Maximum marginal likelihood estimation for semiparametric item analysis

The item characteristic curve (ICC), defining the relation between ability and the probability of choosing a particular option for a test item, can be estimated by using polynomial regression splines. These provide a more flexible family of functions than is given by the three-parameter logistic family. The estimation of spline ICCs is described by maximizing the marginal likelihood formed by integrating ability over a beta prior distribution. Some simulation results compare this approach with the joint estimation of ability and item parameters.IRCAMThe research reported in this paper was supported by Grants APA320 and A4035 from the Natural Sciences and Engineering Research Council of Canada. It was also supported by Contract No. F41689-82-C-10020 from the Air Force Human Resources Laboratory to Educational Testing Service. The author wishes to thank M. Abrahamowicz for his assistance and R. Darrell Bock for providing the parameters for the items used in the simulations.     

Idiographic network analysis of discrete mood states prior to treatment

Idiographic network models based on time‐series data have received recent attention for their ability to model relationships among symptoms and behaviours as they unfold in time within a single individual (cf. Epskamp, Borsboom, & Fried, 2018; Fisher, Medaglia, & Jeronimus, 2018). Rather than examine the correlational relationships between variables in a sample of individuals, an idiographic network examines correlations within a single person, averaged over many time points. Because the approach averages over time, the data must be stationary (i.e. relatively consistent over time). If individuals experience varying states over time—different mixtures of symptoms and behaviours in one moment or another—then averaging over categorically different moments may undermine model accuracy. Fisher and Bosley (2019) address these concerns via the application of Gaussian finite mixture modelling to identify latent classes of time points in intraindividual time‐series data from a sample of adults with major depressive disorder and/or generalised anxiety disorder (n = 45). The present paper outlines an extension of this work, wherein network analysis is used to model within‐class covariation of symptoms. To illustrate this approach, network models were constructed for each intraindividual class identified by Fisher and Bosley (137 networks across the 45 participants, mean classes/person = ~3, range = 2–4 classes/person). We examine the relative consistency in symptom organisation between each individual's multiple mood state networks and assess emergent group‐level patterns. We highlight opportunities for enhanced treatment personalisation and review nomothetic patterns relevant to transdiagnostic conceptualisations of psychopathology. We address opportunities for integrating this approach into clinical practice and outline potential shortcomings.     

A Note on Recurring Misconceptions When Fitting Nonlinear Mixed Models

Nonlinear mixed-effects (NLME) models are used when analyzing continuous repeated measures data taken on each of a number of individuals where the focus is on characteristics of complex, nonlinear individual change. Challenges with fitting NLME models and interpreting analytic results have been well documented in the statistical literature. However, parameter estimates as well as fitted functions from NLME analyses in recent articles have been misinterpreted, suggesting the need for clarification of these issues before these misconceptions become fact. These misconceptions arise from the choice of popular estimation algorithms, namely, the first-order linearization method (FO) and Gaussian-Hermite quadrature (GHQ) methods, and how these choices necessarily lead to population-average (PA) or subject-specific (SS) interpretations of model parameters, respectively. These estimation approaches also affect the fitted function for the typical individual, the lack-of-fit of individuals’ predicted trajectories, and vice versa.     

Priors in perception: Top-down modulation,Bayesian perceptual learning rate,and prediction error minimization

I discuss top-down modulation of perception in terms of a variable Bayesian learning rate, revealing a wide range of prior hierarchical expectations that can modulate perception. I then switch to the prediction error minimization framework and seek to conceive cognitive penetration specifically as prediction error minimization deviations from a variable Bayesian learning rate. This approach retains cognitive penetration as a category somewhat distinct from other top-down effects, and carves a reasonable route between penetrability and impenetrability. It prevents rampant, relativistic cognitive penetration of perception and yet is consistent with the continuity of cognition and perception.     

High-dimensional maximum marginal likelihood item factor analysis by adaptive quadrature

Although the Bock–Aitkin likelihood-based estimation method for factor analysis of dichotomous item response data has important advantages over classical analysis of item tetrachoric correlations, a serious limitation of the method is its reliance on fixed-point Gauss-Hermite (G-H) quadrature in the solution of the likelihood equations and likelihood-ratio tests. When the number of latent dimensions is large, computational considerations require that the number of quadrature points per dimension be few. But with large numbers of items, the dispersion of the likelihood, given the response pattern, becomes so small that the likelihood cannot be accurately evaluated with the sparse fixed points in the latent space. In this paper, we demonstrate that substantial improvement in accuracy can be obtained by adapting the quadrature points to the location and dispersion of the likelihood surfaces corresponding to each distinct pattern in the data. In particular, we show that adaptive G-H quadrature, combined with mean and covariance adjustments at each iteration of an EM algorithm, produces an accurate fast-converging solution with as few as two points per dimension. Evaluations of this method with simulated data are shown to yield accurate recovery of the generating factor loadings for models of upto eight dimensions. Unlike an earlier application of adaptive Gibbs sampling to this problem by Meng and Schilling, the simulations also confirm the validity of the present method in calculating likelihood-ratio chi-square statistics for determining the number of factors required in the model. Finally, we apply the method to a sample of real data from a test of teacher qualifications.     

Note on optimization of individual psychotherapeutic processes

Individual psychotherapy typically involves a sequence of recurrent sessions of client-therapist interaction. Accordingly, the psychotherapeutic process can be conceived of as evolving at least at two different time scales: a fast time scale pertaining to the on-going interaction within each session and a slow time scale associated with sequential regularities occurring between consecutive sessions. It is possible to exploit the sequential regularities between sessions in order to assess and optimize an ongoing individual psychotherapeutic process in real time. In this note a computational paradigm is outlined according to which this can be implemented and applied in flexible ways. Illustrations are given with simulated data. A heuristic summary is provided in the closing section.     

一种新的等值方法：核等值法

该文介绍了一种新的等值方法一核等值法。首先介绍了核等值法的研究过程、它的主要特点以及五个步骤（前平滑处理、估计分数概率、连续化、等值、计算等值标准误）。之后,介绍了核等值法与其他传统的观察分等值方法的差异,最后是对核等值法的评价。     

Estimating latent distributions

Consider vectors of item responses obtained from a sample of subjects from a population in which ability is distributed with densityg(), where the are unknown parameters. Assuming the responses depend on through a fully specified item response model, this paper presents maximum likelihood equations for the estimation of the population parameters directly from the observed responses; i.e., without estimating an ability parameter for each subject. Also provided are asymptotic standard errors and tests of fit, computing approximations, and details of four special cases: a non-parametric approximation, a normal solution, a resolution of normal components, and a beta-binomial solution.The author would like to thank R. Darrell Bock for his comments, suggestions, and encouragement during the course of this work.