Development of uncertainty-based work injury model using Bayesian structural equation modelling

When Bayesian estimation is used to analyze Structural Equation Models (SEMs), prior distributions need to be specified for all parameters in the model. Many popular software programs offer default prior distributions, which is helpful for novel users and makes Bayesian SEM accessible for a broad audience. However, when the sample size is small, those prior distributions are not always suitable and can lead to untrustworthy results. In this tutorial, we provide a non-technical discussion of the risks associated with the use of default priors in small sample contexts. We discuss how default priors can unintentionally behave as highly informative priors when samples are small. Also, we demonstrate an online educational Shiny app, in which users can explore the impact of varying prior distributions and sample sizes on model results. We discuss how the Shiny app can be used in teaching; provide a reading list with literature on how to specify suitable prior distributions; and discuss guidelines on how to recognize (mis)behaving priors. It is our hope that this tutorial helps to spread awareness of the importance of specifying suitable priors when Bayesian SEM is used with small samples.

Animals attacked by predators often enter a state of tonic immobility (TI) in which individuals appear to simulate death. Despite the fact that TI is often used as a proxy of fear in domesticated animals, quantitative data on individual variation is very scarce for wild vertebrates. As a consequence, we lack ecological interpretations for the variability in TI that may exist in wild populations. Here, we tested whether there are consistent differences among individuals in 2 components of TI within wild populations of 2 avian species, the Yellow-crowned bishop (Euplectes afer) and the Tree sparrow (Passer montanus). We next tested whether this variation reflects variation in boldness toward predators (measured as the response to 2 predator models) or is simply related to variation in general activity/restlessness (measured as baseline activity) in the bishop. We analyzed our data by means of Bayesian structural equation modeling (SEM), which has several general advantages and, moreover, allowed us to analyze censored (truncated) data. We found good support for relatively high repeatability within individuals of both components of TI. Measures of TI appeared to be uncorrelated with baseline activity. In contrast, our results suggest that individual variation in TI in a wild vertebrate can be interpreted in a context of boldness toward predators, making TI a meaningful and practical behavioral trait for studies involving personality and antipredation behavior in wild populations. In addition, we show that the Bayesian structural equation modeling approach to analyze censored data had greater statistical power than other approaches. Hence, this rarely implemented technique deserves to be more widely used. Key words: activity, animal personality, antipredation behavior, Bayesian structural equation modeling, boldness, fear, repeatability, tonic immobility. [Behav Ecol]

Almost all scientists benefit from using questionnaire forms in performing statistical analysis. In most cases, these forms consist of mixed-type scales. To analyze such scales is inconvenient because of the measurement differences, and this problem remains unsolved. In many studies, analysis of mixed-type scales is limited based on the score points of the factors. This study proposes an alternative approach to combine mixed-type scale data using linear transformation functions. Using this approach, it is possible to transform mixed data to the same scale, with the main benefit of allowing the analysis of the mixed data. It also makes it possible to interpret among different types of scales. We show that this transformation approach minimizes the loss of information between the original scale structure and the transformed data. To show the usefulness of our approach, we consider Bayesian structural equation modeling (SEM) within the threshold value approach. Application studies demonstrate that our transformation performs well, especially in the presence of non normality. The transformation approach also gains an advantage with respect to timing costs and the simplicity of the models.

The objective of this study is to examine the properties of Bayes estimators of the shape parameter of the Power Function Distribution (PFD-I), by using two different prior distributions for the parameter θ and different loss functions that were compared with the maximum likelihood estimators. In many practical applications, we may have two different prior information about the prior distribution for the shape parameter of the Power Function Distribution, which influences the parameter estimation. So, we used two different kinds of conjugate priors of shape parameter θ of the Power Function Distribution (PFD-I) to estimate it. The conjugate prior function of the shape parameter θ was considered as a combination of two different prior distributions such as gamma distribution with Erlang distribution and Erlang distribution with exponential distribution and Erlang distribution with non-informative distribution and exponential distribution with the non-informative distribution. We derived Bayes estimators for shape parameter θ of the Power Function Distribution (PFD-I) according to different loss functions such as the squared error loss function (SELF), the weighted error loss function (WSELF) and modified linear exponential (MLINEX) loss function (MLF), with two different double priors. In addition to the classical estimation (maximum likelihood estimation). We used simulation to get the results of this study, for different cases of the shape parameter of the Power Function Distribution used to generate data for different samples sizes.

