Pairwise stochastic approximation for confirmatory factor analysis of categorical data.

Pairwise likelihood is a limited-information method widely used to estimate latent variable models, including factor analysis of categorical data. It can often avoid evaluating high-dimensional integrals and, thus, is computationally more efficient than relying on the full likelihood. Despite its computational advantage, the pairwise likelihood approach can still be demanding for large-scale problems that involve many observed variables. We tackle this challenge by employing an approximation of the pairwise likelihood estimator, which is derived from an optimization procedure relying on stochastic gradients. The stochastic gradients are constructed by subsampling the pairwise log-likelihood contributions, for which the subsampling scheme controls the per-iteration computational complexity. The stochastic estimator is shown to be asymptotically equivalent to the pairwise likelihood one. However, finite-sample performance can be improved by compounding the sampling variability of the data with the uncertainty introduced by the subsampling scheme. We demonstrate the performance of the proposed method using simulation studies and two real data applications.

DIF Analysis with Unknown Groups and Anchor Items.

Ensuring fairness in instruments like survey questionnaires or educational tests is crucial. One way to address this is by a Differential Item Functioning (DIF) analysis, which examines if different subgroups respond differently to a particular item, controlling for their overall latent construct level. DIF analysis is typically conducted to assess measurement invariance at the item level. Traditional DIF analysis methods require knowing the comparison groups (reference and focal groups) and anchor items (a subset of DIF-free items). Such prior knowledge may not always be available, and psychometric methods have been proposed for DIF analysis when one piece of information is unknown. More specifically, when the comparison groups are unknown while anchor items are known, latent DIF analysis methods have been proposed that estimate the unknown groups by latent classes. When anchor items are unknown while comparison groups are known, methods have also been proposed, typically under a sparsity assumption - the number of DIF items is not too large. However, DIF analysis when both pieces of information are unknown has not received much attention. This paper proposes a general statistical framework under this setting. In the proposed framework, we model the unknown groups by latent classes and introduce item-specific DIF parameters to capture the DIF effects. Assuming the number of DIF items is relatively small, an L 1 -regularised estimator is proposed to simultaneously identify the latent classes and the DIF items. A computationally efficient Expectation-Maximisation (EM) algorithm is developed to solve the non-smooth optimisation problem for the regularised estimator. The performance of the proposed method is evaluated by simulation studies and an application to item response data from a real-world educational test.

Assessment of generalised Bayesian structural equation models for continuous and binary data.

The paper proposes a novel model assessment paradigm aiming to address shortcoming of posterior predictive p -values, which provide the default metric of fit for Bayesian structural equation modelling (BSEM). The model framework presented in the paper focuses on the approximate zero approach (Psychological Methods, 17, 2012, 313), which involves formulating certain parameters (such as factor loadings) to be approximately zero through the use of informative priors, instead of explicitly setting them to zero. The introduced model assessment procedure monitors the out-of-sample predictive performance of the fitted model, and together with a list of guidelines we provide, one can investigate whether the hypothesised model is supported by the data. We incorporate scoring rules and cross-validation to supplement existing model assessment metrics for BSEM. The proposed tools can be applied to models for both continuous and binary data. The modelling of categorical and non-normally distributed continuous data is facilitated with the introduction of an item-individual random effect. We study the performance of the proposed methodology via simulation experiments as well as real data on the 'Big-5' personality scale and the Fagerstrom test for nicotine dependence.

Rotation to Sparse Loadings Using [Formula: see text] Losses and Related Inference Problems.

Researchers have widely used exploratory factor analysis (EFA) to learn the latent structure underlying multivariate data. Rotation and regularised estimation are two classes of methods in EFA that they often use to find interpretable loading matrices. In this paper, we propose a new family of oblique rotations based on component-wise [Formula: see text] loss functions [Formula: see text] that is closely related to an [Formula: see text] regularised estimator. We develop model selection and post-selection inference procedures based on the proposed rotation method. When the true loading matrix is sparse, the proposed method tends to outperform traditional rotation and regularised estimation methods in terms of statistical accuracy and computational cost. Since the proposed loss functions are nonsmooth, we develop an iteratively reweighted gradient projection algorithm for solving the optimisation problem. We also develop theoretical results that establish the statistical consistency of the estimation, model selection, and post-selection inference. We evaluate the proposed method and compare it with regularised estimation and traditional rotation methods via simulation studies. We further illustrate it using an application to the Big Five personality assessment.

