Correcting for Unreliability and Partial Invariance: A Two-Stage Path Analysis Approach

When estimating path coefficients among psychological constructs measured with error, structural equation modeling (SEM), which simultaneously estimates the measurement and structural parameters, is generally regarded as the gold standard. In practice, however, researchers usually first compute composite scores or factor scores, and use those as observed variables in a path analysis, for purposes of simplifying the model or avoiding model convergence issues. Whereas recent approaches, such as reliability adjustment methods and factor score regression, has been proposed to mitigate the bias induced by ignoring measurement error in composite/factor scores with continuous indicators, those approaches are not yet applicable to models with categorical indicators. In this article, we introduce the two-stage path analysis (2S-PA) with definition variables as a general framework for path modeling to handle categorical indicators, in which estimation of factor scores and path coefficients are separated. It thus allows for different estimation methods in the measurement and the structural path models and easier diagnoses of violations of model assumptions. We conducted three simulation studies, ranging from latent regression to mediation analysis with categorical indicators, and showed that 2S-PA generally produced similar estimates to those using SEM in large samples, but gave better convergence rates, less standard error bias, and better control of Type I error rates in small samples. We illustrate 2S-PA using data from a national data set, and show how researchers can implement it in Mplus and OpenMx. Possible extensions and future directions of 2S-PA are discussed. (PsycInfo Database Record (c) 2022 APA, all rights reserved).

transfer, create conditions for the establishment of farmers' behavioral psychological contracts in the process of agricultural land transfers, and guide farmers to establish relationship psychological contracts. The second is to improve the market system, properly cultivate and develop agricultural land transfer intermediaries, reduce transaction costs, and reduce the probability of farmers' psychological contracts being broken. The third is to guide farmers to establish a positive agricultural land transfer psychology based on their resource endowments such as labor force quality and cultural quality, and encourage farmers to make agricultural land transfer decisions such as subcontracting, leasing, reselling, and interchanging.

Several approaches are available for estimating the relationship of latent class membership to distal outcomes in latent profile analysis (LPA). A three-step approach is commonly used, but has problems with estimation bias and confidence interval coverage. Proposed improvements include the correction method of Bolck, Croon, and Hagenaars (BCH; 2004), Vermunt's (2010) maximum likelihood (ML) approach, and the inclusive three-step approach of Bray, Lanza, & Tan (2015). These methods have been studied in the related case of latent class analysis (LCA) with categorical indicators, but not as well studied for LPA with continuous indicators. We investigated the performance of these approaches in LPA with normally distributed indicators, under different conditions of distal outcome distribution, class measurement quality, relative latent class size, and strength of association between latent class and the distal outcome. The modified BCH implemented in Latent GOLD had excellent performance. The maximum likelihood and inclusive approaches were not robust to violations of distributional assumptions. These findings broadly agree with and extend the results presented by Bakk and Vermunt (2016) in the context of LCA with categorical indicators.

