A unified approach to permutation testing for equivalence

Statistical Methods & Applications - The notion of testing for equivalence of two treatments is widely used in clinical trials, pharmaceutical experiments, bioequivalence and quality control....     

Modeling agricultural risk management policies – The implementation of the Income Stabilization Tool in Italy

This paper investigates the potential impact of the income stabilisation tool (IST), currently introduced in the European Common Agricultural Policy to reduce farmers’ income risks using Italian agriculture as case study. The paper extends the existing literature by investigating the effects of two implementation issues: level of aggregation of mutual funds (MF); definition of farmers’ contribution (i.e. premium) to MF. We use a simulation approach based on a FADN panel data set of 3421 farms over a period of 7 years to investigate effects on (i) farm-level income variability, (ii) the expected level and variability of indemnifications at the level of mutual funds and (iii) the distribution of net benefits from this policy instrument across the farm population. We find that the introduction of the IST would lead to a significant reduction of income variability in Italian agriculture. Our results support the establishment of a national mutual fund due to the high volatility of indemnification levels at more disaggregated (e.g. regional or sectoral) levels. In addition, our results propose that farmers’ contribution to mutual funds, i.e. premiums paid, should be modulated according to farm size as this reduces the inequality of the distribution of benefits of such tool within the farm population.     

A review and some new results on permutation testing for multivariate problems

In recent years permutation testing methods have increased both in number of applications and in solving complex multivariate problems. When available permutation tests are essentially of an exact nonparametric nature in a conditional context, where conditioning is on the pooled observed data set which is often a set of sufficient statistics in the null hypothesis. Whereas, the reference null distribution of most parametric tests is only known asymptotically. Thus, for most sample sizes of practical interest, the possible lack of efficiency of permutation solutions may be compensated by the lack of approximation of parametric counterparts. There are many complex multivariate problems, quite common in empirical sciences, which are difficult to solve outside the conditional framework and in particular outside the method of nonparametric combination (NPC) of dependent permutation tests. In this paper we review such a method and its main properties along with some new results in experimental and observational situations (robust testing, multi-sided alternatives and testing for survival functions).     

Visualizing main effects and interaction in multiple non-symmetric correspondence analysis

Non-symmetric correspondence analysis (NSCA) is a useful technique for analysing a two-way contingency table. Frequently, the predictor variables are more than one; in this paper, we consider two categorical variables as predictor variables and one response variable. Interaction represents the joint effects of predictor variables on the response variable. When interaction is present, the interpretation of the main effects is incomplete or misleading. To separate the main effects and the interaction term, we introduce a method that, starting from the coordinates of multiple NSCA and using a two-way analysis of variance without interaction, allows a better interpretation of the impact of the predictor variable on the response variable. The proposed method has been applied on a well-known three-way contingency table proposed by Bockenholt and Bockenholt in which they cross-classify subjects by person's attitude towards abortion, number of years of education and religion. We analyse the case where the variables education and religion influence a person's attitude towards abortion.     

Extensions of Permutation Solutions to Test for Treatment Effects in Replicated Single-Case Alternation Experiments with Multivariate Response

Single-case experiments are frequently used to do research involving a clinical intervention, since large-n trials are often impractical in clinical research. In order to investigate a possible difference in the effect of the treatments considered in the study, nonparametric instruments are valid tools; in particular, permutation solutions work well when we wish to assess differences in treatment effects. We present an extension of a permutation solution to the multivariate response case and to the case of replicated single-case experiments. A simulation study shows that the approach is both reliable under the null hypothesis and powerful under the alternative. At the end, we present the results of an application to two real experiments.     

A Permutation Solution to Test for Treatment Effects in Alternation Design Single-Case Experiments

Research involving a clinical intervention is normally aimed at testing the treatment effects on a dependent variable, which is assumed to be a relevant indicator of health or quality-of-life status. In much clinical research large-n trials are in fact impractical because the availability of individuals within well-defined categories is limited in this application field. This makes it more and more important to concentrate on single-case experiments. The goal with these is to investigate the presence of a difference in the effect of the treatments considered in the study. In this setting, valid inference generally cannot be made using the parametric statistical procedures that are typically used for the analysis of clinical trials and other large-n designs. Hence, nonparametric tools can be a valid alternative to analyze this kind of data. We propose a permutation solution to assess treatment effects in single-case experiments within alternation designs. An extension to the case of more than two treatments is also presented. A simulation study shows that the approach is both reliable under the null hypothesis and powerful under the alternative, and that it improves the performance of a considered competitor. In the end, we present the results of a real case application.     

Cultural Access and Mental Health: An Exploratory Study

Loss of well-being, rising rates of depression and various psychological illnesses are a public health concern. This study aims to explore the associations between cultural access and mental illness. Applying a panel methodology to the 20 Italian regions (2002–2007 period) the relationship between public health expenditure per-capita (the dependent variable) and hospital discharge rates for different illnesses (the regressors) has been estimated. Then the impact of the private spending in culture (the regressors) on the mental illness—as approximated by the discharge rate for mental illness—(the dependent variable), has been verified via generalised method of moments (GMM) approach. Data came from the National Census of the Italian Institute of Statistics (ISTAT). The results of empirical analysis have highlighted how the discharge rate for mental illness is substantially improved by some forms of cultural consumptions. The coefficients associated with unemployment rates (the control variables) have a positive impact on mental illness, thus suggesting that unemployment has an impact on the discharge rate for mental illness; the greatest impact is observed for the long-term unemployment rate. The results are beneficial for designing and implementing preventive strategies to reduce mental illness and public health expenditure by considering the impact of cultural access.