Considering multiple outcomes with different weights informed the hierarchy of interventions in network meta-analysis.

OBJECTIVES: Ranking metrics in network meta-analysis (NMA) are computed separately for each outcome. Our aim is to 1) present graphical ways to group competing interventions considering multiple outcomes and 2) use conjoint analysis for placing weights on the various outcomes based on the stakeholders' preferences. STUDY DESIGN AND SETTING: We used multidimensional scaling (MDS) and hierarchical tree clustering to visualize the extent of similarity of interventions in terms of the relative effects they produce through a random effect NMA. We reanalyzed a published network of 212 psychosis trials taking three outcomes into account as follows: reduction in symptoms of schizophrenia, all-cause treatment discontinuation, and weight gain. RESULTS: Conjoint analysis provides a mathematical method to transform judgements into weights that can be subsequently used to visually represent interventions on a two-dimensional plane or through a dendrogram. These plots provide insightful information about the clustering of interventions. CONCLUSION: Grouping interventions can help decision makers not only to identify the optimal ones in terms of benefit-risk balance but also choose one from the best cluster based on other grounds, such as cost, implementation etc. Placing weights on outcomes allows considering patient profile or preferences.

A Joint Modeling Approach for Longitudinal Outcomes and Non-ignorable Dropout under Population Heterogeneity in Mental Health Studies.

The paper proposes a joint mixture model to model non-ignorable drop-out in longitudinal cohort studies of mental health outcomes. The model combines a (non)-linear growth curve model for the time-dependent outcomes and a discrete-time survival model for the drop-out with random effects shared by the two sub-models. The mixture part of the model takes into account population heterogeneity by accounting for latent subgroups of the shared effects that may lead to different patterns for the growth and the drop-out tendency. A simulation study shows that the joint mixture model provides greater precision in estimating the average slope and covariance matrix of random effects. We illustrate its benefits with data from a longitudinal cohort study that characterizes depression symptoms over time yet is hindered by non-trivial participant drop-out.

Assessing Dimensionality in Dichotomous Items When Many Subjects Have All-Zero Responses: An Example From Psychiatry and a Solution Using Mixture Models.

Common methods for determining the number of latent dimensions underlying an item set include eigenvalue analysis and examination of fit statistics for factor analysis models with varying number of factors. Given a set of dichotomous items, the authors demonstrate that these empirical assessments of dimensionality often incorrectly estimate the number of dimensions when there is a preponderance of individuals in the sample with all-zeros as their responses, for example, not endorsing any symptoms on a health battery. Simulated data experiments are conducted to demonstrate when each of several common diagnostics of dimensionality can be expected to under- or over-estimate the true dimensionality of the underlying latent variable. An example is shown from psychiatry assessing the dimensionality of a social anxiety disorder battery where 1, 2, 3, or more factors are identified, depending on the method of dimensionality assessment. An all-zero inflated exploratory factor analysis model (AZ-EFA) is introduced for assessing the dimensionality of the underlying subgroup corresponding to those possessing the measurable trait. The AZ-EFA approach is demonstrated using simulation experiments and an example measuring social anxiety disorder from a large nationally representative survey. Implications of the findings are discussed, in particular, regarding the potential for different findings in community versus patient populations.

Use of the Lagrange Multiplier Test for Assessing Measurement Invariance Under Model Misspecification.

This article studies the Type I error, false positive rates, and power of four versions of the Lagrange multiplier test to detect measurement noninvariance in item response theory (IRT) models for binary data under model misspecification. The tests considered are the Lagrange multiplier test computed with the Hessian and cross-product approach, the generalized Lagrange multiplier test and the generalized jackknife score test. The two model misspecifications are those of local dependence among items and nonnormal distribution of the latent variable. The power of the tests is computed in two ways, empirically through Monte Carlo simulation methods and asymptotically, using the asymptotic distribution of each test under the alternative hypothesis. The performance of these tests is evaluated by means of a simulation study. The results highlight that, under mild model misspecification, all tests have good performance while, under strong model misspecification, the tests performance deteriorates, especially for false positive rates under local dependence and power for small sample size under misspecification of the latent variable distribution. In general, the Lagrange multiplier test computed with the Hessian approach and the generalized Lagrange multiplier test have better performance in terms of false positive rates while the Lagrange multiplier test computed with the cross-product approach has the highest power for small sample sizes. The asymptotic power turns out to be a good alternative to the classic empirical power because it is less time consuming. The Lagrange tests studied here have been also applied to a real data set.

