A cautionary note on measurement error corrections in structural equation models.

It is commonly thought that structural equation modeling corrects estimated relationships among latent variables for the biasing effects of measurement error. The purpose of this article is to review the manner in which structural equation models control for measurement error and to demonstrate the conditions in which structural equation models do and do not correct for unreliability. Generalizability theory is used to demonstrate that there are multiple sources of error in most measurement systems and that applications of structural equation modeling rarely account for more than a single source of error. As a result, the parameter estimates in a structural equation model may be severely biased by unassessed sources of measurement error. Recommendations for modeling multiple sources of error in structural equation models are provided. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Model inference or model selection: Discussion of Klugkist, Laudy, and Hoijtink (2005).

I. Klugkist, O. Laudy, and H. Hoijtink (2005) presented a Bayesian approach to analysis of variance models with inequality constraints. Constraints may play 2 distinct roles in data analysis. They may represent prior information that allows more precise inferences regarding parameter values, or they may describe a theory to be judged against the data. In the latter case, the authors emphasized the use of Bayes factors and posterior model probabilities to select the best theory. One difficulty is that interpretation of the posterior model probabilities depends on which other theories are included in the comparison. The posterior distribution of the parameters under an unconstrained model allows one to quantify the support provided by the data for inequality constraints without requiring the model selection framework. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Estimating the nonlinear and interactive effects of latent variables.

Describes a procedure that enables researchers to estimate nonlinear and interactive effects of latent variables in structural equation models. Given that the latent variables are normally distributed, the parameters of such models can be estimated. To do this, products of the measured variables are used as indicators of latent product variables. Estimation must be done using a procedure that allows nonlinear constraints on parameters. The procedure is demonstrated in 3 examples. The 1st 2 examples use artificial data with known parameter values. These parameters are successfully recovered by the procedure. The final complex example uses national election survey data. (14 ref) (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Testing parameters in structural equation modeling: Every "one" matters.

A problem with standard errors estimated by many structural equation modeling programs is described. In such programs, a parameter's standard error is sensitive to how the model is identified (i.e., how scale is set). Alternative but equivalent ways to identify a model may yield different standard errors, and hence different Z tests for a parameter, even though the identifications produce the same overall model fit. This lack of invariance due to model identification creates the possibility that different analysts may reach different conclusions about a parameter's significance level even though they test equivalent models on the same data. The authors suggest that parameters be tested for statistical significance through the likelihood ratio test, which is invariant to the identification choice. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

基于乌鸦搜索算法的行星滚柱丝杠参数优化

针对行星滚柱丝杠结构参数匹配问题,提出一种基于乌鸦搜索算法的参数优化模型.考虑行星滚柱丝杠螺纹啮合点位置的影响,建立丝杠、滚柱以及螺母空间螺旋曲面方程,得到螺纹啮合点处位置与螺纹牙厚之间的关系.根据螺纹副和齿轮副啮合关系,确定内齿圈和滚柱端部轮齿设计参数.利用空间螺旋曲面方程,获得螺纹啮合点处的法向量,并推导行星滚柱丝杠各零件间的受力关系.以行星滚柱丝杠结构参数作为设计变量,以螺母外径、丝杠中径、滚柱长度等参数最小为优化目标,考虑行星滚柱丝杠结构约束和主要承力部件强度约束,利用乌鸦搜索算法作为优化算法,建立行星滚柱丝杠参数优化模型,从而实现优化变量最佳匹配.最后,针对三种负载,利用该优化模型得到三组行星滚柱丝杠结构参数,并将其优化结果与国外产品手册进行对比,从而验证了本文优化模型有效性.     