Background. While the associations between individual lifestyle factors and risk of hepatocellular carcinoma (HCC) were examined substantially, their combined impact on HCC risk has not been evaluated. Methods. The association of a composite score of healthy lifestyle factors, including body mass index, alcohol consumption, cigarette smoking, alternative Mediterranean Diet (aMED), and sleep duration, with the risk of developing HCC was examined in the Singapore Chinese Health Study (SCHS), an on-going prospective cohort of 63,257 Chinese men and women aged 45-74 at enrollment in 1993-1998 with up to 25 years of follow-up. Cox proportional hazard regression method was used to estimate hazard ratio (HR) and its 95% confidence interval (CI) of HCC with the composite score after adjustment for multiple potential confounders. The unconditional logistic regression method was used to confirm the association between the composite lifestyle score and HCC risk among hepatitis B surface antigen (HBsAg) negative individuals to eliminate its potential confounding effect. Results. After a mean follow-up of 17.7 years, 561 participants of the SCHS developed HCC. Individuals with higher composite scores, which represented for healthier lifestyles, were at significantly lower risk of HCC. Compared with the lowest composite score (i.e., 0-4), the HRs (95% CIs) for 5, 6, 7 and 8 were 0.48 (0.36-0.64), 0.44 (0.34-0.67), 0.37 (0.28-0.48), and 0.26 (0.17-0.39), respectively (Ptrend<0.001). A similar inverse association was observed in participants with negative HBsAg serology; HR was 0.12 (95% CI: 0.04-0.38) for the highest versus the lowest category of the composite scores (Ptrend=0.01). Conclusion. Healthy lifestyles are protective against the development of HCC, especially for individuals without viral infection. This finding highlights the importance of a comprehensive lifestyle modification strategy for primary prevention of HCC. Funding: The Singapore Chinese Health Study was supported by the National Institutes of Health (NIH) of the United States (grants # R01 CA144034 and UM1 CA182876). Citation Format: Hung N. Luu, Renwei Wang, Jaideep Behari, Jennifer Adams-Haduch, Andrew O. Odegaard, George Goh Bee, Aizhen Jin, Woon-Puay Koh, Jian-Min Yuan. Composite score of healthy lifestyle factors and risk of hepatocellular carcinoma: Findings from a prospective cohort study [abstract]. In: Proceedings of the Annual Meeting of the American Association for Cancer Research 2020; 2020 Apr 27-28 and Jun 22-24. Philadelphia (PA): AACR; Cancer Res 2020;80(16 Suppl):Abstract nr 2344.

Joint models linking longitudinal biomarkers or recurrent event processes with a terminal event, for example, mortality, have been studied extensively. Motivated by studies of recurrent delirium events in patients receiving care in an intensive care unit (ICU), we devise a joint model for a recurrent event process and multiple terminal events. Being discharged alive from the ICU or experiencing mortality may be associated with a patient's hazard of delirium, violating the assumption of independent censoring. Moreover, the direction of the association between the hazards of delirium and mortality may be opposite of the direction of association between the hazards of delirium and ICU discharge. Hence treating either terminal event as independent censoring may bias inferences. We propose a competing joint model that uses a latent frailty to link a patient's recurrent and competing terminal event processes. We fit our model to data from a completed placebo-controlled clinical trial, which studied whether Haloperidol could prevent death and delirium among ICU patients. The clinical trial served as a foundation for a simulation study, in which we evaluate the properties, for example, bias and confidence interval coverage, of the competing joint model. As part of the simulation study, we demonstrate the shortcomings of using a joint model with a recurrent delirium process and a single terminal event to study delirium in the ICU. Lastly, we discuss limitations and possible extensions for the competing joint model. The competing joint model has been added to frailtypack, an R package for fitting an assortment of joint models.

Expert opinion plays an important role when choosing clusters of chemical compounds for further investigation. Often, the process by which the clusters are assigned to the experts for evaluation, the so-called selection process, and the qualitative ratings given by the experts to the clusters (chosen/not chosen) need to be jointly modeled to avoid bias. This approach is referred to as the joint modeling approach. However, misspecifying the selection model may impact the estimation and inferences on parameters in the rating model, which are of most scientific interest. We propose to incorporate the selection process into the analysis by adding a new set of random effects to the rating model and, in this way, avoid the need to model it parametrically. This approach is referred to as the combined model approach. Through simulations, the performance of the combined and joint models was compared in terms of bias and confidence interval coverage. The estimates from the combined model were nearly unbiased, and the derived confidence intervals had coverage probability around 95% in all scenarios considered. In contrast, the estimates from the joint model were severely biased under some form of misspecification of the selection model, and fitting the model was often numerically challenging. The results show that the combined model may offer a safer alternative on which to base inferences when there are doubts about the validity of the selection model. Importantly, thanks to its greater numerical stability, the combined model may outperform the joint model even when the latter is correctly specified.

