In modeling change over time, developmental theories often emphasize meaningful quantities like peaks, inflections, timing, and tempo. However, longitudinal analyses typically rely on simple polynomial models that estimate powered terms of time in a linear, additive form which are disconnected from these meaningful quantities. While these linear parameterizations are computationally efficient and produce stable results, the quantities estimated in these models are difficult to directly connect to theoretical hypotheses. To address this disconnect between estimation and theory development, I propose several approaches for linear estimation with nonlinear inference (LENI), a framework that transforms results from stable, easily-estimated linear models into nonlinear estimates which align with theoretical quantities of interest through a set of principled transformation functions. I first outline derivations for the interpretable nonlinear parameters, and transform the results of the corresponding linear model—including fixed and random effects as well as conditional covariates effects —into the results we would have obtained by fitting a nonlinear version of the model. I conclude by summarizing a linearized structural equation model approach which can flexibly accommodate any known nonlinear target function within a linearly-estimable framework. I conclude with recommendations for applied researchers and directions for fruitful future work in this area.

Multilevel factor analysis models are widely used in the social sciences to account for heterogeneity in mean structures. In this paper we extend previous work on multilevel models to account for general forms of heterogeneity in confirmatory factor analysis models. We specify various models of mean and covariance heterogeneity in confirmatory factor analysis and develop Markov Chain Monte Carlo (MCMC) procedures to perform Bayesian inference, model checking, and model comparison.

We test our methodology using synthetic data and data from a consumption emotion study. The results from synthetic data show that our Bayesian model perform well in recovering the true parameters and selecting the appropriate model. More importantly, the results clearly illustrate the consequences of ignoring heterogeneity. Specifically, we find that ignoring heterogeneity can lead to sign reversals of the factor covariances, inflation of factor variances and underappreciation of uncertainty in parameter estimates. The results from the emotion study show that subjects vary both in means and covariances. Thus traditional psychometric methods cannot fully capture the heterogeneity in our data.

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.

Social scientists are often faced with data that have a nested structure: pupils are nested within schools, employees are nested within companies, or repeated measurements are nested within individuals. Nested data are typically analyzed using multilevel models. However, when data sets are extremely large or when new data continuously augment the data set, estimating multilevel models can be challenging: the current algorithms used to fit multilevel models repeatedly revisit all data points and end up consuming much time and computer memory. This is especially troublesome when predictions are needed in real time and observations keep streaming in. We address this problem by introducing the Streaming Expectation Maximization Approximation (SEMA) algorithm for fitting multilevel models online (or “row-by-row”). In an extensive simulation study, we demonstrate the performance of SEMA compared to traditional methods of fitting multilevel models. Next, SEMA is used to analyze an empirical data stream. The accuracy of SEMA is competitive to current state-of-the-art methods while being orders of magnitude faster.

Recent research reflects a growing awareness of the value of using structural equation models to analyze repeated measures data. However, such data, particularly in the presence of covariates, often lead to models that either fit the data poorly, are exceedingly general and hard to interpret, or are specified in a manner that is highly data dependent. This article introduces methods for developing parsimonious models for such data. The underlying technology uses reduced-rank representations of the variances, covariances and means of observed and latent variables. The value of this approach, which may be implemented using standard structural equation modeling software, is illustrated in an application study aimed at understanding heterogeneous consumer preferences. In this application, the parsimonious representations characterize systematic relationships among consumer demographics, attitudes and preferences that would otherwise be undetected. The result is a model that is parsimonious, illuminating, and fits the data well, while keeping data dependence to a minimum.

In practice, nondestructive testing (NDT) procedures tend to consider experiments (and their respective models) as distinct, conducted in isolation, and associated with independent data. In contrast, this work looks to capture the interdependencies between acoustic emission (AE) experiments (as meta-models) and then use the resulting functions to predict the model hyperparameters for previously unobserved systems. We utilize a Bayesian multilevel approach (similar to deep Gaussian Processes) where a higher-level meta-model captures the inter-task relationships. Our key contribution is how knowledge of the experimental campaign can be encoded between tasks as well as within tasks. We present an example of AE time-of-arrival mapping for source localization, to illustrate how multilevel models naturally lend themselves to representing aggregate systems in engineering. We constrain the meta-model based on domain knowledge, then use the inter-task functions for transfer learning, predicting hyperparameters for models of previously unobserved experiments (for a specific design).

Difficulties with emotion regulation are integral to borderline personality disorder (BPD) and its hypothesized developmental pathway. Here, we prospectively assess trajectories of emotion processing across childhood, how BPD symptoms impact these trajectories, and whether developmental changes are transdiagnostic or specific to BPD, as major depressive (MDD) and conduct disorders (CD) are also characterized by emotion regulation difficulties. This study included 187 children enriched for those with early symptoms of depression and disruptive behaviors from a longitudinal study. We created multilevel models of multiple components of emotional processing from mean ages 9.05 to 18.55 years, and assessed the effect of late adolescent BPD, MDD, and CD symptoms on these trajectories. Linear trajectories of coping with sadness and anger, and quadratic trajectories of dysregulated expressions of sadness and anger were transdiagnostic, but also exhibited independent relationships with BPD symptoms. Only inhibition of sadness was related to BPD symptoms. The quadratic trajectories of poor emotional awareness and emotional reluctance were also independently related to BPD. Findings support examining separable components of emotion processing across development as potential precursors to BPD, underscoring the importance of understanding these trajectories as not only a marker of potential risk but also potential targets for prevention and intervention.

