It is often necessary to estimate a probability density non-parametrically, that is, without making strong parametric assumptions such as normality. This R (R Core Team, 2019) package provides a non-parametric density estimator that can take advantage of some of the knowledge the user has about the probability density. Kernel density estimation (Silverman, 2018) is a popular method for non-parametric density estimation based on placing kernels on each data point. Hjort & Glad (1995) extended kernel density estimation with parametric starts. The parametric start is a parametric density that is multiplied with the kernel estimate. When the data-generating density is reasonably close to the parametric start density, kernel density estimation with that parametric start will outperform ordinary kernel density estimation.

The tetrachoric correlation is a popular measure of association for binary data and estimates the correlation of an underlying normal latent vector. However, when the underlying vector is not normal the tetrachoric correlation will be different from the underlying correlation. Since assuming underlying normality is often done on pragmatic and not substantial grounds, the estimated tetrachoric correlation may therefore be quite different from the true underlying correlation that is modeled in structural equation modeling. This motivates studying the range of latent correlations that are compatible with given binary data, when the distribution of the latent vector is partly or completely unknown. We show that nothing can be said about the latent correlations unless we know more than what can be derived from the data. We identify an interval constituting all latent correlations compatible with observed data when the marginals of the latent variables are known. Also, we quantify how partial knowledge of the dependence structure of the latent variables affect the range of compatible latent correlations. Implications for tests of underlying normality are briefly discussed.

Publication bias and p-hacking are two well-known phenomena which strongly affect the scientific literature and cause severe problems in meta-analysis studies. Due to these phenomena, the assumptions are seriously violated and the results of the meta-analysis studies cannot be trusted. While publication bias is almost perfectly captured by the model of Hedges, p-hacking is much harder to model and no definitive solution has been found yet. In this paper we propose to model both publication bias and p-hacking with selection models. We derive some properties for these models, and we contrast them both formally and via simulations. Finally, two real data examples are used to show how the models work in practice.

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univariateML is an R (R Core Team, 2019) package for user-friendly univariate maximum likelihood estimation (Cam, 1990). It supports more than 20 densities, the most popular generic functions such as plot, AIC, and confint, and a simple parametric bootstrap (Efron & Tibshirani, 1994) interface.