It is argued that the generalizability theory interpretation of coefficient alpha is important. In this interpretation, alpha is a slightly biased but consistent estimate for the coefficient of generalizability in a subjects x items design where both subjects and items are randomly sampled. This interpretation is based on the “domain sampling” true scores. It is argued that these true scores have a more solid empirical basis than the true scores of Lord and Novick (1968), which are based on “stochastic subjects” (Holland, 1990), while only a single observation is available for each within-subject distribution. Therefore, the generalizability interpretation of coefficient alpha is to be preferred, unless the true scores can be defined by a latent variable model that has undisputed empirical validity for the test and that is sufficiently restrictive to entail a consistent estimate of the reliability—as, for example, McDonald’s omega. If this model implies that the items are essentially tau-equivalent, both the generalizability and the reliability interpretation of alpha can be defensible.

Response process data from computer-based problem-solving items describe respondents’ problem-solving processes as sequences of actions. Such data provide a valuable source for understanding respondents’ problem-solving behaviors. Recently, data-driven feature extraction methods have been developed to compress the information in unstructured process data into relatively low-dimensional features. Although the extracted features can be used as covariates in regression or other models to understand respondents’ response behaviors, the results are often not easy to interpret since the relationship between the extracted features, and the original response process is often not explicitly defined. In this paper, we propose a statistical model for describing response processes and how they vary across respondents. The proposed model assumes a response process follows a hidden Markov model given the respondent’s latent traits. The structure of hidden Markov models resembles problem-solving processes, with the hidden states interpreted as problem-solving subtasks or stages. Incorporating the latent traits in hidden Markov models enables us to characterize the heterogeneity of response processes across respondents in a parsimonious and interpretable way. We demonstrate the performance of the proposed model through simulation experiments and case studies of PISA process data.

Maximum likelihood estimation is computationally infeasible for latent variable models involving multivariate categorical responses, in particular for the LISCOMP model. A three-stage generalized least squares approach introduced by Muthén (1983, 1984) can experience problems of instability, bias, non-convergence, and non-positive definiteness of weight matrices in situations of low prevalence, small sample size and large numbers of observed indicator variables. We propose a quadratic estimating equations approach that only requires specification of the first two moments. By performing simultaneous estimation of parameters, this method does not encounter the problems mentioned above and experiences gains in efficiency. Methods are compared through a numerical study and an application to a study of life-events and neurotic illness.

The purpose of this paper is to introduce a new method for fitting item response theory models with the latent population distribution estimated from the data using splines. A spline-based density estimation system provides a flexible alternative to existing procedures that use a normal distribution, or a different functional form, for the population distribution. A simulation study shows that the new procedure is feasible in practice, and that when the latent distribution is not well approximated as normal, two-parameter logistic (2PL) item parameter estimates and expected a posteriori scores (EAPs) can be improved over what they would be with the normal model. An example with real data compares the new method and the extant empirical histogram approach.

The frequencies of m independent p-way contingency tables are analyzed by a model that assumes that the ordinal categorical data in each of m groups are generated from a latent continuous multivariate normal distribution. The parameters of these multivariate distributions and of the relations between the ordinal and latent variables are estimated by maximum likelihood. Goodness-of-fit statistics based on the likelihood ratio criterion and the Pearsonian chisquare are provided to test the hypothesis that the proposed model is correct, that is, it fits the observed sample data. Hypotheses on the invariance of means, variances, and polychoric correlations of the latent variables across populations are tested by Wald statistics. The method is illustrated on an example involving data on three five-point ordinal scales obtained from male and female samples.

A version of the discrete proportional hazards model is developed for psychometrical applications. In such applications, a primary covariate that influences failure times is a latent variable representing a psychological construct. The Metropolis-Hastings algorithm is studied as a method for performing marginal likelihood inference on the item parameters. The model is illustrated with a real data example that relates the age at which teenagers first experience various substances to the latent ability to avoid the onset of such behaviors.

We consider a bivariate normal distribution with linear correlation ρ whose random components are discretized according to two assigned sets of thresholds. On the resulting bivariate ordinal random variable, one can compute Goodman and Kruskal’s gamma coefficient,γ which is a common measure of ordinal association. Given the known analytical monotonic relationship between Pearson’s ρ and Kendall’s rank correlation τ for the bivariate normal distribution, and since in the continuous case, Kendall’s τ coincides with Goodman and Kruskal’s γ, the change of this association measure before and after discretization is worth studying. We consider several experimental settings obtained by varying the two sets of thresholds, or, equivalently, the marginal distributions of the final ordinal variables. This study, confirming previous findings, shows how the gamma coefficient is always larger in absolute value than Kendall’s rank correlation; this discrepancy lessens when the number of categories increases or, given the same number of categories, when using equally probable categories. Based on these results, a proposal is suggested to build a bivariate ordinal variable with assigned margins and Goodman and Kruskal’s γ by ordinalizing a bivariate normal distribution. Illustrative examples employing artificial and real data are provided.

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.

The most widely-used computer programs for structural equation models analysis are the LISREL series of Jöreskog and Sörbom. The only types of constraints which may be made directly are fixing parameters at a constant value and constraining parameters to be equal. Rindskopf (1983) showed how these simple properties could be used to represent models with more complicated constraints, namely inequality constraints on unique variances. In this paper, two new concepts are introduced which enable a much wider variety of constraints to be made. The concepts, “phantom” and “imaginary” latent variables, allow fairly general equality and inequality constraints on factor loadings and structural model coefficients.

