A stimulus (or stimulus-complex) is pictured as giving rise to a random series of sensory nerve “pulses,” which manifest themselves in contractions of individual muscle fibers. Assuming the expected time-frequency of these pulses to be proportional to the intensity of the stimulus, probability distributions are computed representing the cumulative effect of these pulses on the state of the organism, that is, on its degree of awareness of the stimulus. Preliminary results suggest a modification of the Weber-Fechner formula for intensity discrimination for certain types of stimuli: the psychological scale to be measured by I1/2 instead of log I.

The Polytomous Local Independence Model (PoLIM) by Stefanutti, de Chiusole, Anselmi, and Spoto, is an extension of the Basic Local Independence Model (BLIM) to accommodate polytomous items. BLIM, a model for analyzing responses to binary items, is based on Knowledge Space Theory, a framework developed by cognitive scientists and mathematical psychologists for modeling human knowledge acquisition and representation. The purpose of this commentary is to show that PoLIM is simply a paraphrase of a DINA model in cognitive diagnosis for polytomous items. Specifically, BLIM is shown to be equivalent to the DINA model when the BLIM-items are conceived as binary single-attribute items, each with a distinct attribute; thus, PoLIM is equivalent to the DINA for polytomous single-attribute items, each with a distinct attribute.

There is now an expanding body of literature on the significant problem of business non-compliance with minimum labour standards including ‘wage theft’. Extended liability regulation beyond the direct employer is seen as one solution to this non-compliance in fragmented but hierarchically organised industries—such as the cleaning industry. This article uses empirical evidence to assess the effectiveness of one such regulatory scheme, the Cleaning Accountability Framework (CAF), in addressing non-compliance with minimum labour standards (including provisions of the Fair Work Act 2009 (Cth) and the Cleaning Services Award 2020). We find that CAF has been successful in identifying and rectifying certain non-compliance, improving working conditions for some cleaners involved in the scheme. We synthesise the key success factors of CAF in view of envisioning the adoption of such co-regulation frameworks in other industries. We also propose legal reforms that will support change across the cleaning industry.

In the context of covariance structure analysis, a unified approach to the asymptotic theory of alternative test criteria for testing parametric restrictions is provided. The discussion develops within a general framework that distinguishes whether or not the fitting function is asymptotically optimal, and allows the null and alternative hypothesis to be only approximations of the true model. Also, the equivalent of the information matrix, and the asymptotic covariance matrix of the vector of summary statistics, are allowed to be singular. When the fitting function is not asymptotically optimal, test statistics which have asymptotically a chi-square distribution are developed as a natural generalization of more classical ones. Issues relevant for power analysis, and the asymptotic theory of a testing related statistic, are also investigated.

We investigate how different forms of scrutiny affect dishonesty, using Gneezy’s [Am Econ Rev 95:384–394 (2005)] deception game. We add a third player whose interests are aligned with those of the sender. We find that lying behavior is not sensitive to revealing the sender’s identity to the observer. The option for observers to communicate with the sender, and the option to reveal the sender’s lies to the receiver also do not affect lying behavior. Even more striking, senders whose identity is revealed to their observer do not lie less when their interests are misaligned with those of the observer.

A combination is achieved of two lines of psychometric interest: a) multidimensional scaling and b) factor analysis. This is accomplished with the use of three-mode factor analysis of scalar product matrices, one for each subject. Two of the modes are the groups of objects scaled and the third mode is the sample of subjects. Results are an object space, a person space, and a system for changing weights given to dimensions and of angles between dimensions in the object space for individuals located at different places in the person space. The development is illustrated with data from an adjective similarity study.

This note suggests that the reflection of residuals in the centroid method of factor analysis should be continued, whenever possible, after all the sums of the columns in the correlation matrix, excluding diagonal values, are positive. A criterion is given for determining whether further reflection is possible in such cases.