While the associations between individual lifestyle factors and risk of hepatocellular carcinoma (HCC) have been described previously, their combined impact on HCC risk is unknown. The association of a composite score of healthy lifestyle factors, including body mass index, alcohol consumption, cigarette smoking, alternative Mediterranean diet, and sleep duration, and HCC risk was examined in the Singapore Chinese Health Study, an ongoing prospective cohort study of 63,257 Chinese men and women. Cox proportional hazard regression method was used to estimate HR and its 95% confidence interval (CI). Conditional logistic regression method was used to evaluate this composite lifestyle score-HCC risk association among a subset of individuals who tested negative for hepatitis B surface antigen (HBsAg) and anti-hepatitis C antibody. After a mean follow-up of 17.7 years, 561 participants developed HCC. Individuals with higher composite scores representing healthier lifestyles (range 0-8) were at significantly lower risk of HCC. Compared with the lowest composite score category (0-4), the HRs (95% CIs) for the composite scores of 5, 6, 7, and 8 were 0.67 (0.62-0.85), 0.61 (0.48-0.77), 0.49 (0.37-0.65), and 0.13 (0.06-0.30), respectively (P trend < 0.0001). A similar inverse association was observed in participants with negative HBsAg and anti-hepatitis C virus (HCV)-negative serology (HR, 0.38; 95% CI, 0.19-0.79; for the highest vs. the lowest category of the composite scores; P trend = 0.001). Healthy lifestyles protect against HCC development, especially for individuals without hepatitis B virus and HCV infections. This study highlights the importance of a comprehensive lifestyle modification strategy for HCC primary prevention.

A study on the influence factors of the university library service image based on SEM

A latent multivariate regression model is developed that employs a generalized asymmetric Laplace (GAL) prior distribution for regression coefficients. The model is designed for high-dimensional applications where an approximate sparsity condition is satisfied, such that many regression coefficients are near zero after accounting for all the model predictors. The model is applicable to large-scale assessments such as the National Assessment of Educational Progress (NAEP), which includes hundreds of student, teacher, and school predictors of latent achievement. Monte Carlo evidence suggests that employing the GAL prior provides more precise estimation of coefficients that equal zero in comparison to a multivariate normal (MVN) prior, which translates to more accurate model selection. Furthermore, the GAL yielded less biased estimates of regression coefficients in smaller samples. The developed model is applied to mathematics achievement data from the 2011 NAEP for 175,200 eighth graders. The GAL and MVN NAEP estimates were similar, but the GAL was more parsimonious by selecting 12 fewer (i.e., 83 of the 148) variable groups. There were noticeable differences between estimates computed with a GAL prior and plausible value regressions with the AM software (beta version 0.06.00). Implications of the results are discussed for test developers and applied researchers.

Statistical mediation analysis is used in the social sciences and public health to uncover potential mechanisms, known as mediators, by which a treatment led to a change in an outcome. Recently, the estimation of the treatment-by-mediator interaction (i.e., the XM interaction) has been shown to play a pivotal role in understanding the equivalence between the traditional mediation effects in linear models and the causal mediation effects in the potential outcomes framework. However, there is limited guidance on how to estimate the XM interaction when the mediator is latent. In this article, we discuss eight methods to accommodate latent XM interactions in statistical mediation analysis, which fall in two categories: using structural models (e.g., latent moderated structural equations, Bayesian mediation, unconstrained product indicator method, multiple-group models) or scoring the mediator prior to estimating the XM interaction (e.g., summed scores and factor scores, with and without attenuation correction). Simulation results suggest that finite-sample bias is low, type 1 error rates and coverage of percentile bootstrap confidence intervals and Bayesian credible intervals are close to the nominal values, and statistical power is similar across approaches. The methods are demonstrated with an applied example, syntax is provided for their implementation, and general considerations are discussed.