A mathematical evaluation of the multiple breath nitrogen washout (MBNW) technique and the multiple inert gas elimination technique (MIGET)

We consider two and 50 compartment lung models for use with two techniques used to investigate the efficiency of the lungs: the Multiple Breath Nitrogen Washout (MBNW) technique used for investigating the ventilation-volume distribution; and the Multiple Inert Gas Elimination Technique (MIGET) used for investigating the ventilation-perfusion distribution. In each of these techniques pulmonary respiratory gas exchange is described by conservation of mass equations which may be written in identical form, and in each the underlying distributions of ventilation to volume and ventilation to perfusion are assumed to be continuous functions (usually assumed to be a linear sum of log-normal distributions). The mathematical models used to describe the lung have predominantly used a collection of discrete compartments to approximate these continuous distributions. The most commonly used models have used one, two or 50 compartments. In this paper, we begin by showing that in the limit as the width of the peaks of the distribution tend to zero, the continuous distributions may be replaced by a single discrete compartment placed at each peak of the distribution. We investigate the various methods used previously for parameter recovery, and show that one commonly used method for the MBNW is not suitable and suggest a modification to this recovery technique. Using simulated error-free data, we show that both the two compartment model and the 50 compartment model contain information about the ventilation-volume (or ventilation-perfusion) distribution, and investigate the extent to which this information can be used to recover the parameters which define these distributions. We go on to use Monte-Carlo methods to investigate the stability of the recovery process.     

Testing model nesting and equivalence.

When using existing technology, it can be hard or impossible to determine whether two structural equation models that are being considered may be nested. There is also no routine technology for evaluating whether two very different structural models may be equivalent. A simple nesting and equivalence testing (NET) procedure is proposed that uses random sample and model-reproduced moment matrices to evaluate both model nesting and equivalence. The analysis is “local” rather than “global” in nature, but its use with simulation or bootstrapping can imply global conclusions. Two standard applications of NET are to verify whether or not two proposed models are equivalent and whether a baseline model used in an incremental fit index is appropriately nested. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Uncertainty, variability, and sensitivity analysis in physiological pharmacokinetic models

Physiologically based pharmacokinetic (PBPK) models are now commonly used to predict the dose of toxic metabolites of chemical substances reaching target tissues. A typical PBPK model can involve 20 or more physiological, physiochemical, and biochemical parameters, each of which is estimated with some degree of error. In this article, methods for assessing the impact of uncertainty in the parameter values on prediction of tissue dose are proposed, along with methods for identifying those parameters to which predictions of tissue doses are most sensitive. Many of the model parameters are related to body weight, which is assumed to vary in accordance with a doubly truncated normal distribution. The application of the proposed methods is illustrated using a PBPK model for benzene.     

A Priori Identifiability of Unsaturated Soil Parameters

A priori identifiability (i.e., identifiability under perfect data) is a necessary condition for posteriori identifiability (i.e., identifiability under real data), and by implication a priori nonidentifiability is a sufficient condition for posteriori nonidentifiability. Therefore, it is important to prove a priori identifiability before attempting to estimate model parameters through nonlinear regression with real noisy data. This paper investigates the a priori (also called classical, structural, or deterministic) identifiability of soil parameters using Richards's equation with perfect distributed pressure data and prescribed initial and boundary conditions. The study of a priori identifiability is made possible through the concept of linear independence of vectors. As expected, it is shown that the unsaturated soil parameters are not a priori identifiable, and thus not posteriori identifiable, with either zero flow pressure data or steady-state flow pressure data. In addition, it is shown that models with more than two parameters are not a priori identifiable with transient pressure data. Therefore, models with more than two parameters are not posteriori identifiable with real pressure data regardless of the quantity and quality of this data. However, it is found that two parameter models are a priori identifiable with transient pressure data. Hence, the necessary condition for the posteriori identifiability of two parameter models is proven.     

Growth curve models for indistinguishable dyads using multilevel modeling and structural equation modeling: The case of adolescent twins' conflict with their mothers.

