We study flexible Bayesian methods that are amenable to a wide range of learning problems involving complex high dimensional data structures, with minimal tuning. We consider parametric and semiparametric Bayesian models, that are applicable to both static and dynamic data, arising from a multitude of areas such as economics, finance and…

When estimating causal effects, unmeasured confounding and model misspecification are both potential sources of bias. We propose a method to simultaneously address both issues in the form of a semi-parametric sensitivity analysis. In particular, our approach incorporates Bayesian Additive Regression Trees into a two-parameter sensitivity analysis…

There has been much research and discussion on the principles of standards-based grading, and there is a growing consensus of best practice. Even so, the actual process of implementing standards-based grading at a school or district level can be a significant challenge. There are very practical questions that remain unclear, such as how the grades…

In many surveys, the data comprise a large number of categorical variables that suffer from item nonresponse. Standard methods for multiple imputation, like log-linear models or sequential regression imputation, can fail to capture complex dependencies and can be difficult to implement effectively in high dimensions. We present a fully Bayesian,…

This study explores the attitudes of mathematics pre-service teachers, based on their initial exposure to a model-eliciting challenge. The new Curriculum and Assessment Policy Statement determines that mathematics students should be able to identify, investigate and solve problems via modelling. The unpreparedness of mathematics teachers in…

The possibility of using component analysis for nominal data is discussed. Two nominal scale correlation coefficients are applicable. Tschuprow's coefficient and the J index. The reason is that they satisfy the requirements of a scalar product between normalized vectors in a Euclidean space. Some characteristics of these coefficients are…

Stochastic ordering properties are investigated for a broad class of item response theory (IRT) models for which the monotone likelihood ratio does not hold. A taxonomy is given for nonparametric and parametric models for polytomous models based on the hierarchical relationship between the models. (SLD)

Consider the nonparametric regression model Y = m(X)+ [tau](X)[epsilon], where X and [epsilon] are independent random variables, [epsilon] has a median of zero and variance [sigma][squared], [tau] is some unknown function used to model heteroscedasticity, and m(X) is an unknown function reflecting some conditional measure of location associated…

Asymptotic distribution theory of Brogden's form of biserial correlation coefficient is derived and large sample estimates of its standard error obtained. Its relative efficiency to the biserial correlation coefficient is examined. Recommendations for choice of estimator of biserial correlation are presented. (Author/JKS)

Inference procedures appropriate for the analysis of nominal and ordinal data are discussed. Matching models are shown to be useful under certain constraints. (JKS)

Most researchers using factor analysis extract factors from a matrix of Pearson product-moment correlation coefficients. A method is presented for extracting factors in a non-parametric way, by extracting factors from a matrix of Spearman rho (rank correlation) coefficients. It is possible to factor analyze a matrix of association such that…

A nonparametric Mokken scale analysis and program is described. Three procedures of scaling (a search procedure, evaluation of the whole set of items as a scale, and extension of an existing scale) provided a coefficient of scalability for all the items together that satisfy the criteria of the Mokken model. (Author/LMO)

The G index is a measure of the similarity between individuals over dichotomous items. Some tests for the G-index are described. For each case an example is included. (Author/GK)

The normal scores test for scale (variance) is presented as an alternative for evaluating the equality of dispersion for two independent populations. Test development is indicated as well as examples illustrating large and small sample situations. Reference is made to comparisons with the F, Mood, and Siegel-Tukey tests. (Author/JKS)

A description of a Mokken test program to test the robustness of nonparametric Stochastic scales is presented. For each sample and the whole population, different scale statistics (both on scale and on item level) are computed recursively. A statistic T is presented for testing the robustness of the scales in the samples. (Author)