Under consideration is a test battery of binary items. The responses of n individuals are assumed to follow a Rasch model. It is further assumed that the latent individual parameters are distributed within a given population in accordance with a normal distribution. Methods are then considered for estimating the mean and variance of this latent population distribution. Also considered are methods for checking whether a normal population distribution fits the data. The developed methods are applied to data from an achievement test and from an attitude test.

First, I thank Sijtsma, Clark, Kane, and Heiser for taking the time and effort to provide a commentary on my paper, and the Editor for allowing me to respond to them. In general, the commentators agree with the thesis that psychometrics and psychology are, to an extent that must be deemed problematic, disconnected. They further agree with the upshot of this diagnosis: Psychometricians need to work harder to make a difference in psychology, and psychologists need to develop a greater awareness of important psychometric developments. However, the commentators also raise several points of disagreement and criticism.

Cognitive diagnosis models are partially ordered latent class models and are used to classify students into skill mastery profiles. The deterministic inputs, noisy “and” gate model (DINA) is a popular psychometric model for cognitive diagnosis. Application of the DINA model requires content expert knowledge of a Q matrix, which maps the attributes or skills needed to master a collection of items. Misspecification of Q has been shown to yield biased diagnostic classifications. We propose a Bayesian framework for estimating the DINA Q matrix. The developed algorithm builds upon prior research (Chen, Liu, Xu, & Ying, in J Am Stat Assoc 110(510):850–866, 2015) and ensures the estimated Q matrix is identified. Monte Carlo evidence is presented to support the accuracy of parameter recovery. The developed methodology is applied to Tatsuoka’s fraction-subtraction dataset.

A formula for the determinant of a partitioned matrix, possibly with singular submatrices, is derived and applied to some psychometric and numerical problems.

Meredith's method of extracting a factorially invariant solution is adapted to longitudinal settings. An explorational estimation procedure is presented which attempts to identify the longitudinal factor components of an across occasion variance-covariance matrix. This is effected by transforming an initial factor pattern matrix to stationarity. The estimation is performed in two parts, the first employing a stepwise algorithm to ascertain the dimensionality and existence of the longitudinal components and the second being the direct estimation of the existing factor pattern.

Chang and Stout (1993) presented a derivation of the asymptotic posterior normality of the latent trait given examinee responses under nonrestrictive nonparametric assumptions for dichotomous IRT models. This paper presents an extention of their results to polytomous IRT models in a fairly straightforward manner. In addition, a global information function is defined, and the relationship between the global information function and the currently used information functions is discussed. An information index that combines both the global and local information is proposed for adaptive testing applications.

The hypothesis that two variables have a perfect disattenuated correlation and hence measure the same trait, except for errors of measurement, is discussed. Equivalently, the underlying variables, the true scores, are related linearly. We show that several previously proposed ad hoc tests are in fact likelihood ratio tests. The cases when the linear relation is specified and when it is unspecified are both discussed.

Mean corrected higher order sample moments are asymptotically normally distributed. It is shown that both in the literature and popular software the estimates of their asymptotic covariance matrices are incorrect. An introduction to the infinitesimal jackknife is given and it is shown how to use it to correctly estimate the asymptotic covariance matrices of higher order sample moments. Another advantage in using the infinitesimal jackknife is the ease with which it may be used when stacking or sub-setting estimators. The estimates given are used to test the goodness of fit of a non-linear factor analysis model. A computationally accelerated form for infinitesimal jackknife estimates is given.

Is fiscal decentralisation in a polity divided by languages, cultures, tribes, and geography a means to nation-building or a route to secession? I consider the case of Bougainville in Papua New Guinea to provide nuanced information on the above question. This case study reveals that fiscal decentralisation, agreed to as part of a peace agreement signed in 2001 following a decade-long civil war in Bougainville, provided the opportunity for national consolidation. However, tensions surrounding the implementation of arrangements for budgetary support of Bougainville are forcing further fracturing. A definitive answer to the question of whether fiscal decentralisation helped or hindered nation-building will be provided by the referendum, due by mid-2020, when the people of Bougainville will have the option to vote for independence from Papua New Guinea.