Typical Bayesian methods for models with latent variables (or random effects) involve directly sampling the latent variables along with the model parameters. In high-level software code for model definitions (using, e.g., BUGS, JAGS, Stan), the likelihood is therefore specified as conditional on the latent variables. This can lead researchers to perform model comparisons via conditional likelihoods, where the latent variables are considered model parameters. In other settings, however, typical model comparisons involve marginal likelihoods where the latent variables are integrated out. This distinction is often overlooked despite the fact that it can have a large impact on the comparisons of interest. In this paper, we clarify and illustrate these issues, focusing on the comparison of conditional and marginal Deviance Information Criteria (DICs) and Watanabe–Akaike Information Criteria (WAICs) in psychometric modeling. The conditional/marginal distinction corresponds to whether the model should be predictive for the clusters that are in the data or for new clusters (where “clusters” typically correspond to higher-level units like people or schools). Correspondingly, we show that marginal WAIC corresponds to leave-one-cluster out cross-validation, whereas conditional WAIC corresponds to leave-one-unit out. These results lead to recommendations on the general application of the criteria to models with latent variables.

Ignorable likelihood (IL) approaches are often used to handle missing data when estimating a multivariate model, such as a structural equation model. In this case, the likelihood is based on all available data, and no model is specified for the missing data mechanism. Inference proceeds via maximum likelihood or Bayesian methods, including multiple imputation without auxiliary variables. Such IL approaches are valid under a missing at random (MAR) assumption. Rabe-Hesketh and Skrondal (Ignoring non-ignorable missingness. Presidential Address at the International Meeting of the Psychometric Society, Beijing, China, 2015; Psychometrika, 2023) consider a violation of MAR where a variable A can affect missingness of another variable B also when A is not observed. They show that this case can be handled by discarding more data before proceeding with IL approaches. This data-deletion approach is similar to the sequential estimation of Mohan et al. (in: Advances in neural information processing systems, 2013) based on their ordered factorization theorem but is preferable for parametric models. Which kind of data-deletion or ordered factorization to employ depends on the nature of the MAR violation. In this article, we therefore propose two diagnostic tests, a likelihood-ratio test for a heteroscedastic regression model and a kernel conditional independence test. We also develop a test-based estimator that first uses diagnostic tests to determine which MAR violation appears to be present and then proceeds with the corresponding data-deletion estimator. Simulations show that the test-based estimator outperforms IL when the missing data problem is severe and performs similarly otherwise.

A first-order autoregressive growth model is proposed for longitudinal binary item analysis where responses to the same items are conditionally dependent across time given the latent traits. Specifically, the item response probability for a given item at a given time depends on the latent trait as well as the response to the same item at the previous time, or the lagged response. An initial conditions problem arises because there is no lagged response at the initial time period. We handle this problem by adapting solutions proposed for dynamic models in panel data econometrics. Asymptotic and finite sample power for the autoregressive parameters are investigated. The consequences of ignoring local dependence and the initial conditions problem are also examined for data simulated from a first-order autoregressive growth model. The proposed methods are applied to longitudinal data on Korean students’ self-esteem.

We propose a dyadic Item Response Theory (dIRT) model for measuring interactions of pairs of individuals when the responses to items represent the actions (or behaviors, perceptions, etc.) of each individual (actor) made within the context of a dyad formed with another individual (partner). Examples of its use include the assessment of collaborative problem solving or the evaluation of intra-team dynamics. The dIRT model generalizes both Item Response Theory models for measurement and the Social Relations Model for dyadic data. The responses of an actor when paired with a partner are modeled as a function of not only the actor’s inclination to act and the partner’s tendency to elicit that action, but also the unique relationship of the pair, represented by two directional, possibly correlated, interaction latent variables. Generalizations are discussed, such as accommodating triads or larger groups. Estimation is performed using Markov-chain Monte Carlo implemented in Stan, making it straightforward to extend the dIRT model in various ways. Specifically, we show how the basic dIRT model can be extended to accommodate latent regressions, multilevel settings with cluster-level random effects, as well as joint modeling of dyadic data and a distal outcome. A simulation study demonstrates that estimation performs well. We apply our proposed approach to speed-dating data and find new evidence of pairwise interactions between participants, describing a mutual attraction that is inadequately characterized by individual properties alone.

Group-level variance estimates of zero often arise when fitting multilevel or hierarchical linear models, especially when the number of groups is small. For situations where zero variances are implausible a priori, we propose a maximum penalized likelihood approach to avoid such boundary estimates. This approach is equivalent to estimating variance parameters by their posterior mode, given a weakly informative prior distribution. By choosing the penalty from the log-gamma family with shape parameter greater than 1, we ensure that the estimated variance will be positive. We suggest a default log-gamma(2,λ) penalty with λ→0, which ensures that the maximum penalized likelihood estimate is approximately one standard error from zero when the maximum likelihood estimate is zero, thus remaining consistent with the data while being nondegenerate. We also show that the maximum penalized likelihood estimator with this default penalty is a good approximation to the posterior median obtained under a noninformative prior.

