Conditional Inference in Small Sample Scenarios Using a Resampling Approach

This paper discusses a non-parametric resampling technique in the context of multidimensional or multiparameter hypothesis testing of assumptions of the Rasch model. It is based on conditional distributions and it is suggested in small sample size scenarios as an alternative to the application of asymptotic or large sample theory. The exact sampling distribution of various well-known chi-square test statistics like Wald, likelihood ratio, score, and gradient tests as well as others can be arbitrarily well approximated in this way. A procedure to compute the power function of the tests is also presented. A number of examples of scenarios are discussed in which the power function of the test does not converge to 1 with an increasing deviation of the true values of the parameters of interest from the values specified in the hypothesis to be tested. Finally, an attempt to modify the critical region of the tests is made aiming at improving the power and an R package is provided.

Nonparametric inference for interventional effects with multiple mediators

Understanding the pathways whereby an intervention has an effect on an outcome is a common scientific goal. A rich body of literature provides various decompositions of the total intervention effect into pathway-specific effects. Interventional direct and indirect effects provide one such decomposition. Existing estimators of these effects are based on parametric models with confidence interval estimation facilitated via the nonparametric bootstrap. We provide theory that allows for more flexible, possibly machine learning-based, estimation techniques to be considered. In particular, we establish weak convergence results that facilitate the construction of closed-form confidence intervals and hypothesis tests and prove multiple robustness properties of the proposed estimators. Simulations show that inference based on large-sample theory has adequate small-sample performance. Our work thus provides a means of leveraging modern statistical learning techniques in estimation of interventional mediation effects.

Conditional or Pseudo Exact Tests with an Application in the Context of Modeling Response Times

This paper treats a so called pseudo exact or conditional approach of testing assumptions of a psychometric model known as the Rasch model. Draxler and Zessin derived the power function of such tests. They provide an alternative to asymptotic or large sample theory, i.e., chi square tests, since they are also valid in small sample scenarios. This paper suggests an extension and applies it in a research context of investigating the effects of response times. In particular, the interest lies in the examination of the influence of response times on the unidimensionality assumption of the model. A real data example is provided which illustrates its application, including a power analysis of the test, and points to possible drawbacks.

Left-censored dementia incidences in estimating cohort effects

We estimate the dementia incidence hazard in Germany for the birth cohorts 1900 until 1954 from a simple sample of Germany’s largest health insurance company. Followed from 2004 to 2012, 36,000 uncensored dementia incidences are observed and further 200,000 right-censored insurants included. From a multiplicative hazard model we find a positive and linear trend in the dementia hazard over the cohorts. The main focus of the study is on 11,000 left-censored persons who have already suffered from the disease in 2004. After including the left-censored observations, the slope of the trend declines markedly due to Simpson’s paradox, left-censored persons are imbalanced between the cohorts. When including left-censoring, the dementia hazard increases differently for different ages, we consider omitted covariates to be the reason. For the standard errors from large sample theory, left-censoring requires an adjustment to the conditional information matrix equality.