Pairwise likelihood estimation for confirmatory factor analysis models with categorical variables and data that are missing at random.

Methods for the treatment of item non-response in attitudinal scales and in large-scale assessments under the pairwise likelihood (PL) estimation framework and under a missing at random (MAR) mechanism are proposed. Under a full information likelihood estimation framework and MAR, ignorability of the missing data mechanism does not lead to biased estimates. However, this is not the case for pseudo-likelihood approaches such as the PL. We develop and study the performance of three strategies for incorporating missing values into confirmatory factor analysis under the PL framework, the complete-pairs (CP), the available-cases (AC) and the doubly robust (DR) approaches. The CP and AC require only a model for the observed data and standard errors are easy to compute. Doubly-robust versions of the PL estimation require a predictive model for the missing responses given the observed ones and are computationally more demanding than the AC and CP. A simulation study is used to compare the proposed methods. The proposed methods are employed to analyze the UK data on numeracy and literacy collected as part of the OECD Survey of Adult Skills.

A forward search algorithm for detecting extreme study effects in network meta-analysis.

In a quantitative synthesis of studies via meta-analysis, it is possible that some studies provide a markedly different relative treatment effect or have a large impact on the summary estimate and/or heterogeneity. Extreme study effects (outliers) can be detected visually with forest/funnel plots and by using statistical outlying detection methods. A forward search (FS) algorithm is a common outlying diagnostic tool recently extended to meta-analysis. FS starts by fitting the assumed model to a subset of the data which is gradually incremented by adding the remaining studies according to their closeness to the postulated data-generating model. At each step of the algorithm, parameter estimates, measures of fit (residuals, likelihood contributions), and test statistics are being monitored and their sharp changes are used as an indication for outliers. In this article, we extend the FS algorithm to network meta-analysis (NMA). In NMA, visualization of outliers is more challenging due to the multivariate nature of the data and the fact that studies contribute both directly and indirectly to the network estimates. Outliers are expected to contribute not only to heterogeneity but also to inconsistency, compromising the NMA results. The FS algorithm was applied to real and artificial networks of interventions that include outliers. We developed an R package (NMAoutlier) to allow replication and dissemination of the proposed method. We conclude that the FS algorithm is a visual diagnostic tool that helps to identify studies that are a potential source of heterogeneity and inconsistency.

Guideline Assessment Project II: statistical calibration informed the development of an AGREE II extension for surgical guidelines.

OBJECTIVE: To inform the development of an AGREE II extension specifically tailored for surgical guidelines. AGREE II was designed to inform the development, reporting, and appraisal of clinical practice guidelines. Previous research has suggested substantial room for improvement of the quality of surgical guidelines. METHODS: A previously published search in MEDLINE for clinical practice guidelines published by surgical scientific organizations with an international scope between 2008 and 2017, resulted in a total of 67 guidelines. The quality of these guidelines was assessed using AGREE II. We performed a series of statistical analyses (reliability, correlation and Factor Analysis, Item Response Theory) with the objective to calibrate AGREE II for use specifically in surgical guidelines. RESULTS: Reliability/correlation/factor analysis and Item Response Theory produced similar results and suggested that a structure of 5 domains, instead of 6 domains of the original instrument, might be more appropriate. Furthermore, exclusion and re-arrangement of items to other domains was found to increase the reliability of AGREE II when applied in surgical guidelines. CONCLUSIONS: The findings of this study suggest that statistical calibration of AGREE II might improve the development, reporting, and appraisal of surgical guidelines.

Single- and Multiple-Group Penalized Factor Analysis: A Trust-Region Algorithm Approach with Integrated Automatic Multiple Tuning Parameter Selection.

Penalized factor analysis is an efficient technique that produces a factor loading matrix with many zero elements thanks to the introduction of sparsity-inducing penalties within the estimation process. However, sparse solutions and stable model selection procedures are only possible if the employed penalty is non-differentiable, which poses certain theoretical and computational challenges. This article proposes a general penalized likelihood-based estimation approach for single- and multiple-group factor analysis models. The framework builds upon differentiable approximations of non-differentiable penalties, a theoretically founded definition of degrees of freedom, and an algorithm with integrated automatic multiple tuning parameter selection that exploits second-order analytical derivative information. The proposed approach is evaluated in two simulation studies and illustrated using a real data set. All the necessary routines are integrated into the R package penfa.