The calibration of probability or confidence judgments concerns the association between the judgments and some estimate of the correct probabilities of events. Researchers rely on estimates using relative frequencies computed by aggregating data over observations. We show that this approach creates conceptual problems, and may result in the confounding of explanatory variables or unstable estimates. To circumvent these problems we propose using probability estimates obtained from statistical models—specifically mixed models for binary data—in the analysis of calibration. We illustrate this methodology by re-analyzing data from a published study and comparing the results from this approach to those based on relative frequencies. The model-based estimates avoid problems with confounding variables and provided more precise estimates, resulting in better inferences.

Wrongful convictions are an increasing salient feature of criminal justice discourse in the United States. Many states have adopted reforms to mitigate the likelihood of wrongful convictions, discover errors, and provide redress in the wake of exonerations, yet we know little about why some are seemingly more committed to reducing such errors than others. We argue that public opinion is consequential for policy reform, but its effects are contingent on the electoral vulnerability of state lawmakers. We also suggest that advocacy organizations play a critical role in policy adoption. Incorporating data from all 50 states from 1989 to 2018, we investigate the adoption of five types of wrongful conviction reforms: (1) changes to eyewitness identification practices, (2) mandatory recording of interrogations, (3) the preservation of biological evidence, (4) access to postconviction DNA testing, and (5) exoneree compensation. Our results highlight a more nuanced view of how public opinion shapes policy.

When working with grouped data, investigators may choose between “fixed effects” models (FE) with specialized (e.g., cluster-robust) standard errors, or “multilevel models” (MLMs) employing “random effects.” We review the claims given in published works regarding this choice, then clarify how these approaches work and compare by showing that: (i) random effects employed in MLMs are simply “regularized” fixed effects; (ii) unmodified MLMs are consequently susceptible to bias—but there is a longstanding remedy; and (iii) the “default” MLM standard errors rely on narrow assumptions that can lead to undercoverage in many settings. Our review of over 100 papers using MLM in political science, education, and sociology show that these “known” concerns have been widely ignored in practice. We describe how to debias MLM’s coefficient estimates, and provide an option to more flexibly estimate their standard errors. Most illuminating, once MLMs are adjusted in these two ways the point estimate and standard error for the target coefficient are exactly equal to those of the analogous FE model with cluster-robust standard errors. For investigators working with observational data and who are interested only in inference on the target coefficient, either approach is equally appropriate and preferable to uncorrected MLM.

Although modern lines for dealing with missing data are well established from the 1970s, today there is a challenge when researchers encounter this problem in multilevel models. First, there is a variety of existing software to handle missing data based on multiple imputation (MI), currently pointed out by experts as the most promising strategy. Second, the two principal paradigms of MI are joint modelling (JM) and fully conditional specification (FCS), one more complication because they are not equally useful depending on the combination of multilevel model and the estimated parameters affected by missing data. Technical literature do not contribute to ease the number of decisions that researcher has to do. Given these inconveniences, the present paper has three objectives. (1) To present a thorough revision of the most recently developed software and functions about multiple imputation in multilevel models. (2) We derive a set of suggestions, recommendations, and guides for helping researchers to handle missing data. We list a number of key questions to consider when analyzing multilevel models. (3) Finally, based on the previous relevant questions, we present two detailed examples using the recommended R packages to be easy for the researcher applying multiple imputation in multilevel models.

Does direct democracy strengthen popular control of public policy in the United States? A major challenge in evaluating policy representation is the measurement of state-level public opinion and public policy. Although recent studies of policy responsiveness and congruence have provided improved measures of public opinion using multilevel regression and poststratification (MRP) techniques, these analyses are limited by their static nature and cross-sectional design. Issue attitudes, unlike more general political orientations, often vary considerably over time. Unless the dynamics of issue-specific public opinion are appropriately incorporated into the analyses, tests of policy responsiveness and congruence may be misleading. Thus, we assess the degree of policy representation in direct democracy states regarding same-sex relationship recognition policies using dynamic models of policy adoption and congruence that employ dynamic MRP estimates of attitudes toward same-sex marriage. We find that direct democracy institutions increase both policy responsiveness and congruence with issue-specific public opinion.

This article presents results from survey experiments investigating conditions under which Britons are willing to pay taxes on polluting activities. People are no more willing if revenues are hypothecated for spending on environmental protection, while making such taxes more relevant to people – by naming petrol and electricity as products to which they will apply – has a modestly negative effect. Public willingness increases sharply if people are told that new environmental taxes would be offset by cuts to other taxes, but political distrust appears to undermine much of this effect. Previous studies have argued that political trust shapes public opinion with respect to environmental and many other policies. But this article provides the first experimental evidence suggesting that the relationship is causal, at least for one specific facet: cynicism about public officials’ honesty and integrity. The results suggest a need to make confidence in the trustworthiness of public officials and their promises more central to conceptualizations of political trust.

This study examined the socioeconomic pathways linking partnership status to physical functioning, assessed using objective measures of late life physical functioning, including peak flow and grip strength. Using Wave 4 of the Survey of Health, Ageing and Retirement in Europe (SHARE), we ran multilevel models to examine the relationship between partnership status and physical function in late life, adjusting for social-network characteristics, socioeconomic factors, and health behaviours. We found a robust relationship between partnership status and physical function. Incorporating social-network characteristics, socioeconomic factors, and health behaviours showed independent robust relationships with physical function. Co-variates attenuated the impact of cohabitation, separation, and widowhood on physical function; robust effects were found for singlehood and divorce. Sex-segregated analyses suggest that associations between cohabitation, singlehood, divorce, and widowhood were larger for men than for women. Results suggest that social ties are important to improved physical function.