In confirmatory factor analysis, measurement invariance is needed both to ensure that a questionnaire measures individuals equivalently across covariates (e.g., age, gender) and to justify interpreting any differences in latent factor means or relations as substantive rather than artefactual. Commonly, measurement invariance is investigated by turning (often continuous) covariates into categories and then use multi-group confirmatory factor analysis (MGCFA) in a structural equation modeling framework. However, this practice discards information and can undermine the validity of conclusions about measurement invariance and differential item functioning. Moderated (Non-)linear Factor Analysis (MNLFA) overcomes these limitations by allowing both continuous and categorical covariates to act as moderators of any parameter in a latent factor model. This allows to study measurement invariance and differential item functioning without discretizing covariates. However, current implementations of MNLFA require complex code in R or commercial software (Mplus), and do not have intuitive point-and-click user interfaces. To make MNLFA accessible to a broad range of applied researchers, we have implemented it in the free, open-source software JASP and provide a step-by-step tutorial on assessing measurement invariance using MNLFA in JASP. This implementation allows researchers to conduct more precise and informative invariance analyses without extensive programming effort.

This study, using data from the 2022–2023 INVALSI assessment, examined whether differences in mathematics and reading achievement, in terms of both mean scores and variability, exist between northern and southern Italian provinces and between boys and girls in fifth grade (Mage = 10.96, SD = 0.30, range = 9–13). We used a moderated factor analysis on a representative sample of about 10,000 students to test whether the differences reflected true underlying abilities or item-specific biases. As for mathematics, results showed that girls scored slightly lower and showed less variability compared to boys, while students from southern provinces showed a negligible mean advantage. In reading, girls scored higher. Students from southern provinces scored lower, with no meaningful variability differences. The analysis also revealed differential item functioning in both mathematics and reading, suggesting item-specific biases in relation to sex and provinces. Overall, these findings suggest that the achievement gaps reflect the complex interaction between student abilities and item-specific bias across different demographic characteristics.

BACKGROUND:Personality disorders are highly prevalent worldwide imposing substantial personal and social challenges. Schema Therapy is an effective psychotherapeutic approach for personality pathology and other complex characterological problems. New scientific insights prompted a re-evaluation of its theoretical underpinnings leading to a reformulated Schema Therapy theory. Furthermore, the assumed cross-cultural universality of the Schema Therapy model has not been tested. AIMS:This project has two primary aims: (1) To develop revised instruments based on the reformulated theory that are psychometrically sound and valid across diverse cultures and languages. (2) To validate the Schema Therapy-related constructs and their inter-relationships across cultures. METHODS:New draft versions of the Young Schema Questionnaire, Schema Coping Inventory, and Schema Mode Inventory were developed. Before dissemination, these instruments will undergo rigorous psychometric evaluation to refine item sets and ensure linguistic and conceptual consistency. A minimum of 100 adult mental health patients and 100 non-patients from each participating country will complete the revised instruments. Sociodemographic and mental health-related variables will also be assessed. Statistical analyses will evaluate (a) internal consistency, (b) unidimensionality, (c) cross-cultural invariance, (d) factorial validity (if possible), and (e) known-group validity. Malfunctioning items will be deleted, and subscales will be shortened, if possible, targeting internal consistency of ≥.80. EXPECTED OUTCOMES:This study is expected to yield optimized versions of the three instruments aligned with the reformulated theory. These findings will inform subsequent international studies to further assess the structural and cross-cultural validity of the revised scales. The resulting empirically validated scales will be openly accessible, facilitating worldwide utilization. DISCUSSION:This protocol outlines the first international study based on the reformulated theory, aiming to extend the psychopathological coverage and enhance the cross-cultural application of evidence-based treatments for personality pathology. Results will be disseminated through peer-reviewed publications and conference presentations. Potential limitations are discussed.

In moderated factor analysis, the parameters of the traditional common factor model are a function of an external continuous moderator variable. Handling missing values on the observed indicator variables of the common factors is straightforward as the parameters can be estimated using full information maximum likelihood. However, for cases with missing values on the moderator variable the likelihood function cannot be evaluated. Consequently, in practical applications of the moderated factor model, these cases are omitted from the analysis by listwise deletion. As listwise deletion is known to potentially affect the consistency and precision of the results, we propose a moderated factor model based multiple imputation procedure for handling missing values on the moderator variable in the presence of missing values on the indicator variables. We compare this new procedure with listwise deletion and predictive mean matching. The results show that both listwise deletion and predictive mean matching have less power and produce more bias in parameter estimates than multiple imputation under the moderated factor model.

