Sparse principal component analysis is a very active research area in the last decade. It produces component loadings with many zero entries which facilitates their interpretation and helps avoid redundant variables. The classic factor analysis is another popular dimension reduction technique which shares similar interpretation problems and could greatly benefit from sparse solutions. Unfortunately, there are very few works considering sparse versions of the classic factor analysis. Our goal is to contribute further in this direction. We revisit the most popular procedures for exploratory factor analysis, maximum likelihood and least squares. Sparse factor loadings are obtained for them by, first, adopting a special reparameterization and, second, by introducing additional ${\ell }_1$\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\ell _1$$\end{document}-norm penalties into the standard factor analysis problems. As a result, we propose sparse versions of the major factor analysis procedures. We illustrate the developed algorithms on well-known psychometric problems. Our sparse solutions are critically compared to ones obtained by other existing methods.

Whether, when, and why perceivers are able to accurately infer the personality traits of other individuals is a key topic in psychological science. Studies examining this question typically ask a number of perceivers to judge a number of targets with regard to a specific trait. The resulting data are then analyzed by averaging the judgments across perceivers or by computing the respective statistic for each single perceiver. Here, we discuss the limitations of the average-perceiver and single-perceiver approaches. Furthermore, we argue that and illustrate how cross-classified structural equation models can be used for the flexible analysis of accuracy data.

Ecological momentary assessment data consist of in-the-moment sampling several times per day aimed at capturing phenomena that are highly variable. When research questions are focused on the association between a construct measured repeatedly and an event that occurs sporadically over time interspersed between repeated measures, the data consist of correlated observed or censored times to an event. In such a case, specialized time-to-event models that account for correlated observations are required to properly assess the relationships under study. In the current study, we apply two time-to-event analysis techniques, proportional hazards, and accelerated failure time modeling, to data from a study of affective states and sexual behavior in depressed adolescents and illustrate differing interpretations from the models.

The assumption of conditional independence between response time and accuracy given speed and ability is commonly made in response time modelling. However, this assumption might be violated in some cases, meaning that the relationship between the response time and the response accuracy of the same item cannot be fully explained by the correlation between the overall speed and ability. We propose to explicitly model the residual dependence between time and accuracy by incorporating the effects of the residual response time on the intercept and the slope parameter of the IRT model for response accuracy. We present an empirical example of a violation of conditional independence from a low-stakes educational test and show that our new model reveals interesting phenomena about the dependence of the item properties on whether the response is relatively fast or slow. For more difficult items responding slowly is associated with a higher probability of a correct response, whereas for the easier items responding slower is associated with a lower probability of a correct response. Moreover, for many of the items slower responses were less informative for the ability because their discrimination parameters decrease with residual response time.

Tests for a change point (e.g., Chen and Gupta, Parametric statistical change point analysis (2nd ed.). Birkhuser, Boston, 2012; Hawkins et al., J Qual Technol 35:355–366, 2003) have recently been brought into the spotlight for their potential uses in psychometrics. They have been successfully applied to detect an unusual change in the mean score of a sequence of administrations of an international language assessment (Lee and von Davier, Psychometrika 78:557–575, 2013) and to detect speededness of examinees (Shao et al., Psychometrika, 2015). The differences in the type of data used, the test statistics, and the manner in which the critical values were obtained in these papers lead to questions such as “what type of psychometric problems can be solved by tests for a change point?” and “what test statistics should be used with tests for a change point in psychometric problems?” This note attempts to answer some of these questions by providing a general overview of tests for a change point with a focus on application to psychometric problems. A discussion is provided on the choice of an appropriate test statistic and on the computation of a corresponding critical value for tests for a change point. Then, three real data examples are provided to demonstrate how tests for a change point can be used to make important inferences in psychometric problems. The examples include some clarifications and remarks on the critical values used in Lee and von Davier (Psychometrika, 78:557–575, 2013) and Shao et al. (Psychometrika, 2015). The overview and the examples provide insight on tests for a change point above and beyond Lee and von Davier (Psychometrika, 78:557–575, 2013) and Shao et al. (Psychometrika, 2015). Thus, this note extends the research of Lee and von Davier (Psychometrika, 78:557–575, 2013) and Shao et al. (Psychometrika, 2015) on tests for a change point.

