09Diagnostic and therapeutic competences are necessary for the effectiveness of didactic and educational interventions undertaken by a professional specialist school teacher. In order for the teacher to be able to cope with the tasks assigned by special pedagogy, he must have theoretical and practical preparation in the field of diagnosis and therapy. The future of a special school pupil will depend on his knowledge and skills. The article presents research on declarative sources of teaching knowledge and skills in the field of diagnosis and therapy as well as their selfassessment, taking into account nominal variables (age and job seniority).