Growth modeling is a useful tool for studying change over time, and it is becoming increasingly popular with developmental researchers. There is a considerable methodological literature surrounding growth modeling for individuals; however, far less attention has been focused on growth models for pairs of related individuals (i.e., dyads). In this article, the authors consider dyadic growth models for those cases where there are no relevant variables that can empirically distinguish between dyad members (e.g., same-sex twins or best friends). The authors describe how researchers can estimate growth models for indistinguishable dyads using both multilevel modeling and structural equation modeling. Although both approaches can be used to estimate the same underlying models, the authors focus on practical similarities and differences between the two approaches. They illustrate modeling issues using an overtime study of adolescent twins' conflict with their mothers, a substantively important topic given the enduring interest in parent-child relationships during adolescence. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Estimating, testing, and comparing specific effects in structural equation models: The phantom model approach.

The phantom model approach for estimating, testing, and comparing specific effects within structural equation models (SEMs) is presented. The rationale underlying this novel method consists in representing the specific effect to be assessed as a total effect within a separate latent variable model, the phantom model that is added to the main model. The following favorable features characterize the method: (a) It enables the estimation, testing, and comparison of arbitrary specific effects for recursive and nonrecursive models with latent and manifest variables; (b) it enables the bootstrapping of confidence intervals; and (c) it can be applied with all standard SEM programs permitting latent variables, the specification of equality constraints, and the bootstrapping of total effects. These features along with the fact that no manipulation of matrices and formulas is required make the approach particularly suitable for applied researchers. The method is illustrated by means of 3 examples with real data sets. (PsycINFO Database Record (c) 2011 APA, all rights reserved)     

Masking misfit in confirmatory factor analysis by increasing unique variances: A cautionary note on the usefulness of cutoff values of fit indices.

Fit indices are widely used in order to test the model fit for structural equation models. In a highly influential study, Hu and Bentler (1999) showed that certain cutoff values for these indices could be derived, which, over time, has led to the reification of these suggested thresholds as “golden rules” for establishing the fit or other aspects of structural equation models. The current study shows how differences in unique variances influence the value of the global chi-square model test and the most commonly used fit indices: Root-mean-square error of approximation, standardized root-mean-square residual, and the comparative fit index. Using data simulation, the authors illustrate how the value of the chi-square test, the root-mean-square error of approximation, and the standardized root-mean-square residual are decreased when unique variances are increased although model misspecification is present. For a broader understanding of the phenomenon, the authors used different sample sizes, number of observed variables per factor, and types of misspecification. A theoretical explanation is provided, and implications for the application of structural equation modeling are discussed. (PsycINFO Database Record (c) 2011 APA, all rights reserved)     

Psychometric approaches for developing commensurate measures across independent studies: Traditional and new models.

[Correction Notice: An erratum for this article was reported in Vol 14(4) of Psychological Methods (see record 2009-22665-007). In this article, the authors wrote, "To our knowledge, the multisample framework is the only available option within these [latent variable] programs that allows for the moderation of all types of parameters, and this approach requires a single categorical moderator variable to define the samples.” Bengt Muthén has clarified for the authors that some programs, including Mplus and Mx, can allow for continuous moderation through the implementation of nonlinear constraints involving observed variables, further enlarging the class of MNLFA models that can be fit with these programs.] When conducting an integrative analysis of data obtained from multiple independent studies, a fundamental problem is to establish commensurate measures for the constructs of interest. Fortunately, procedures for evaluating and establishing measurement equivalence across samples are well developed for the linear factor model and commonly used item response theory models. A newly proposed moderated nonlinear factor analysis model generalizes these models and procedures, allowing for items of different scale types (continuous or discrete) and differential item functioning across levels of categorical and/or continuous variables. The potential of this new model to resolve the problem of measurement in integrative data analysis is shown via an empirical example examining changes in alcohol involvement from ages 10 to 22 years across 2 longitudinal studies. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Evaluation of goodness-of-fit indices for structural equation models.