Parameter recovery and item utilization were investigated for different designs for online test item calibration. The design was adaptive in a double sense: it assumed both adaptive testing of examinees from an operational pool of previously calibrated items and adaptive assignment of field-test items to the examinees. Four criteria of optimality for the assignment of the field-test items were used, each of them based on the information in the posterior distributions of the examinee’s ability parameter during adaptive testing as well as the sequentially updated posterior distributions of the field-test item parameters. In addition, different stopping rules based on target values for the posterior standard deviations of the field-test parameters and the size of the calibration sample were used. The impact of each of the criteria and stopping rules on the statistical efficiency of the estimates of the field-test parameters and on the time spent by the items in the calibration procedure was investigated. Recommendations as to the practical use of the designs are given.

Item cloning is increasingly used to generate slight differences in tasks for use in psychological experiments and educational assessments. This paper investigates the psychometric issues that arise when item cloning introduces variation into the difficulty parameters of the item clones. Four models are proposed and evaluated in simulation studies with conditions representing possible types of variation due to item cloning. Depending on the model specified, unaccounted variance in the item clone difficulties propagates to other parameters in the model, causing specific and predictable patterns of bias. Person parameters are largely unaffected by the choice of model, but for inferences related to the item parameters, the choice is critical and can even be leveraged to identify problematic item cloning.

Item nonresponse is a common problem in educational and psychological assessments. The probability of unplanned missing responses due to omitted and not-reached items may stochastically depend on unobserved variables such as missing responses or latent variables. In such cases, missingness cannot be ignored and needs to be considered in the model. Specifically, multidimensional IRT models, latent regression models, and multiple-group IRT models have been suggested for handling nonignorable missing responses in latent trait models. However, the suitability of the particular models with respect to omitted and not-reached items has rarely been addressed. Missingness is formalized by response indicators that are modeled jointly with the researcher’s target model. We will demonstrate that response indicators have different statistical properties depending on whether the items were omitted or not reached. The implications of these differences are used to derive a joint model for nonignorable missing responses with ability to appropriately account for both omitted and not-reached items. The performance of the model is demonstrated by means of a small simulation study.

This commentary concerns the theoretical properties of the estimation procedure in “A General Method of Empirical Q-matrix Validation” by Jimmy de la Torre and Chia-Yi Chiu. It raises the consistency issue of the estimator, proposes some modifications to it, and also makes some conjectures.

This paper assesses the psychometric value of allowing test-takers choice in standardized testing. New theoretical results examine the conditions where allowing choice improves score precision. A hierarchical framework is presented for jointly modeling the accuracy of cognitive responses and item choices. The statistical methodology is disseminated in the ‘cIRT’ R package. An ‘answer two, choose one’ (A2C1) test administration design is introduced to avoid challenges associated with nonignorable missing data. Experimental results suggest that the A2C1 design and payout structure encouraged subjects to choose items consistent with their cognitive trait levels. Substantively, the experimental data suggest that item choices yielded comparable information and discrimination ability as cognitive items. Given there are no clear guidelines for writing more or less discriminating items, one practical implication is that choice can serve as a mechanism to improve score precision.

The social relations model (SRM) is commonly used in the analysis of interpersonal judgments and behaviors that arise in groups. The SRM was developed only for use with cross-sectional data. Here, we introduce an extension of the SRM to longitudinal data. The social relations growth model represents a person’s repeated SRM judgments of another person as a function of time. We show how the model’s parameters can be estimated using restricted maximum likelihood, and how the effects of covariates on interindividual and interdyad variability in growth can be computed. An example is presented to illustrate the suggested approach. We also present the results of a small simulation study showing the suitability of the social relations growth model for the analysis of longitudinal SRM data.

When word learning is supported by instruction in experimental studies for adolescents, word knowledge outcomes tend to be collected from complex data structure, such as multiple aspects of word knowledge, multilevel reader data, multilevel item data, longitudinal design, and multiple groups. This study illustrates how generalized linear mixed models can be used to measure and explain word learning for data having such complexity. Results from this application provide deeper understanding of word knowledge than could be attained from simpler models and show that word knowledge is multidimensional and depends on word characteristics and instructional contexts.

This rejoinder responds to the commentary by Liu (Psychometrika, 2015) entitled “On the consistency of Q-matrix estimation: A commentary” on the paper “A general method of empirical Q-matrix validation” by de la Torre and Chiu (Psychometrika, 2015). It discusses and addresses three concerns raised in the commentary, namely the estimation accuracy when a provisional Q-matrix is used, the consistency of the Q-matrix estimator, and the computational efficiency of the proposed method.