• Corpus ID: 220495805

Reliability of decisions based on tests: Fourier analysis of Boolean decision functions

  title={Reliability of decisions based on tests: Fourier analysis of Boolean decision functions},
  author={Lourens J. Waldorp and Maarten Marsman and Denny Borsboom},
  journal={arXiv: Methodology},
Items in a test are often used as a basis for making decisions and such tests are therefore required to have good psychometric properties, like unidimensionality. In many cases the sum score is used in combination with a threshold to decide between pass or fail, for instance. Here we consider whether such a decision function is appropriate, without a latent variable model, and which properties of a decision function are desirable. We consider reliability (stability) of the decision function, i… 

Figures from this paper



The Use of Test Scores for Classification Decisions with Threshold Utility

The classification problem consists of assigning subjects to one of several available treatments on the basis of their test scores, where the success of each treatment is measured by a different

Confidence intervals and hypothesis testing for high-dimensional regression

This work considers here high-dimensional linear regression problem, and proposes an efficient algorithm for constructing confidence intervals and p-values, based on constructing a 'de-biased' version of regularized M-estimators.

Noise stability of functions with low influences: Invariance and optimality

An invariance principle for multilinear polynomials with low influences and bounded degree is proved; it shows that under mild conditions the distribution of such polynmials is essentially invariant for all product spaces.

Speed-Accuracy Response Models: Scoring Rules based on Response Time and Accuracy

Starting from an explicit scoring rule for time limit tasks incorporating both response time and accuracy, and a definite trade-off between speed and accuracy, a response model is derived. Since the

Logistic regression and Ising networks: prediction and estimation when violating lasso assumptions

The consequences for both prediction and estimation when the sparsity and restricted eigenvalue assumptions are not satisfied are determined, using the idea of connected copies (extreme multicollinearity) to explain the fact that prediction becomes better when either sparsity or multicoll inearity is not satisfied.

A characterization of monotone unidimensional latent variable models

Recently, the problem of characterizing monotone unidimensional latent variable models for binary repeated measures was studied by Ellis and van den Wollenberg and by Junker. We generalize their work

Statistical Theories of Mental Test Scores.

This is a reprint of the orginal book released in 1968. Our primary goal in this book is to sharpen the skill, sophistication, and in- tuition of the reader in the interpretation of mental test data,

An Introduction to Network Psychometrics: Relating Ising Network Models to Item Response Theory Models

A broad equivalence is shown between the Ising model and the IRT model, which describes the probability distribution associated with item responses in a psychometric test as a function of a latent variable.

Probabilistic Networks and Expert Systems

This book gives a thorough and rigorous mathematical treatment of the underlying ideas, structures, and algorithms of probabilistic expert systems, emphasizing those cases in which exact answers are obtainable.

Reliability of test scores in nonparametric item response theory

Three methods for estimating reliability are studied within the context of nonparametric item response theory. Two were proposed originally by Mokken (1971) and a third is developed in this paper.