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The new software package OpenMx 2.0 for structural equation and other statistical modeling is introduced and its features are described. OpenMx is evolving in a modular direction and now allows a mix-and-match computational approach that separates model expectations from fit functions and optimizers. Major backend architectural improvements include a move to swappable open-source optimizers such as the newly written CSOLNP. Entire new methodologies such as item factor analysis and state space modeling have been implemented. New model expectation functions including support for the expression of models in LISREL syntax and a simplified multigroup expectation function are available. Ease-of-use improvements include helper functions to standardize model parameters and compute their Jacobian-based standard errors, access to model components through standard R $ mechanisms, and improved tab completion from within the R Graphical User Interface.

Multilevel models are an increasingly popular method to analyze data that originate from a clustered or hierarchical structure. To effectively utilize multilevel models, one must have an adequately large number of clusters; otherwise, some model parameters will be estimated with bias. The goals for this paper are to (1) raise awareness of the problems associated with a small number of clusters, (2) review previous studies on multilevel models with a small number of clusters, (3) to provide an illustrative simulation to demonstrate how a simple model becomes adversely affected by small numbers of clusters, (4) to provide researchers with remedies if they encounter clustered data with a small number of clusters, and (5) to outline methodological topics that have yet to be addressed in the literature.

Establishing construct validity for the interpretations from a measure is critical to high quality assessment and subsequent research using outcomes data from the measure. [...]FA should be a researcher's best friend during the development and validation of a new measure or when adapting a measure to a new population. If you sum the squared factor loadings of Factor 1, you will get the eigenvalue, which is 2.1 and dividing the eigenvalue by four (2.1/4= 0.52) we will get the proportion of variance accounted for Factor 1, which is 52 %. Since PCA does not separate specific variance and error variance, it often inflates factor loadings and limits the potential for the factor structure to be generalized and applied with other samples in subsequent study. [...]Maximum likelihood and Principal Axis Factoring extraction methods separate common and unique variance (specific and error variance), which overcomes the issue attached to PCA. [...]the proportion of variance explained by an extracted factor more precisely reflects the extent to which the latent construct is measured by the instrument items. [...]the analysis of the second-order factors is not possible.

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 introduce the network model as a formal psychometric model, conceptualizing the covariance between psychometric indicators as resulting from pairwise interactions between observable variables in a network structure. This contrasts with standard psychometric models, in which the covariance between test items arises from the influence of one or more common latent variables. Here, we present two generalizations of the network model that encompass latent variable structures, establishing network modeling as parts of the more general framework of structural equation modeling (SEM). In the first generalization, we model the covariance structure of latent variables as a network. We term this framework latent network modeling (LNM) and show that, with LNM, a unique structure of conditional independence relationships between latent variables can be obtained in an explorative manner. In the second generalization, the residual variance–covariance structure of indicators is modeled as a network. We term this generalization residual network modeling (RNM) and show that, within this framework, identifiable models can be obtained in which local independence is structurally violated. These generalizations allow for a general modeling framework that can be used to fit, and compare, SEM models, network models, and the RNM and LNM generalizations. This methodology has been implemented in the free-to-use software package lvnet , which contains confirmatory model testing as well as two exploratory search algorithms: stepwise search algorithms for low-dimensional datasets and penalized maximum likelihood estimation for larger datasets. We show in simulation studies that these search algorithms perform adequately in identifying the structure of the relevant residual or latent networks. We further demonstrate the utility of these generalizations in an empirical example on a personality inventory dataset.

This article explains perceived loneliness among people in Europe by accounting for cultural factors as well as social isolation. Culturally, it measures the impact of both personal and societal individualism-collectivism on loneliness. It accounts for social isolation by looking at the separate effects of living alone, emotional isolation, and relational isolation. Using a 2014 European Social Survey sample comprising 36,760 individuals in 21 countries, the study predicts loneliness using multilevel logistic regression modeling using both maximum likelihood and Bayesian estimation procedures. Results indicate that societal individualism may strongly reduce loneliness, even after taking into account that social isolation partially mediates this relationship. Further, the effects of living alone and relational isolation depend upon whether one is personally an individualist or collectivist. Living alone and relational isolation greatly increase loneliness, and such negative effects are somewhat reduced for individualists. However, individualists are not protected from the negative impacts of emotional isolation at all, and the above moderation effects do not hold for the most severe forms of loneliness. Based on this analysis, the best case for reduced loneliness for individualists and collectivists alike is that they maintain a strong degree of multiple forms of social integration and live in an individualist society.

Like many developing tissues, the vertebrate neural tube is patterned by antiparallel morphogen gradients. To understand how these inputs are interpreted, we measured morphogen signaling and target gene expression in mouse embryos and chick ex vivo assays. From these data, we derived and validated a characteristic decoding map that relates morphogen input to the positional identity of neural progenitors. Analysis of the observed responses indicates that the underlying interpretation strategy minimizes patterning errors in response to the joint input of noisy opposing gradients. We reverse-engineered a transcriptional network that provides a mechanistic basis for the observed cell fate decisions and accounts for the precision and dynamics of pattern formation. Together, our data link opposing gradient dynamics in a growing tissue to precise pattern formation.

Variation in vectorial capacity for human malaria among Anopheles mosquito species is determined by many factors, including behavior, immunity, and life history. To investigate the genomic basis of vectorial capacity and explore new avenues for vector control, we sequenced the genomes of 16 anopheline mosquito species from diverse locations spanning ~100 million years of evolution. Comparative analyses show faster rates of gene gain and loss, elevated gene shuffling on the X chromosome, and more intron losses, relative to Drosophila . Some determinants of vectorial capacity, such as chemosensory genes, do not show elevated turnover but instead diversify through protein-sequence changes. This dynamism of anopheline genes and genomes may contribute to their flexible capacity to take advantage of new ecological niches, including adapting to humans as primary hosts. Virtually everyone has first-hand experience with mosquitoes. Few recognize the subtle biological distinctions among these bloodsucking flies that render some bites mere nuisances and others the initiation of a potentially life-threatening infection. By sequencing the genomes of several mosquitoes in depth, Neafsey et al. and Fontaine et al. reveal clues that explain the mystery of why only some species of one genus of mosquitoes are capable of transmitting human malaria (see the Perspective by Clark and Messer). Science , this issue 10.1126/science.1258524 and 10.1126/science.1258522 ; see also p. 27 Comparison of several genomes reveals the genetic history of mosquitoes’ ability to vector malaria among humans. [Also see Perspective by Clark and Messer ]

A scaled difference test statistic that can be computed from standard software of structural equation models (SEM) by hand calculations was proposed in Satorra and Bentler (Psychometrika 66:507–514, 2001 ). The statistic is asymptotically equivalent to the scaled difference test statistic introduced in Satorra (Innovations in Multivariate Statistical Analysis: A Festschrift for Heinz Neudecker, pp. 233–247, 2000 ), which requires more involved computations beyond standard output of SEM software. The test statistic has been widely used in practice, but in some applications it is negative due to negativity of its associated scaling correction. Using the implicit function theorem, this note develops an improved scaling correction leading to a new scaled difference statistic that avoids negative chi-square values.