The standardized root mean squared residual (SRMR) is commonly reported to evaluate approximate fit of latent variable models. As traditionally defined, SRMR summarizes the discrepancy between observed covariance elements and implied covariance elements. However, current applications of latent variable models often include additional features like overidentified mean structures and covariates, to which the traditional SRMR definition is not applicable. To date, SRMR extensions for models with covariates have received limited attention. Nonetheless, mainstream software provide SRMR for models with covariates, but values differ based on model specification and differ across programs. The goal of this paper is to formalize SRMR definitions for models with covariates. We develop possible SRMR definitions corresponding to different model specifications with covariates, discussing the advantages and disadvantages of each. Importantly, some SRMR definitions are susceptible to confounding misfit and model size such that SRMR values systematically decrease and suggest better fit when covariates are present, even if covariates have null effects. The primary conclusion is that there may not be a single unifying SRMR definition for covariates, but practically, researchers reporting SRMR with covariates should be aware (a) which definition is being used and (b) which information is and is not included in the particular definition.

Methods of incorporating a ridge type of regularization into partial redundancy analysis (PRA), constrained redundancy analysis (CRA), and partial and constrained redundancy analysis (PCRA) were discussed. The usefulness of ridge estimation in reducing mean square error (MSE) has been recognized in multiple regression analysis for some time, especially when predictor variables are nearly collinear, and the ordinary least squares estimator is poorly determined. The ridge estimation method was extended to PRA, CRA, and PCRA, where the reduced rank ridge estimates of regression coefficients were obtained by minimizing the ridge least squares criterion. It was shown that in all cases they could be obtained in closed form for a fixed value of ridge parameter. An optimal value of the ridge parameter is found by G-fold cross validation. Illustrative examples were given to demonstrate the usefulness of the method in practical data analysis situations.

We propose a two-step estimator for multilevel latent class analysis (LCA) with covariates. The measurement model for observed items is estimated in its first step, and in the second step covariates are added in the model, keeping the measurement model parameters fixed. We discuss model identification, and derive an Expectation Maximization algorithm for efficient implementation of the estimator. By means of an extensive simulation study we show that (1) this approach performs similarly to existing stepwise estimators for multilevel LCA but with much reduced computing time, and (2) it yields approximately unbiased parameter estimates with a negligible loss of efficiency compared to the one-step estimator. The proposal is illustrated with a cross-national analysis of predictors of citizenship norms.

In many areas of research, the round-robin design is used to study interpersonal judgments and behaviors. The resulting data are analyzed with the social relations model (SRM), whereby almost all previously published studies have used ANOVA-based methods or multilevel-based methods to obtain SRM parameter estimates. In this article, the SRM is embedded into the linear mixed model framework, and it is shown how restricted maximum likelihood can be employed to estimate the SRM parameters. It is also described how the effect of covariates on the SRM-specific effects can be estimated. An example is presented to illustrate the approach. We also present the results of a simulation study in which the performance of the proposed approach is compared to the ANOVA method.

How often do articles depend on suppression effects for their findings? How often do they disclose this fact? By suppression effects, we mean control-variable-induced increases in estimated effect sizes. Researchers generally scrutinize suppression effects as they want reassurance that authors have a strong explanation for them, especially when the statistical significance of the key finding depends on them. In a reanalysis of observational studies from a leading journal, we find that over 30% of articles depend on suppression effects for statistical significance. Although increases in key effect estimates from including control variables are of course potentially justifiable, none of the articles justify or disclose them. These findings may point to a hole in the review process: journals are accepting articles that depend on suppression effects without readers, reviewers, or editors being made aware.

In 2003/2004 a field trial was conducted in Northern Ireland to assess the diagnostic accuracy of six serological tests for bovine brucellosis caused by Brucella abortus. Whereas between-test comparisons have been used to calculate test performances so far, the present study used a latent class approach to estimate diagnostic test accuracy parameters in the absence of a gold standard for these six tests simultaneously and to estimate the true prevalence, while accounting for clustering in the study population and risk factors for true prevalence. Results obtained in this study with regard to prevalence, sensitivity and specificity were largely in accordance with previous findings. Screening tests (SAT and EDTA) appeared to be the most sensitive; however, at low prevalences the EDTA and CFT showed the highest positive predictive values of all investigated tests. The specificities and negative predictive values of all diagnostic tests were found to be very high. Differences of prevalence between three groups of the study population with different risk of exposure could be attributed to the mode of sampling indicating that a more risk-based sampling will result in a higher prevalence than a cross-sectional sampling mode. Age, dairy status and history of abortion were shown to influence the prediction of the latent true infection status.