An Attempt to Apply Canonical Analysis to Investigate the Dependencies between the Level of Organic Farming Development in Poland and the Chosen Environmental Determinants

Polish organic agriculture has faced rapid growth in the recent two decades. Nevertheless, one may observe considerable discrepancies in organic agriculture development in specific regions of Poland. Therefore, it is necessary to recognize the key conditions for this development and its spatial differentiation. Since the relationship between organic farming and the natural environment has a fundamental meaning in this production system, it is crucial to study the development determinants of environmental characters. Thus the paper aims to identify the level of organic farming development in Polish districts and to investigate multidimensional relations between this level and selected environmental conditions. In order to identify the range and direction of those multidimensional relations between the discussed phenomena, canonical analysis was applied. Within the conducted study, proprietary synthetic measures were constructed (using the TOPSIS—Technique for Order of Preference by Similarity to Ideal Solution), and linear ordering of the objects described by a large number of variables was employed. To define the strength and direction of the dependencies among constructed synthetic indices of the level of organic farming development and environmental conditions, a correlation analysis was performed. All 380 districts in Poland were considered as the investigated objects. Based on the variables describing selected environmental conditions, one may explain nearly 26.7% of the variance of variables related to organic agriculture development.

Canonical analysis of new non-relativistic string action and uniform light-cone gauge formulation

We perform canonical analysis of new non-relativistic string action that was found recently in [32]. We also discuss its gauge fixed form.

Determinants of Investments in Energy Sector in Poland

There is much research about the determinants of investments, but there is a shortage of similar studies for Poland. Therefore, the overall goal of the paper is to analyze the determinants of investments made by enterprises from the energy sector as well as their delays in Poland in the years 2000–2019. In this period, a strong growth of investments in energy was observed in the country. In connection to this, the authors set four hypotheses and verified them with the following statistical methods: canonical analysis, linear and causality correlation, autocorrelation and cointegration tests. The paper found that there is a relationship between public consumption and investment spending of small enterprises in Poland. That means that only some macroeconomic parameters are connected with investments. Moreover, the changes in the value of past investments has a negative influence in current investments.

New canonical analysis for higher order topologically massive gravity

A detailed Gitman–Lyakhovich–Tyutin analysis for higher-order topologically massive gravity is performed. The full structure of the constraints, the counting of physical degrees of freedom, and the Dirac algebra among the constraints are reported. Moreover, our analysis presents a new structure into the constraints and we compare our results with those reported in the literature where a standard Ostrogradski framework was developed.

“Green Energy” and the Standard of Living of the EU Residents

The author intended to present the relationship between the standard of living of EU citizens and the level of the development of renewable energy. It is particularly important in the context of the implementation of the sustainable development idea, by ensuring a high standard of living for both current and future generations, with rational use of available natural resources. The first, theoretical part of the article presents the problem related to the impact of renewable energy on the standard of living in a synthetic way. The second part involves empirical research conducted in all countries of the EU. To evaluate the level of renewable energy development and the standard of living, the author constructed original measures based on the TOPSIS method. Variables were selected on the basis of substantive, statistical and formal criteria (primarily the completeness and availability of data in 2019). Within the framework of the conducted study, the author obtained, among other things, a relatively high value of Spearman’s rank correlation coefficient between the constructed synthetic measures (0.47). Canonical analysis was used to identify the relationship between them. Numerous indicators, including canonical correlations, complete redundancy and extracted variances, were determined with the use of canonical analysis. Seven statistically significant canonical variables were identified. The value of the greatest and most statistically significant canonical correlation exceeded 0.94, and for the last statistically significant canonical variable, the value reached over 0.31. Statistical data were primarily obtained from the publicly available EUROSTAT database.

Discriminant Canonical Analysis as a Validation Tool for Multivariety Native Breed Egg Commercial Quality Classification

This study aimed to develop a tool to validate multivariety breed egg quality classification depending on quality-related internal and external traits using a discriminant canonical analysis approach. A flock of 60 Utrerana hens (Franciscan, White, Black, and Partridge) and a control group of 10 Leghorn hens were placed in individual cages to follow the traceability of the eggs and perform an individual internal and external quality assessment. Egg groups were determined depending on their commercial size (S, M, L, and XL), laying hen breed, and variety. Egg weight, major diameter, minor diameter, shell b*, albumen height, and the presence or absence of visual defects in yolk and/or albumen showed multicollinearity problems (variance inflation factor (VIF) > 5) and were discarded. Albumen weight, eggshell weight, and yolk weight were the most responsible traits for the differences among egg quality categories (Wilks’ lambda: 0.335, 0.539, and 0.566 for albumen weight, eggshell weight, and yolk weight, respectively). The combination of traits in the first two dimensions explained 55.02% and 20.62% variability among groups, respectively. Shared properties between Partridge and Franciscan varieties may stem from their eggs presenting heavier yolks and slightly lower weights, while White Utrerana and Leghorn hens’ similarities may be ascribed to hybridization reminiscences.

rdacca.hp: an R package for generalizing hierarchical and variation partitioning in multiple regression and canonical analysis

SummaryCanonical analysis, a generalization of multiple regression to multiple response variables, is widely used in ecology. Because these models often involve large amounts of parameters (one slope per response per predictor), they pose challenges to model interpretation. Currently, multi-response canonical analysis is constrained by two major challenges. Firstly, we lack quantitative frameworks for estimating the overall importance of single predictors. Secondly, although the commonly used variation partitioning framework to estimate the importance of groups of multiple predictors can be used to estimate the importance of single predictors, it is currently computationally constrained to a maximum of four predictor matrices.We established that commonality analysis and hierarchical partitioning, widely used for both estimating predictor importance and improving the interpretation of single-response regression models, are related and complementary frameworks that can be expanded for the analysis of multiple-response models.In this application, we aim at: a) demonstrating the mathematical links between commonality analysis, variation and hierarchical partitioning; b) generalizing these frameworks to allow the analysis of any number of responses, predictor variables or groups of predictor variables in the case of variation partitioning; and c) introducing and demonstrating the usage of the R package rdacca.hp that implements these generalized frameworks.