Latent Class Analysis: Insights about design and analysis of schistosomiasis diagnostic studies.

Various global health initiatives are currently advocating the elimination of schistosomiasis within the next decade. Schistosomiasis is a highly debilitating tropical infectious disease with severe burden of morbidity and thus operational research accurately evaluating diagnostics that quantify the epidemic status for guiding effective strategies is essential. Latent class models (LCMs) have been generally considered in epidemiology and in particular in recent schistosomiasis diagnostic studies as a flexible tool for evaluating diagnostics because assessing the true infection status (via a gold standard) is not possible. However, within the biostatistics literature, classical LCM have already been criticised for real-life problems under violation of the conditional independence (CI) assumption and when applied to a small number of diagnostics (i.e. most often 3-5 diagnostic tests). Solutions of relaxing the CI assumption and accounting for zero-inflation, as well as collecting partial gold standard information, have been proposed, offering the potential for more robust model estimates. In the current article, we examined such approaches in the context of schistosomiasis via analysis of two real datasets and extensive simulation studies. Our main conclusions highlighted poor model fit in low prevalence settings and the necessity of collecting partial gold standard information in such settings in order to improve the accuracy and reduce bias of sensitivity and specificity estimates.

A Note on Likelihood Ratio Tests for Models with Latent Variables.

The likelihood ratio test (LRT) is widely used for comparing the relative fit of nested latent variable models. Following Wilks' theorem, the LRT is conducted by comparing the LRT statistic with its asymptotic distribution under the restricted model, a [Formula: see text] distribution with degrees of freedom equal to the difference in the number of free parameters between the two nested models under comparison. For models with latent variables such as factor analysis, structural equation models and random effects models, however, it is often found that the [Formula: see text] approximation does not hold. In this note, we show how the regularity conditions of Wilks' theorem may be violated using three examples of models with latent variables. In addition, a more general theory for LRT is given that provides the correct asymptotic theory for these LRTs. This general theory was first established in Chernoff (J R Stat Soc Ser B (Methodol) 45:404-413, 1954) and discussed in both van der Vaart (Asymptotic statistics, Cambridge, Cambridge University Press, 2000) and Drton (Ann Stat 37:979-1012, 2009), but it does not seem to have received enough attention. We illustrate this general theory with the three examples.

Approximated Penalized Maximum Likelihood for Exploratory Factor Analysis: An Orthogonal Case.

The problem of penalized maximum likelihood (PML) for an exploratory factor analysis (EFA) model is studied in this paper. An EFA model is typically estimated using maximum likelihood and then the estimated loading matrix is rotated to obtain a sparse representation. Penalized maximum likelihood simultaneously fits the EFA model and produces a sparse loading matrix. To overcome some of the computational drawbacks of PML, an approximation to PML is proposed in this paper. It is further applied to an empirical dataset for illustration. A simulation study shows that the approximation naturally produces a sparse loading matrix and more accurately estimates the factor loadings and the covariance matrix, in the sense of having a lower mean squared error than factor rotations, under various conditions.

Knowledge of Greek adolescents on human papilloma virus (HPV) and vaccination: A national epidemiologic study.

The aim of the present study was to identify the sexual behavior, attitudes, beliefs, and knowledge on sexually transmitted infections (STIs) focused on human papilloma virus (HPV) in the Greek adolescent population. The participants were 4547 adolescents, a representative sample for Greek territory with a mean age of 17 years. After written permission from Greek ministry of education each student completed a questionnaire with 36 questions. The fields covered were demographic characteristics, sexual life data, and basic knowledge on HPV. In the present study, 43% and 75% of the participants knew about HPV or cervical cancer, while more than 6 out of 10 did not know the association between the 2. More than 60% of the participants could not answer correctly neither about HPV infection and cervical cancer frequency in sexually active women, nor about protection methods against HPV and cervical cancer. This study shows that the low vaccination coverage of the Greek population may be due to lack of information and awareness of the adolescents and their parents. It is our duty to increase our efforts in order to better educate the population and vaccinate the population as early as possible in their reproductive years.

Detecting outlying studies in meta-regression models using a forward search algorithm.

