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.

This paper generalizes the p* class of models for social network data to predict individual-level attributes from network ties. The p* model for social networks permits the modeling of social relationships in terms of particular local relational or network configurations. In this paper we present methods for modeling attribute measures in terms of network ties, and so construct p* models for the patterns of social influence within a network. Attribute variables are included in a directed dependence graph and the Hammersley-Clifford theorem is employed to derive probability models whose parameters can be estimated using maximum pseudo-likelihood. The models are compared to existing network effects models. They can be interpreted in terms of public or private social influence phenomena within groups. The models are illustrated by an empirical example involving a training course, with trainees' reactions to aspects of the course found to relate to those of their network partners.

The increasing use of diary methods calls for the development of appropriate statistical methods. For the resulting panel data, latent Markov models can be used to model both individual differences and temporal dynamics. The computational burden associated with these models can be overcome by exploiting the conditional independence relations implied by the model. This is done by associating a probabilistic model with a directed acyclic graph, and applying transformations to the graph. The structure of the transformed graph provides a factorization of the joint probability function of the manifest and latent variables, which is the basis of a modified and more efficient E-step of the EM algorithm. The usefulness of the approach is illustrated by estimating a latent Markov model involving a large number of measurement occasions and, subsequently, a hierarchical extension of the latent Markov model that allows for transitions at different levels. Furthermore, logistic regression techniques are used to incorporate restrictions on the conditional probabilities and to account for the effect of covariates. Throughout, models are illustrated with an experience sampling methodology study on the course of emotions among anorectic patients.

Log-multiplicative association (LMA) models, which are special cases of log-linear models, have interpretations in terms of latent continuous variables. Two theoretical derivations of LMA models based on item response theory (IRT) arguments are presented. First, we show that Anderson and colleagues (Anderson & Vermunt, 2000; Anderson & Böckenholt, 2000; Anderson, 2002), who derived LMA models from statistical graphical models, made the equivalent assumptions as Holland (1990) when deriving models for the manifest probabilities of response patterns based on an IRT approach. We also present a second derivation of LMA models where item response functions are specified as functions of rest-scores. These various connections provide insights into the behavior of LMA models as item response models and point out philosophical issues with the use of LMA models as item response models. We show that even for short tests, LMA and standard IRT models yield very similar to nearly identical results when data arise from standard IRT models. Log-multiplicative association models can be used as item response models and do not require numerical integration for estimation.

When modeling the relationship between two nominal categorical variables, it is often desirable to include covariates to understand how individuals differ in their response behavior. Typically, however, not all the relevant covariates are available, with the result that the measured variables cannot fully account for the associations between the nominal variables. Under the assumption that the observed and unobserved variables follow a homogeneous conditional Gaussian distribution, this paper proposes RC(M) regression models to decompose the residual associations between the polytomous variables. Based on Goodman's (1979, 1985)RC(M) association model, a distinctive feature of RC(M) regression models is that they facilitate the joint estimation of effects due to manifest and omitted (continuous) variables without requiring numerical integration. The RC(M) regression models are illustrated using data from the High School and Beyond study (Tatsuoka & Lohnes, 1988).

Birnbaum and Quispe-Torreblanca (2018) evaluated a set of six models developed under true-and-error theory against data in which people made choices in repeated gambles. They concluded the three models based on expected utility theory were inadequate accounts of the behavioral data, and argued in favor of the simplest of the remaining three more general models. To reach these conclusions, they used non-Bayesian statistical methods: frequentist point estimation of parameters, bootstrapped confidence intervals of parameters, and null hypothesis significance testing of models. We address the same research goals, based on the same models and the same data, using Bayesian methods. We implement the models as graphical models in JAGS to allow for computational Bayesian analysis. Our results are based on posterior distribution of parameters, posterior predictive checks of descriptive adequacy, and Bayes factors for model comparison. We compare the Bayesian results with those of Birnbaum and Quispe-Torreblanca (2018). We conclude that, while the very general conclusions of the two approaches agree, the Bayesian approach offers better detailed answers, especially for the key question of the evidence the data provide for and against the competing models. Finally, we discuss the conceptual and practical advantages of using Bayesian methods in judgment and decision making research highlighted by this case study.

We demonstrate the usefulness of cognitive models for combining human estimates of probabilities in two experiments. The first experiment involves people’s estimates of probabilities for general knowledge questions such as “What percentage of the world’s population speaks English as a first language?” The second experiment involves people’s estimates of probabilities in football (soccer) games, such as “What is the probability a team leading 1–0 at half time will win the game?”, with ground truths based on analysis of large corpus of games played in the past decade. In both experiments, we collect people’s probability estimates, and develop a cognitive model of the estimation process, including assumptions about the calibration of probabilities and individual differences. We show that the cognitive model approach outperforms standard statistical aggregation methods like the mean and the median for both experiments and, unlike most previous related work, is able to make good predictions in a fully unsupervised setting. We also show that the parameters inferred as part of the cognitive modeling, involving calibration and expertise, provide useful measures of the cognitive characteristics of individuals. We argue that the cognitive approach has the advantage of aggregating over latent human knowledge rather than observed estimates, and emphasize that it can be applied in predictive settings where answers are not yet available.

Conditional mean risk sharing appears to be effective to distribute total losses amongst participants within an insurance pool. This paper develops analytical results for this allocation rule in the individual risk model with dependence induced by the respective position within a graph. Precisely, losses are modelled by zero-augmented random variables whose joint occurrence distribution and individual claim amount distributions are based on network structures and can be characterised by graphical models. The Ising model is adopted for occurrences and loss amounts obey decomposable graphical models that are specific to each participant. Two graphical structures are thus used: the first one to describe the contagion amongst member units within the insurance pool and the second one to model the spread of losses inside each participating unit. The proposed individual risk model is typically useful for modelling operational risks, catastrophic risks or cybersecurity risks.

We present an application of statistical graphical models to simulate economic variables for the purpose of risk calculations over long time horizons. We show that this approach is relatively easy to implement, and argue that it is appealing because of the transparent yet flexible means of achieving dimension reduction when many variables must be modelled. Using the United Kingdom data as an example, we demonstrate the development of an economic scenario generator that can be used by life insurance companies and pension funds.We compare different algorithms to select a graphical model, based on p-values, AIC, BIC and deviance. We find the economic scenario generator to yield reasonable results and relatively stable structures in our example, suggesting that it would be beneficial for actuaries to include graphical models in their toolkit.