This paper explores the utilisation of Bayesian structural equation modelling (BSEM) in psychology, highlighting its advantages over frequentist methods for handling complex models and small sample sizes. Basic concepts and fundamental issues relevant to BSEM are introduced, such as prior setting, model convergence, and model fit evaluation and so on. The paper also provides illustrative examples of commonly employed BSEMs, including confirmatory factor analysis (CFA) models, mediation models and multigroup CFA models, accompanied by empirical data and computer codes to facilitate implementation. Our goal is to provide researchers with novel ideas for empirical research and equip them to overcome challenges inherent to traditional methods. As BSEM continues to gain traction in various fields, we anticipate its development will feature improved methods, techniques and reporting standards.

Practical use of Bayesian estimation procedures is often associated with difficulties related to elicitation of prior information, and its formalization into the respective prior distribution. The two-parameter Weibull distribution is a particularly difficult case, because it requires a two-dimensional joint prior distribution of the Weibull parameters. The novelty of the procedure suggested here is that the prior information can be presented in the form of the interval assessment of the reliability function (as opposed to that on the Weibull parameters), which is generally easier to obtain. Based on this prior information, the procedure allows constructing the continuous joint prior distribution of Weibull parameters as well as the posterior estimates of the mean and standard deviation of the estimated reliability function (or the CDF) at any given value of the exposure variable. A numeric example is discussed as an illustration. We additionally elaborate on a new parametric form of the prior distribution for the scale parameter of the exponential distribution. This distribution is not a Gamma (as might intuitively be expected); its mode is available in a closed form, and the mean is obtainable through a series approximation.

Thermodynamic modeling and uncertainty quantification of CO2-loaded aqueous MEA solutions

Muthén and Asparouhov (2012) made a strong case for the advantages of Bayesian methodology in factor analysis and structural equation models. I show additional extensions and adaptations of their methods and show how non-Bayesians can take advantage of many (though not all) of these advantages by using interval restrictions on parameters. By keeping parameters restricted to intervals (such as loadings between -.3 and .3 to produce small loadings), frequentists using standard structural equation modeling software can do something similar to what a Bayesian does by putting prior distributions on these parameters.

The Bayesian approach is a powerful tool which allows the researcher to take into consideration the prior knowledge which may be available about the model under investigation and this in turn can lead to safer and more reliable conclusions. In the present study, the basic methodologies of the Bayesian approach, applied to structural equation models, will be used in order to investigate the decision of young people studying in the Department of Social Sciences of Democritus University of Thrace to go abroad after completing their studies. One of the objectives of the paper is the comparison of the resulting models with the application of both informative and non-informative prior distributions. In this study all the required procedures will be first reviewed analytically. For the dataset processing, R software will be used, which incorporates command packages that implement the required simulation methods, and also can handle Bayesian methods used in structural equation modeling.

The objective of this study is to understand the impact of a variety of factors on the frequency and severity of pedestrian-vehicle collisions that involve pedestrian spatial violations at mid-blocks. To that end, the historical collision records of the City of Hamilton between 2010 and 2017 were obtained, and collisions that had occurred at mid-blocks were filtered out. A Bayesian structural equation modeling (SEM) framework was developed to investigate the impact of a wide range of factors on such collisions. First, a classical SEM was developed to group the different factors into sets of latent variables. Four latent variables were defined, including location amenities and attractions, pedestrian/road network characteristics, exposure parameters, and location/collision-specific factors. The Bayesian SEM was then implemented to investigate the relationship between the latent variables and collisions. The results showed that the amenities and attractions of a location (e.g., parks, schools, bike-share stations, and bus stops) were the most influential factor on the frequency of collisions that involve spatial violation, followed by pedestrian network characteristics. Pedestrian network characteristics and location/collision-specific factors were found to be the most influential factors on the severity of collisions. The location of bike-share stations, pedestrian network connectivity, exposure to walkers, and the number of lanes were the four observed variables that explained the highest percentage of the variance in each latent group, respectively. The results of this study should assist engineers and planners to develop better design concepts to mitigate collisions that are caused by pedestrian spatial violations in urban areas.