Measurement invariance is the condition that an instrument measures a target construct in the same way across subgroups, settings, and time. In psychological measurement, usually only partial, but not full, invariance is achieved, which potentially biases subsequent parameter estimations and statistical inferences. Although existing literature shows that a correctly specified partial invariance model can remove such biases, it ignores the model uncertainty in the specification search step: flagging the wrong items may lead to additional bias and variability in subsequent inferences. On the other hand, several new approaches, including Bayesian approximate invariance and alignment optimization methods, have been proposed; these methods use an approximate invariance model to adjust for partial measurement invariance without the need to directly identify noninvariant items. However, there has been limited research on these methods in situations with a small number of groups. In this paper, we conducted three systematic simulation studies to compare five methods for adjusting partial invariance. While specification search performed reasonably well when the proportion of noninvariant parameters was no more than one-third, alignment optimization overall performed best across conditions in terms of efficiency of parameter estimates, confidence interval coverage, and type I error rates. In addition, the Bayesian version of alignment optimization performed best for estimating latent means and variances in small-sample and low-reliability conditions. We thus recommend the use of the alignment optimization methods for adjusting partial invariance when comparing latent constructs across a few groups.

Structural equation modeling (SEM) has been deemed as a proper method when variables contain measurement errors. In contrast, path analysis with composite scores is preferred for prediction and diagnosis of individuals. While path analysis with composite scores has been criticized for yielding biased parameter estimates, recent literature pointed out that the population values of parameters in a latent-variable model depend on artificially assigned scales. Consequently, bias in parameter estimates is not a well-grounded concept for models involving latent constructs. This article compares path analysis with composite scores against SEM with respect to effect size and statistical power in testing the significance of the path coefficients, via the z- or t-statistics. The data come from many sources with various models that are substantively determined. Results show that SEM is not as powerful as path analysis even with equally weighted composites. However, path analysis with Bartlett-factor scores and the partial least-squares approach to SEM perform the best with respect to effect size and power.

A high environmental composite quality factor score was associated with the risk of sick building syndrome among adults in northeast China

It is well known that methods that fail to account for measurement error in observed variables, such as regression and path analysis (PA), can result in poor estimates and incorrect inference. On the other hand, methods that fully account for measurement error, such as structural equation modeling with latent variables and multiple indicators, can produce highly variable estimates in small samples. This article advocates a family of intermediate models for small samples (N < 200), referred to as single indicator (SI) models. In these models, each latent variable has a single composite indicator, with its reliability fixed to a plausible value. A simulation study compared three versions of the SI method with PA and with a multiple-indicator structural equation model (SEM) in small samples (N = 30 to 200). Two of the SI models fixed the reliability of each construct to a value chosen a priori (either .7 or .8). The third SI model (referred to as "SIα") estimated the reliability of each construct from the data via coefficient alpha. The results showed that PA and fixed-reliability SI methods that overestimated reliability slightly resulted in the most accurate estimates as well as in the highest power. Fixed-reliability SI methods also maintained good coverage and Type I error rates. The SIα and SEM methods had intermediate performance. In small samples, use of a fixed-reliability SI method is recommended. (PsycINFO Database Record (c) 2019 APA, all rights reserved).

ABSTRACTMultilevel structural equation models are increasingly applied in psychological research. With increasing model complexity, estimation becomes computationally demanding, and small sample sizes pose further challenges on estimation methods relying on asymptotic theory. Recent developments of Bayesian estimation techniques may help to overcome the shortcomings of classical estimation techniques. The use of potentially inaccurate prior information may, however, have detrimental effects, especially in small samples. The present Monte Carlo simulation study compares the statistical performance of classical estimation techniques with Bayesian estimation using different prior specifications for a two-level SEM with either continuous or ordinal indicators. Using two software programs (Mplus and Stan), differential effects of between- and within-level sample sizes on estimation accuracy were investigated. Moreover, it was tested to which extent inaccurate priors may have detrimental effects on parameter estimates in categorical indicator models. For continuous indicators, Bayesian estimation did not show performance advantages over ML. For categorical indicators, Bayesian estimation outperformed WLSMV solely in case of strongly informative accurate priors. Weakly informative inaccurate priors did not deteriorate performance of the Bayesian approach, while strong informative inaccurate priors led to severely biased estimates even with large sample sizes. With diffuse priors, Stan yielded better results than Mplus in terms of parameter estimates.