Improving Likert scale big data analysis in psychometric health economics: reliability of the new compositional data approach.

Bipolar psychometric scales data are widely used in psychologic healthcare. Adequate psychological profiling benefits patients and saves time and costs. Grant funding depends on the quality of psychotherapeutic measures. Bipolar Likert scales yield compositional data because any order of magnitude of agreement towards an item assertion implies a complementary order of magnitude of disagreement. Using an isometric log-ratio (ilr) transformation the bivariate information can be transformed towards the real valued interval scale yielding unbiased statistical results increasing the statistical power of the Pearson correlation significance test if the Central Limit Theorem (CLT) of statistics is satisfied. In practice, however, the applicability of the CLT depends on the number of summands (i.e., the number of items) and the variance of the data generating process (DGP) of the ilr transformed data. Via simulation we provide evidence that the ilr approach also works satisfactory if the CLT is violated. That is, the ilr approach is robust towards extremely large or infinite variances of the underlying DGP increasing the statistical power of the correlation test. The study generalizes former results pointing out the universality and reliability of the ilr approach in psychometric big data analysis affecting psychometric health economics, patient welfare, grant funding, economic decision making and profits.

The CPCAT as a novel tool to overcome the shortcomings of NOEC/LOEC statistics in ecotoxicology: a simulation study to evaluate the statistical power.

Species reproduction is an important determinant of population dynamics. As such, this is an important parameter in environmental risk assessment. The closure principle computational approach test (CPCAT) was recently proposed as a method to derive a NOEC/LOEC for reproduction count data such as the number of juvenile Daphnia. The Poisson distribution used by CPCAT can be too restrictive as a model of the data-generating process. In practice, the generalized Poisson distribution could be more appropriate, as it allows for inequality of the population mean µ and the population variance σ 2 . It is of fundamental interest to explore the statistical power of CPCAT and the probability of determining a regulatory relevant effect correctly. Using a simulation, we varied between Poisson distribution ( µ = σ 2 ) and generalized Poisson distribution allowing for over-dispersion ( µ < σ 2 ) and under-dispersion ( µ > σ 2 ). The results indicated that the probability of detecting the LOEC/NOEC correctly was ≥ 0.8 provided the effect was at least 20% above or below the mean level of the control group and mean reproduction of the control was at least 50 individuals while over-dispersion was missing. Specifically, under-dispersion increased, whereas over-dispersion reduced the statistical power of the CPCAT. Using the well-known Hampel identifier, we propose a simple and straight forward method to assess whether the data-generating process of real data could be over- or under-dispersed.

A new approach for assessing the state of environment using isometric log-ratio transformation and outlier detection for computation of mean PCDD/F patterns in biota.

To assess the state of the environment, various compartments are examined as part of monitoring programs. Within monitoring, a special focus is on chemical pollution. One of the most toxic substances ever synthesized is the well-known dioxin 2,3,7,8-TCDD (2,3,7,8-tetra-chlor-dibenzo-dioxin). Other PCDD/F (polychlorinated-dibenzo-dioxin and furan) can act toxic too. They are ubiquitary and persistent in various environmental compartments. Assessing the state of environment requires knowledge of typical local patterns of PCDD/F for as many compartments as possible. For various species of wild animals and plants (so called biota), I present the mean local congenere profiles of ubiquitary PCDD/F contamination reflecting typical patterns and levels of environmental burden for various years. Trends in time series of means can indicate success or failure of a measure of PCDD/F reduction. For short time series of mean patterns, it can be hard to detect trends. A new approach regarding proportions of outliers in the corresponding annual cross-sectional data sets in parallel can help detect decreasing or increasing environmental burden and support analysis of time series. Further, in this article, the true structure of PCDD/F data in biota is revealed, that is, the compositional data structure. It prevents direct application of statistical standard procedures to the data rendering results of statistical analysis meaningless. Results indicate that the compositional data structure of PCDD/F in biota is of great interest and should be taken into account in future studies. Isometric log-ratio (ilr) transformation is used, providing data statistical standard procedures that can be applied too. Focusing on the identification of typical PCDD/F patterns in biota, outliers are removed from annual data since they represent an extraordinary situation in the environment. Identification of outliers yields two advantages. First, typical (mean) profiles and levels of PCDD/F contamination can be identified. Second, decreasing (increasing) proportions of outliers could indicate decreasing (increasing) numbers of extraordinary environmental burden rendering the success of PCDD/F reduction strategies for biota. Therefore, probabilities and proportions of outlier contamination are estimated too. To reveal the enormous influence of the method of outlier detection, the applied two well-known procedures are compared, that is, robust Mahalanobis distance and a projection pursuit-based approach.