In latent space item response models (LSIRMs), subjects and items are embedded in a low-dimensional Euclidean latent space. As such, interactions among persons and/or items can be revealed that are unmodeled in conventional item response theory models. Current estimation approach for LSIRMs is a fully Bayesian procedure with Markov Chain Monte Carlo, which is, while practical, computationally challenging, hampering applied researchers to use the models in a wide range of settings. Therefore, we propose an LSIRM based on two variants of regularized joint maximum likelihood (JML) estimation: penalized JML and constrained JML. Owing to the absence of integrals in the likelihood, the JML methods allow for various models to be fit in limited amount of time. This computational speed facilitates a practical extension of LSIRMs to ordinal data, and the possibility to select the dimensionality of the latent space using cross-validation. In this study, we derive the two JML approaches and address different issues that arise when using maximum likelihood to estimate the LSIRM. We present a simulation study demonstrating acceptable parameter recovery and adequate performance of the cross-validation procedure. In addition, we estimate different binary and ordinal LSIRMs on real datasets pertaining to deductive reasoning and personality. All methods are implemented in R package 'LSMjml' which is available from CRAN.

When using tests to assess individuals, precision of individual test scores is of great importance. Although it is generally known that different test scores are measured with varying precision, traditionally, measurement precision is quantified using a single value known as the standard error of measurement. In the practice of testing, the standard error of measurement is used as a one-size-fits-all measure for each test score. This practice emphasizes the need for a conditional precision estimate that shows which scores are precise and which scores lack precision. We discuss several conditional precision estimates based on classical test theory and item response theory, and provide open-source statistical software included in the software package JASP that enables computation of these estimates. Using conditional precision estimates, decisions based on test scores are expected to show less bias than the common unconditional standard error of measurement.

Recent research shows that amortized variational inference (AVI) can be used to efficiently estimate high-dimensional latent variable models on large datasets. However, its use has remained limited to item response theory (IRT), and generalizing the approach to discrete latent variable models is not straightforward. We propose two ways to deal with this problem. In an initial simulation, we verify that these approaches can be used to estimate simple discrete latent variable models, such as latent class analysis and the generalized deterministic inputs, noisy and gate model. In these cases, AVI provides accurate parameter estimates, although the computational advantage over marginal maximum likelihood (MML) and standard variational inference (VI) is limited. We then apply the same approach to estimate mixture IRT models. In this case, AVI is computationally faster than MML estimation and standard VI. To demonstrate the practical applicability of our AVI approach, we use it to fit a seven-dimensional mixture IRT model to a narcissism inventory. Whereas quadrature-based methods cannot feasibly estimate models of this dimensionality, the efficient AVI approach even allows for computation of bootstrapped standard errors. We provide our code, along with an easy-to-use tool for fitting these models to new datasets.

In various research settings, responses to questionnaire items are continuously distributed and bounded from below and above. Suitable item response theory (IRT) models are available for the response data; however, implementations of these models differ significantly in their estimation method, availability, and user-friendliness. These differences hamper the application of such models in general, and model fit comparison in particular. Therefore, in this paper, BoundIRT is presented, which implements four popular bounded IRT models from the literature in the R statistical computing environment. The package provides various facilities for model estimation and model fit assessment. In addition, once a suitable model has been established for a given dataset, the factor score regression facilities can be used to conduct regression analyses of the latent variable in the model with respect to other variables.

When using tests to assess individuals, precision of individual test scores is of great importance. Although it is generally known that different test scores are measured with varying precision, traditionally, measurement precision is quantified using a single value known as the standard error of measurement (SEM). In the practice of testing, the SEM is used as a one-size-fits-all measure for each test score. This practice emphasizes the need for a score-related precision estimate that shows which scores are precise and which scores lack precision. We discuss several score-related precision estimates based on classical test theory and item response theory, and provide open-source statistical software included in JASP that enables computation of these estimates. Using score-related precision estimates, decisions based on test scores are expected to show less bias than the common score-unrelated SEM.

Theories of reading state that the development of word reading fluency is dependent on a shift from a slow letter-by-letter decoding process to the faster parallel processing of the letters in a word. We examined developmental changes in these reading processes based on the accuracy and speed of the reading of isolated words. We also investigated to what extent changes in these within-word reading processes account for individual differences in word reading fluency, conceived as the reading of a series of words. Data from de Jong (2011) were analyzed. Participants were 70 Grade 1 (52.9% boys), 73 Grade 2 (53.4% boys) and 127 Grade 4 Dutch-speaking children (47.2% boys) learning to read in Dutch. Children read sets of one-syllable and two-syllable words. Reading accuracy and reaction time per word were registered. Response mixture modeling was used to separate slow and fast reading times at the word level. Also, measures of word reading fluency and serial rapid naming were included. The proportion of words read in parallel across grades increased for both one- and two-syllable words. Unexpectedly, within grades a clear separation was observed into groups of children reading most words through decoding or in parallel. These changes in reading processes only partly captured differences in word reading fluency development. Independent contributions of the speeding up of each within-word process and the growing importance of serial rapid naming were found. These results suggest the need for a further specification and refinement of theories of reading development.