Examining how well a hypothesized model fits observed data is pivotal in Bayesian structural equation modeling (SEM). Recent efforts have aimed to formulate Bayesian SEM fit indices akin to those used in frequentist SEM. However, the assessment of these fit indices in Bayesian SEM has been limited in scope. This research entailed two simulation studies to explore the impact of various factors, including prior choices, model misspecification, model size, and sample size, on the sensitivity of fit indices. The first study delved into the prior sensitivity of Bayesian SEM fit indices (BRMSEA [Bayesian root mean square error of approximation], BCFI [Bayesian comparative fit index], BTLI [Bayesian Tucker–Lewis index], and PPp [posterior predictive p-value]) under latent factor and cross-loading misspecifications. The second study explored how alterations in model complexity influenced the prior sensitivity of these fit indices to model misspecifications. The findings indicate a robust performance of Bayesian fit indices under relatively severe model misspecification, suggesting a preference for highly informative priors when prior knowledge is certain. As model size increased, PPp exhibited a balanced performance between true and false positive rates, whereas BRMSEA was less reliable in the presence of latent factor misspecification. Implications for applied research are discussed.

The Overexcitability Questionnaire-Two (OEQ-II) measures the degree and nature of overexcitability, which assists in determining the developmental potential of an individual according to Dabrowski's Theory of Positive Disintegration. Previous validation studies using frequentist confirmatory factor analysis, which postulates exact parameter constraints, led to model rejection and a long series of model modifications. Bayesian structural equation modeling (BSEM) allows the application of zero-mean, small-variance priors for cross-loadings, residual covariances, and differences in measurement parameters across groups, better reflecting substantive theory and leading to better model fit and less overestimation of factor correlations. Our BSEM analysis with a sample of 516 students in higher education yields positive results regarding the factorial validity of the OEQ-II. Likewise, applying BSEM-based alignment with approximate measurement invariance, the absence of non-invariant factor loadings and intercepts across gender is supportive of the psychometric quality of the OEQ-II. Compared to males, females scored significantly higher on emotional and sensual overexcitability, and significantly lower on psychomotor overexcitability.

Influence of environmental factors on well-being and care burden of elderly family caregivers: a bayesian structural equation modeling approach

Revised assessment of cancer risk to dichloromethane: Part I Bayesian PBPK and dose–response modeling in mice

Decision makers in various sectors, such as manufacturing and transportation, strive to minimize downtime costs. Often, brief-planned stoppage times allow for changes in shifts and line configurations and longer periods are scheduled for major repairs. It is quite important to proactively make use of these downtimes to reduce the costs of unexpected downtimes due to failures. Among many aspects, the availability of spare parts significantly affects the operational costs of such systems. Current sensor technologies enable the condition monitoring of critical components and degradation-based spare parts management. This paper focuses on Bayesian degradation modelling for spare parts inventory management for a new system. We propose a stochastic dynamic program to minimize the expected spare parts inventory cost for a fixed planning horizon. A numerical example illustrates the value of Bayesian analysis in this management setting. The proposed methodology finds the optimal time between long stoppages and optimal spare parts order quantity when the prior information about the degradation process is accurate. The methodology can be used to analyse the sensitivity of the optimal solution to changes in the accuracy and bias of the prior distributions of the model parameters, the cost structure and the number of machines in the system.