Our default method provides better estimates of model parameters and standard errors than the maximum likelihood or the restricted maximum likelihood estimators. The log-gamma family can also be used to convey substantive prior information. In either case—pure penalization or prior information—our recommended procedure gives nondegenerate estimates and in the limit coincides with maximum likelihood as the number of groups increases.

We propose a unifying framework for multilevel modeling of polytomous data and rankings, accommodating dependence induced by factor and/or random coefficient structures at different levels. The framework subsumes a wide range of models proposed in disparate methodological literatures. Partial and tied rankings, alternative specific explanatory variables and alternative sets varying across units are handled. The problem of identification is addressed. We develop an estimation and prediction methodology for the model framework which is implemented in the generally available gllamm software. The methodology is applied to party choice and rankings from the 1987–1992 panel of the British Election Study. Three levels are considered: elections, voters and constituencies.

We propose a class of confirmatory factor analysis models that include multiple sets of secondary or specific factors and a general factor. The general factor accounts for the common variance among manifest variables, whereas multiple sets of secondary factors account for the remaining source-specific dependency among subsets of manifest variables. A special case of the model is further proposed which constrains the specific factor loadings to be proportional to the general factor loadings. This proportional model substantially reduces the number of model parameters while preserving the essential structure of the general model. Furthermore, the proportional model allows for the interpretation of latent variables as the expected values of the observed manifest variables, decomposition of the variances, and the inclusion of interactions, similar to generalizability theory. We provide two applications to illustrate the utility of the proposed class of models.

An additive multilevel item structure (AMIS) model with random residuals is proposed. The model includes multilevel latent regressions of item discrimination and item difficulty parameters on covariates at both item and item category levels with random residuals at both levels. The AMIS model is useful for explanation purposes and also for prediction purposes as in an item generation context. The parameters can be estimated with an alternating imputation posterior algorithm that makes use of adaptive quadrature, and the performance of this algorithm is evaluated in a simulation study.

In psychometrics, the canonical use of conditional likelihoods is for the Rasch model in measurement. Whilst not disputing the utility of conditional likelihoods in measurement, we examine a broader class of problems in psychometrics that can be addressed via conditional likelihoods. Specifically, we consider cluster-level endogeneity where the standard assumption that observed explanatory variables are independent from latent variables is violated. Here, “cluster” refers to the entity characterized by latent variables or random effects, such as individuals in measurement models or schools in multilevel models and “unit” refers to the elementary entity such as an item in measurement. Cluster-level endogeneity problems can arise in a number of settings, including unobserved confounding of causal effects, measurement error, retrospective sampling, informative cluster sizes, missing data, and heteroskedasticity. Severely inconsistent estimation can result if these challenges are ignored.

Composite links and exploded likelihoods are powerful yet simple tools for specifying a wide range of latent variable models. Applications considered include survival or duration models, models for rankings, small area estimation with census information, models for ordinal responses, item response models with guessing, randomized response models, unfolding models, latent class models with random effects, multilevel latent class models, models with log-normal latent variables, and zero-inflated Poisson models with random effects. Some of the ideas are illustrated by estimating an unfolding model for attitudes to female work participation.

The classical missing at random (MAR) assumption, as defined by Rubin (Biometrika 63:581–592, 1976), is often not required for valid inference ignoring the missingness process. Neither are other assumptions sometimes believed to be necessary that result from misunderstandings of MAR. We discuss three strategies that allow us to use standard estimators (i.e., ignore missingness) in cases where missingness is usually considered to be non-ignorable: (1) conditioning on variables, (2) discarding more data, and (3) being protective of parameters.

A unifying framework for generalized multilevel structural equation modeling is introduced. The models in the framework, called generalized linear latent and mixed models (GLLAMM), combine features of generalized linear mixed models (GLMM) and structural equation models (SEM) and consist of a response model and a structural model for the latent variables. The response model generalizes GLMMs to incorporate factor structures in addition to random intercepts and coefficients. As in GLMMs, the data can have an arbitrary number of levels and can be highly unbalanced with different numbers of lower-level units in the higher-level units and missing data. A wide range of response processes can be modeled including ordered and unordered categorical responses, counts, and responses of mixed types. The structural model is similar to the structural part of a SEM except that it may include latent and observed variables varying at different levels. For example, unit-level latent variables (factors or random coefficients) can be regressed on cluster-level latent variables. Special cases of this framework are explored and data from the British Social Attitudes Survey are used for illustration. Maximum likelihood estimation and empirical Bayes latent score prediction within the GLLAMM framework can be performed using adaptive quadrature in gllamm, a freely available program running in Stata.