Neural networks like variational autoencoders have been proposed as a statistical tool to fit item factor models to data. Advantages are that high dimensional models can be estimated more efficiently as compared to conventional approaches. In this study, we demonstrate advantages of a specific autoencoder as a tool for amortized joint maximum likelihood estimation of item factor models. Contrary to contemporary joint maximum likelihood estimation and marginal maximum likelihood estimation, no additional parameter constraints are necessary to ensure standard asymptotic theory to apply. In a simulation study, the performance of the autoencoder is compared to constrained joint maximum likelihood and various forms of marginal maximum likelihood under different distributions for the factor scores. Results show that the amortized joint maximum likelihood estimates of the factors scores are overall less biased as compared to the other approaches. We illustrate the use of the autoencoder in two real data examples.

Simulation studies are commonly used to improve understanding of psychometric models. For many common models, an essential feature of the simulation is the relative (to variation in person parameters) variation in item difficulties. A common practice has been to generate both item difficulty parameters and person parameters directly from a standard normal distribution or to otherwise stipulate distributions for both parameters at the outset of the simulation. This approach implicitly assumes that these distributions can adequately represent empirical data—an assumption that warrants careful examination. In this paper, leveraging 73 datasets from the Item Response Warehouse (Domingue et al., 2023), we examine the variability of item difficulty distributions in real-world datasets and investigate how this variation influences estimation and simulation. We identify key distributional characteristics (e.g., variance and skewness) and propose a new method for simulating realistic item difficulties based on empirical data. This method enhances the realism and applicability of simulation results, making them more reflective of real-world measurement conditions and improving the robustness of psychometric model evaluation

In experiments requiring extreme darkness, such as experiments probing the limits of human vision, assessment of the background photon flux is essential. However, direct measurement thereof with standard single-photon detectors is challenged by dark counts and their fluctuations. Here we report an experiment and detailed statistical analysis of a direct measurement of darkness in a dedicated dark chamber suitable for human vision experiments, only using a standard single-photon detector and a mechanical shutter. From a Bayesian analysis of 616 h of data, we find substantial to decisive evidence for absolute darkness (depending on the choice of prior distribution) based on the Savage-Dickey ratio and a light level <0.039 cnt/s (posterior 0.95 highest density interval).

Background and aims:Problematic smartphone use (PSU) has gained attention, but its definition remains debated. This study aimed to develop and validate a new scale measuring PSU-the Smartphone Use Problems Identification Questionnaire (SUPIQ). Methods:Using two separate samples, a university community sample (N = 292) and a general population sample (N = 397), we investigated: (1) the construct validity of the SUPIQ through exploratory and confirmatory factor analyses; (2) the convergent validity of the SUPIQ with correlation analyses and the visualized partial correlation network analyses; (3) the psychometric equivalence of the SUPIQ across two samples through multigroup confirmatory factor analyses; (4) the explanatory power of the SUPIQ over the Short Version of Smartphone Addiction Scale (SAS-SV) with hierarchical multiple regressions. Results:The results showed that the SUPIQ included 26 items and 7 factors (i.e., Craving, Coping, Habitual Use, Social Conflicts, Risky Use, Withdrawal, and Tolerance), with good construct and convergent validity. The configural measurement invariance across samples was established. The SUPIQ also explained more variances in mental health problems than the SAS-SV. Discussion and conclusions:The findings suggest that the SUPIQ shows promise as a tool for assessing PSU. Further research is needed to enhance and refine the SUPIQ as well as to investigate its clinical utility.

Measurement invariance is an assumption underlying the regression of a latent variable on a background variable. It requires the measurement model parameters of the latent variable to be equal across the levels of the background variable. Item-specific violations of this assumption are referred to as differential item functioning and are ideally substantively explainable to warrant theoretically valid and meaningful results. Past research has focused on developing statistical approaches to explain differential item functioning effects in terms of item- or person-specific covariates. In this study, we propose a modeling approach that can be used to test if differences in item response times can be used to statistically explain differential item functioning. To this end, we operationalize a latent response process factor and test if item-specific group differences on this factor can account for the observed differences in item scores. We investigate the properties of the model in a simulation study, and we apply the model to a real data set.

Assessing measurement invariance is an important step in establishing a meaningful comparison of measurements of a latent construct across individuals or groups. Most recently, moderated nonlinear factor analysis (MNLFA) has been proposed as a method to assess measurement invariance. In MNLFA models, measurement invariance is examined in a single-group confirmatory factor analysis model by means of parameter moderation. The advantages of MNLFA over other methods is that it (a) accommodates the assessment of measurement invariance across multiple continuous and categorical background variables and (b) accounts for heteroskedasticity by allowing the factor and residual variances to differ as a function of the background variables. In this article, we aim to make MNLFA more accessible to researchers without access to commercial structural equation modeling software by demonstrating how this method can be applied with the open-source R package OpenMx. (PsycInfo Database Record (c) 2024 APA, all rights reserved).