When considering data from many trials, it is likely that some of them present a markedly different intervention effect or exert an undue influence on the summary results. We develop a forward search algorithm for identifying outlying and influential studies in meta-analysis models. The forward search algorithm starts by fitting the hypothesized model to a small subset of likely outlier-free studies and proceeds by adding studies into the set one-by-one that are determined to be closest to the fitted model of the existing set. As each study is added to the set, plots of estimated parameters and measures of fit are monitored to identify outliers by sharp changes in the forward plots. We apply the proposed outlier detection method to two real data sets; a meta-analysis of 26 studies that examines the effect of writing-to-learn interventions on academic achievement adjusting for three possible effect modifiers, and a meta-analysis of 70 studies that compares a fluoride toothpaste treatment to placebo for preventing dental caries in children. A simple simulated example is used to illustrate the steps of the proposed methodology, and a small-scale simulation study is conducted to evaluate the performance of the proposed method. Copyright © 2016 John Wiley & Sons, Ltd.

Pairwise Likelihood Ratio Tests and Model Selection Criteria for Structural Equation Models with Ordinal Variables.

Correlated multivariate ordinal data can be analysed with structural equation models. Parameter estimation has been tackled in the literature using limited-information methods including three-stage least squares and pseudo-likelihood estimation methods such as pairwise maximum likelihood estimation. In this paper, two likelihood ratio test statistics and their asymptotic distributions are derived for testing overall goodness-of-fit and nested models, respectively, under the estimation framework of pairwise maximum likelihood estimation. Simulation results show a satisfactory performance of type I error and power for the proposed test statistics and also suggest that the performance of the proposed test statistics is similar to that of the test statistics derived under the three-stage diagonally weighted and unweighted least squares. Furthermore, the corresponding, under the pairwise framework, model selection criteria, AIC and BIC, show satisfactory results in selecting the right model in our simulation examples. The derivation of the likelihood ratio test statistics and model selection criteria under the pairwise framework together with pairwise estimation provide a flexible framework for fitting and testing structural equation models for ordinal as well as for other types of data. The test statistics derived and the model selection criteria are used on data on 'trust in the police' selected from the 2010 European Social Survey. The proposed test statistics and the model selection criteria have been implemented in the R package lavaan.

Nonequivalence of measurement in latent variable modeling of multigroup data: A sensitivity analysis.

In studies of multiple groups of respondents, such as cross-national surveys and cross-cultural assessments in psychological or educational testing, an important methodological consideration is the comparability or "equivalence" of measurement across the groups. Ideally full equivalence would hold, but very often it does not. If nonequivalence of measurement is ignored when it is present, substantively interesting comparisons between the groups may become distorted. We consider this question in multigroup latent variable modeling of multiple-item scales, specifically latent trait models for categorical items. We use numerical sensitivity analyses to examine the nature and magnitude of the distortions in different circumstances, and the factors that affect them. The results suggest that estimates of multigroup latent variable models can be sensitive to assumptions about measurement, in that nonequivalence of measurement does not need to be extreme before ignoring it may substantially affect cross-group comparisons. We also discuss the implications of such findings on the analysis of large comparative studies.

IRT Modeling in the Presence of Zero-Inflation With Application to Psychiatric Disorder Severity.

Item response theory (IRT) has been increasingly utilized in psychiatry for the purpose of describing the relationship among items in psychiatric disorder symptom batteries hypothesized to be indicators of an underlying latent continuous trait representing the severity of the psychiatric disorder. It is common to find zero-inflated (ZI) data such that a large proportion of the sample has none of the symptoms. It has been argued that standard IRT models of psychiatric disorder symptoms may be problematic due to the unipolar nature of many clinical traits. In the current article, the authors propose to address this by using a mixture model to approximate the unknown latent trait distribution in the IRT model while allowing for the presence of a non-pathological subgroup. The basic idea is that instead of assuming normality for the underlying trait, the latent trait will be allowed to follow a mixture of normals including a degenerate component that is fixed to represent a non-pathological group for whom the psychiatric symptoms simply are not relevant and hence are all expected to be zero. The authors demonstrate how the ZI mixture IRT method can be implemented in Mplus and present a simulation study comparing its performance with a standard IRT model assuming normality under different scenarios representative of psychiatric disorder symptom batteries. The model incorrectly assuming normality is shown to have biased discrimination and severity estimates. An application further illustrates the method using data from an alcohol use disorder criteria battery.