The sum score on a psychological test is, and should continue to be, a tool central in psychometric practice. This position runs counter to several psychometricians’ belief that the sum score represents a pre-scientific conception that must be abandoned from psychometrics in favor of latent variables. First, we reiterate that the sum score stochastically orders the latent variable in a wide variety of much-used item response models. In fact, item response theory provides a mathematically based justification for the ordinal use of the sum score. Second, because discussions about the sum score often involve its reliability and estimation methods as well, we show that, based on very general assumptions, classical test theory provides a family of lower bounds several of which are close to the true reliability under reasonable conditions. Finally, we argue that eventually sum scores derive their value from the degree to which they enable predicting practically relevant events and behaviors. None of our discussion is meant to discredit modern measurement models; they have their own merits unattainable for classical test theory, but the latter model provides impressive contributions to psychometrics based on very few assumptions that seem to have become obscured in the past few decades. Their generality and practical usefulness add to the accomplishments of more recent approaches.

In this rejoinder to McNeish (2024) and Mislevy (2024), who both responded to our focus article on the merits of the simple sum score (Sijtsma et al., 2024), we address several issues. Psychometrics education and in particular psychometricians’ outreach may help researchers to use IRT models as a precursor for the responsible use of the latent variable score and the sum score. Different methods used for test and questionnaire construction often do not produce highly different results, and when they do, this may be due to an unarticulated attribute theory generating noisy data. The sum score and transformations thereof, such as normalized test scores and percentiles, may help test practitioners and their clients to better communicate results. Latent variables prove important in more advanced applications such as equating and adaptive testing where they serve as technical tools rather than communication devices. Decisions based on test results are often binary or use a rather coarse ordering of scale levels, hence, do not require a high level of granularity (but nevertheless need to be precise). A gap exists between psychology and psychometrics which is growing deeper and wider, and that needs to be bridged. Psychology and psychometrics must work together to attain this goal.

We investigate some aspects of the problem of the estimation of birth distributions (BDs) in multi-type Galton–Watson trees (MGWs) with unobserved types. More precisely, we consider two-type MGWs called spinal-structured trees. This kind of tree is characterized by a spine of special individuals whose BD $\nu$ is different from the other individuals in the tree (called normal, and whose BD is denoted by $\mu$). In this work, we show that even in such a very structured two-type population, our ability to distinguish the two types and estimate $\mu$ and $\nu$ is constrained by a trade-off between the growth-rate of the population and the similarity of $\mu$ and $\nu$. Indeed, if the growth-rate is too large, large deviation events are likely to be observed in the sampling of the normal individuals, preventing us from distinguishing them from special ones. Roughly speaking, our approach succeeds if $r\lt \mathfrak{D}(\mu,\nu)$, where r is the exponential growth-rate of the population and $\mathfrak{D}$ is a divergence measuring the dissimilarity between $\mu$ and $\nu$.

We present a method for estimating the ideology of political YouTube videos. The subfield of estimating ideology as a latent variable has often focused on traditional actors such as legislators, while more recent work has used social media data to estimate the ideology of ordinary users, political elites, and media sources. We build on this work to estimate the ideology of a political YouTube video. First, we start with a matrix of political Reddit posts linking to YouTube videos and apply correspondence analysis to place those videos in an ideological space. Second, we train a language model with those estimated ideologies as training labels, enabling us to estimate the ideologies of videos not posted on Reddit. These predicted ideologies are then validated against human labels. We demonstrate the utility of this method by applying it to the watch histories of survey respondents to evaluate the prevalence of echo chambers on YouTube in addition to the association between video ideology and viewer engagement. Our approach gives video-level scores based only on supplied text metadata, is scalable, and can be easily adjusted to account for changes in the ideological landscape.

The study of coup-proofing holds significant importance in political science as it offers insights into critical topics such as military coups, authoritarian governance, and international conflicts. However, due to the multifaceted nature of coup-proofing and empirical inconsistencies with existing indicators, there is a need for a more profound understanding and a new measurement methodology. We propose a new measure of the extent of coup-proofing, utilizing a Bayesian item response theory. We estimate the extent of coup-proofing using a sample of 76 countries between 1965 and 2005 and theoretically relevant observed indicators. The findings from the estimation demonstrate that the extent of coup-proofing varies across regime type, country, and time. Furthermore, we verify the construct validity of our measurement.

In the present study, we evaluated the effect of process-induced common bean hardness on structural properties of in vivo generated boluses and the consequences for in vitro starch digestion. Initially, the impact of human mastication on the particle size distribution (PSD) of oral boluses from common beans with different process-induced hardness levels was investigated through a mastication study. Then the effect of structural properties of selected boluses on in vitro starch digestion kinetics was assessed. For a particular process-induced hardness level, oral boluses had similar PSD despite differences in masticatory parameters between participants of the mastication study. At different hardness levels, a clear effect of processing (P<0·0001) was observed. However, the effect of mastication behaviour (P=0·1141) was not significant. Two distinctive fractions were present in all boluses. The first one was a cotyledon-rich fraction consisting of majorly small particles (40–125 µm), which could be described as individual cells based on microscopic observations. This fraction increased with a decrease in process-induced hardness. The second fraction (>2000 µm) mostly contained seed coat material and did not change based on hardness levels. The in vitro starch digestion kinetics of common bean boluses was only affected by process-induced hardness. After kinetic modelling, significant differences were observed between the reaction rate constant of boluses generated from the hardest beans and those obtained from softer ones. Overall this work demonstrated that the in vitro nutritional functionality of common beans is affected to a greater extent by structural properties induced by processing than by mechanical degradation in the mouth.