We present a variational maximization–maximization algorithm for approximate maximum likelihood estimation of generalized linear mixed models with crossed random effects (e.g., item response models with random items, random raters, or random occasion-specific effects). The method is based on a factorized variational approximation of the latent variable distribution given observed variables, which creates a lower bound of the log marginal likelihood. The lower bound is maximized with respect to the factorized distributions as well as model parameters. With the proposed algorithm, a high-dimensional intractable integration is translated into a two-dimensional integration problem. We incorporate an adaptive Gauss–Hermite quadrature method in conjunction with the variational method in order to increase computational efficiency. Numerical studies show that under the small sample size conditions that are considered the proposed algorithm outperforms the Laplace approximation.

Background. Prevalence of childhood anxiety disorders at specific ages and genetic etiological influences on anxiety disorders in young children have been little studied. The present study reports prevalence estimates in a community sample of 6-year-old twins, and patterns of genetic and environmental influences on these early-onset anxiety disorders.

Method. Using a two-phase design 4662 twin-pairs were sampled and 854 pairs were assessed in the second phase by maternal-informant diagnostic interview using DSM-IV criteria.

Results. The most common conditions were separation anxiety disorder (SAD) [2·8%, 95% confidence interval (CI) 2·1–3·8, for current disorder] and specific phobia (10·8%, 95% CI 8·4–13·6, for current disorder). Behavioral genetic modeling was feasible for these two conditions, applied to two phenotypes: symptom syndrome (regardless of impairment) and the narrower one of diagnostic status (symptom syndrome with associated impairment). The heritability estimate for SAD diagnostic status was high, 73%, with remaining variance attributed to non-shared environment. The heritability estimates for specific phobia were also high, 80% for the symptom syndrome and 60% for diagnostic status, with remaining variance attributed in both cases to non-shared environment.

Conclusions. Compared with previous epidemiological surveys of children and adolescents in wide age-bands, the current estimates suggest that rates of anxiety disorders assessed in young childhood are generally at least as high and perhaps higher compared with those found in older children. The heritability estimates suggest that the genetic effects on these early-onset anxiety disorders are substantial and more significant than environmental effects, whether shared or non-shared.

The aim of this study was to determine if there are differences in cognitive flexibility in anorexia nervosa and bulimia nervosa. Fifty-three patients with an eating disorder (34 with anorexia nervosa and 19 with bulimia nervosa) and 35 healthy controls participated in the study. A battery of neuropsychological tests for cognitive flexibility was used, including Trail Making B, the Brixton Test, Verbal Fluency, the Haptic Illusion Test, a cognitive shifting task (CatBat) and a picture set test. Using exploratory factor analysis, four factors were obtained: 1: Simple Alternation; 2: Mental Flexibility; 3: Perseveration; and 4: Perceptual Shift. Patients with anorexia nervosa had abnormal scores on Factors 1 and 4. Patients with bulimia nervosa showed a different pattern, with significant impairments in Factors 2 and 4. These findings suggest that differential neuropsychological disturbance in the domain of mental flexibility/rigidity may underlie the spectrum of eating disorders. (JINS, 2004, 10, 513–520.)

Work on implicit memory in normal subjects has demonstrated the influence of stimulus modality on the retrieval of semantic information. The present study examined the effects of auditory and visual semantic priming on the recognition of visual words using a lexical decision task. Performance was studied in a group of 20 patients with DSM–IV schizophrenia and 26 normal volunteers of similar age and sex. There were two versions of the task: ipsimodal, in which the word or nonword visual target followed 400 ms after the onset of a visual word prime which may or may not be semantically related to the target; and cross-modal, in which the visual target followed 400 ms after the onset of an auditory word prime. Both groups showed significant priming in both modality conditions, although the schizophrenia patients exhibited significantly greater priming in the cross-modal condition. Priming effects in the ipsimodal condition did not differ substantially between patients and controls. The priming effects in the two conditions correlated with each other in the schizophrenia patients only. The results suggest that priming may occur through amodal semantic representations. In schizophrenia, there appears to be increased cross-modal connectivity (reduced modality modularity and informational encapsulation) between lexical representations that could result in impaired language, particularly speech, processing. (JINS, 2002, 8, 884–892.)

As part of a UNICEF-sponsored Psychosocial Programme in Bosnia, data were collected from a representative sample of 339 children aged 9–14 years, their mothers, and their teachers in order to investigate risk and moderating factors in children's psychological reactions to war. Self-report data from children revealed high levels of post-traumatic stress symptoms and grief reactions, but normal levels of depression and anxiety. Mothers' self-reports also indicated high levels of post-traumatic stress reactions, but normal levels of depression and anxiety. Child distress was related to both their level of exposure and to maternal reactions. Structural equation modeling was used to quantify the relationships between these risk factors and child distress, and to examine putative pathways to account for the association between child and maternal health. Children's adjustment was associated significantly with both exposure (ϕ = ·37) and maternal mental health (ϕ = ·37). Modeling also revealed a significant distorting effect of mother's own mental health on behavioural ratings of her child (ψ = ·59). Although evidence exists for an association between maternal mental health and mother rating errors, there is also a substantive association between maternal mental health and children's adjustment following war.