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Multi‐species occupancy models for estimating the effects of environmental covariates on species occurrences while accounting for the effects of false‐negative errors in detection were developed more than 20 years ago. Only recently have these models been extended to include correlations in occurrence between species. Tobler et al. (2019) proposed two of these models wherein species occurrences are specified using a probit‐regression model of correlated multivariate binary outcomes. In one model, correlations in occurrence between species are formal parameters. In the other model, a factor‐analytic approximation of these correlations is used. After conducting extensive simulation studies to compare the performance of these models, Tobler et al. (2019) recommended the latter model in favour of the former owing to difficulties in fitting the former to simulated or real data. The same software (JAGS) was used to fit both models. Since the former model specifies the actual process used to generate species occurrences, we hypothesized that shortcomings in the software were responsible for the difficulties reported by Tobler et al. (2019). We therefore devised an efficient Markov chain Monte Carlo algorithm for fitting the data‐generating, multi‐species occupancy model using parameter‐expanded data augmentation. Using this algorithm, we conducted analyses of simulated data sets to re‐evaluate and compare the performance of the two multi‐species occupancy models. We also compared the results of fitting these models to a real dataset collected in camera‐trap surveys of mammalian species on the Tibetan Plateau. Our analyses of simulated data revealed that estimators of species occurrence, correlation and detection parameters had similar performance in terms of average bias, average root‐mean‐squared error and average coverage of 95% credible intervals regardless of whether the data‐generating model or its factor‐analytic approximation was used to analyse the data. However, our analyses also revealed the presence of systematic bias in the correlation estimates of both models, wherein strongly negative correlations were overestimated and strongly positive correlations were underestimated. Systematic bias was not evident in correlations estimated by fitting a multivariate probit regression model to latent species occurrences; therefore, the systematic bias in correlation estimates of the two occupancy models must have been produced by the failure of these models to estimate latent species occurrences accurately.

The study of human behaviour and in particular individual choices is of great interest in the field of environmental economics. Substantial attention has been paid to the way in which preferences vary across individuals, and there is a realisation that such differences are at least in part due to underlying attitudes and convictions. While this has been confirmed in empirical work, the methods typically employed are based on the arguably misguided use of responses to attitudinal questions as direct measures of underlying attitudes. As discussed in other literature, especially in transport research, this potentially leads to measurement error and endogeneity bias, and attitudes should rather be treated as latent variables. In this paper, we illustrate the use of such an Integrated Choice and Latent Variable model in the context of beach visitors’ willingness-to-pay for improvements in water quality. We show how a latent attitudinal variable, which we refer to as a pro-intervention attitude, helps explain both the responses from the stated choice exercise as well as answers to various rating questions related to respondent attitudes. The incorporation of the latent variable leads to important gains in model fit and substantially different willingness-to-pay patterns.

Measurement is fundamental to all research in psychology and should be accorded greater scrutiny than typically occurs. Among other claims, McNeish and Wolf (Thinking twice about sum scores. Behavior Research Methods , 52 , 2287-2305) argued that use of sum scores (a) implies that a highly constrained latent variable model underlies items comprising a scale, and (b) may misrepresent or bias relations with other criteria. The central claim by McNeish and Wolf that use of sum scores requires the assumption that a parallel test model underlies item responses is incorrect and without psychometric merit. Instead, if a set of items is unidimensional, estimators of reliability are available even if the factor model underlying the set of items does not have a highly constrained form. Thus, dimensionality of a set of items is the key issue, and whether strict constraints on parameter estimates do or do not hold dictate the appropriate way to estimate reliability. McNeish and Wolf also claimed that more precise forms of scoring, such as estimating factor scores, would be preferable to sum scores. We provide analytic bases for reliability estimation and then provide several demonstrations of reliability estimation and the relative advantages of sum scores and factor scores. We contend that several claims by McNeish and Wolf are questionable and that, as a result, multiple recommendations they made and conclusions they drew are incorrect. The upshot is that, once the dimensional structure of a set of items is verified, sum scores often have a solid psychometric basis and therefore are frequently quite adequate for psychological research.

We provide statistical guarantees for a family of variational approximations to Bayesian posterior distributions, called α-VB, which has close connections with variational approximations of tempered posteriors in the literature. The standard variational approximation is a special case of α-VB with α = 1. When α ∈ (0, 1], a novel class of variational inequalities are developed for linking the Bayes risk under the variational approximation to the objective function in the variational optimization problem, implying that maximizing the evidence lower bound in variational inference has the effect of minimizing the Bayes risk within the variational density family. Operating in a frequentist setup, the variational inequalities imply that point estimates constructed from the α-VB procedure converge at an optimal rate to the true parameter in a wide range of problems. We illustrate our general theory with a number of examples, including the mean-field variational approximation to (low)-highdimensional Bayesian linear regression with spike and slab priors, Gaussian mixture models and latent Dirichlet allocation.

The question of whether psychopathology constructs are discrete kinds or continuous dimensions represents an important issue in clinical psychology and psychiatry. The present paper reviews psychometric modelling approaches that can be used to investigate this question through the application of statistical models. The relation between constructs and indicator variables in models with categorical and continuous latent variables is discussed, as are techniques specifically designed to address the distinction between latent categories as opposed to continua (taxometrics). In addition, we examine latent variable models that allow latent structures to have both continuous and categorical characteristics, such as factor mixture models and grade-of-membership models. Finally, we discuss recent alternative approaches based on network analysis and dynamical systems theory, which entail that the structure of constructs may be continuous for some individuals but categorical for others. Our evaluation of the psychometric literature shows that the kinds–continua distinction is considerably more subtle than is often presupposed in research; in particular, the hypotheses of kinds and continua are not mutually exclusive or exhaustive. We discuss opportunities to go beyond current research on the issue by using dynamical systems models, intra-individual time series and experimental manipulations.

We propose a novel sparse tensor decomposition method, namely the tensor truncated power method, that incorporates variable selection in the estimation of decomposition components. The sparsity is achieved via an efficient truncation step embedded in the tensor power iteration. Our method applies to a broad family of high dimensional latent variable models, including high dimensional Gaussian mixtures and mixtures of sparse regressions. A thorough theoretical investigation is further conducted. In particular, we show that the final decomposition estimator is guaranteed to achieve a local statistical rate, and we further strengthen it to the global statistical rate by introducing a proper initialization procedure. In high dimensional regimes, the statistical rate obtained significantly improves those shown in the existing nonsparse decomposition methods. The empirical advantages of tensor truncated power are confirmed in extensive simulation results and two real applications of click-through rate prediction and high dimensional gene clustering.

As the field of computational cognitive neuroscience continues to expand and generate new theories, there is a growing need for more advanced methods to test the hypothesis of brain-behavior relationships. Recent progress in Bayesian cognitive modeling has enabled the combination of neural and behavioral models into a single unifying framework. However, these approaches require manual feature extraction, and lack the capability to discover previously unknown neural features in more complex data. Consequently, this would hinder the expressiveness of the models. To address these challenges, we propose a Neurocognitive Variational Autoencoder (NCVA) to conjoin high-dimensional EEG with a cognitive model in both generative and predictive modeling analyses. Importantly, our NCVA enables both the prediction of EEG signals given behavioral data and the estimation of cognitive model parameters from EEG signals. This novel approach can allow for a more comprehensive understanding of the triplet relationship between behavior, brain activity, and cognitive processes. •Provide a deeper understanding of the triple relationship between EEG data, cognitive models, and behavioral measures.•Autonomously identifies task-relevant neural features to enhance the capacity to uncover critical neural behavior correlates.•Generalize to other physiological measures paired with behavioral observations by an end-to-end framework.

Cronbach’s (1957) famous division of scientific psychology into two disciplines is still apparent for the fields of cognition (general mechanisms) and intelligence (dimensionality of individual differences). The welcome integration of the two fields requires the construction of mechanistic models of cognition and cognitive development that explain key phenomena in individual differences research. In this paper, we argue that network modeling is a promising approach to integrate the processes of cognitive development and (developing) intelligence into one unified theory. Network models are defined mathematically, describe mechanisms on the level of the individual, and are able to explain positive correlations among intelligence subtest scores—the empirical basis for the well-known g-factor—as well as more complex factorial structures. Links between network modeling, factor modeling, and item response theory allow for a common metric, encompassing both discrete and continuous characteristics, for cognitive development and intelligence.

The pivotal problem of comorbidity research lies in the psychometric foundation it rests on, that is, latent variable theory , in which a mental disorder is viewed as a latent variable that causes a constellation of symptoms. From this perspective, comorbidity is a (bi)directional relationship between multiple latent variables. We argue that such a latent variable perspective encounters serious problems in the study of comorbidity, and offer a radically different conceptualization in terms of a network approach , where comorbidity is hypothesized to arise from direct relations between symptoms of multiple disorders. We propose a method to visualize comorbidity networks and, based on an empirical network for major depression and generalized anxiety, we argue that this approach generates realistic hypotheses about pathways to comorbidity, overlapping symptoms, and diagnostic boundaries, that are not naturally accommodated by latent variable models: Some pathways to comorbidity through the symptom space are more likely than others; those pathways generally have the same direction (i.e., from symptoms of one disorder to symptoms of the other); overlapping symptoms play an important role in comorbidity; and boundaries between diagnostic categories are necessarily fuzzy.

Bayesian network models with latent variables are widely used in statistics and machine learning. In this paper, we provide a complete algebraic characterization of these models when the observed variables are discrete and no assumption is made about the state-space of the latent variables. We show that it is algebraically equivalent to the so-called nested Markov model, meaning that the two are the same up to inequality constraints on the joint probabilities. In particular, these two models have the same dimension, differing only by inequality constraints for which there is no general description. The nested Markov model is therefore the closest possible description of the latent variable model that avoids consideration of inequalities. A consequence of this is that the constraint finding algorithm of Tian and Pearl [In Proceedings of the 18th Conference on Uncertainty in Artificial Intelligence (2002) 519–527] is complete for finding equality constraints. Latent variable models suffer from difficulties of unidentifiable parameters and nonregular asymptotics; in contrast the nested Markov model is fully identifiable, represents a curved exponential family of known dimension, and can easily be fitted using an explicit parameterization.