Discusses how current goodness-of-fit indices fail to assess parsimony and hence disconfirmability of a model and are insensitive to misspecifications of causal relations (a) among latent variables when measurement model with many indicators is correct and (b) when causal relations corresponding to free parameters expected to be nonzero turn out to be zero or near zero. A discussion of philosophy of parsimony elucidates relations of parsimony to parameter estimation, disconfirmability, and goodness of fit. AGFI in {lisrel} is rejected. A method of adjusting goodness-of-fit indices by a parsimony ratio is described. Also discusses less biased estimates of goodness of fit and a relative normed-fit index for testing fit of structural model exclusive of the measurement model. (PsycINFO Database Record (c) 2011 APA, all rights reserved)     

Theories of Aerodynamic Forces on Decks of Long Span Bridges

Long span bridges are one of the most challenging kinds of structures in civil engineering. Wind loading and wind effects are highly important aspects when designing this typology. The interaction between wind and structure, studied by using aeroelasticity theory, allows us to understand several classes of structural instabilities that may appear. Also, wind tunnel data, obtained by conducting careful testing of reduced models of bridges, produce useful information about prototypes' characteristics. A fundamental aspect of bridge design under aeroelastic constraints is identification of aerodynamic forces; several models for this purpose are presented in this paper. First, a model based on a two-degrees-of-freedom plane plate moving in an incompressible fluid is reviewed; this approach, although useful in airfoil engineering, is not valid any longer in civil engineering, as bridge decks are bluff bodies. Second, a linearized theory, also based on a two-degrees-of-freedom model is analyzed; in this case, obtaining aerodynamic forces requires identification of a set of coefficients, called flutter derivatives, that can be found by carrying out testing of reduced models of a segment of bridge deck. Finally, an extension of that approach, leading to a linearized theory of a three-degrees-of-freedom model is presented.     

Distinguishing between moderator and quadratic effects in multiple regression.

Moderated regression analysis is commonly used to test for multiplicative influences of independent variables in regression models. D. Lubinski and L. G. Humphreys (1990) have shown that significant moderator effects can exist even when stronger quadratic effects are present. They recommend comparing effect sizes associated with both effect types and selecting the model that yields the strongest effect. The authors show that this procedure of comparing effect sizes is biased in favor of the moderated model when multicollinearity is high because of the differential reliability of the quadratic and multiplicative terms in the regression models. Fortunately, levels of multicollinearity under which this bias is most problematic may be outside the range encountered in many empirical studies. The authors discuss causes and implications of this phenomenon as well as alternative procedures for evaluating structural relationships among variables. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Assessing the distribution of parameters in models of ligand-receptor interaction: to log or not to log

It is quite common to see experimental data analysed according to a variety of models of ligand-receptor interaction. Often, parameters derived from such models are compared statistically. The most commonly employed statistical analyses contain explicit assumptions about the underlying distributions of the model parameters being compared, yet the validity of these assumptions is not often ascertained. In this article, Arthur Christopoulos describes a general approach to Monte Carlo simulation of data, and outlines how the analysis of such simulated data may be used to address the question of the distribution of model parameters. The results of such an exercise can guide the researcher to the appropriate choice of statistical test or data transform.     

Mathematical models of diffusion-limited gas bubble dynamics in tissue

Mathematical models of bubble evolution in tissue have recently been incorporated into risk functions for predicting the incidence of decompression sickness (DCS) in human subjects after diving and/or flying exposures. Bubble dynamics models suitable for these applications assume the bubble to be either contained in an unstirred tissue (two-region model) or surrounded by a boundary layer within a well-stirred tissue (three-region model). The contrasting premises regarding the bubble-tissue system lead to different expressions for bubble dynamics described in terms of ordinary differential equations. However, the expressions are shown to be structurally similar with differences only in the definitions of certain parameters that can be transformed to make the models equivalent at large tissue volumes. It is also shown that the two-region model is applicable only to bubble evolution in tissues of infinite extent and cannot be readily applied to bubble evolution in finite tissue volumes to simulate how such evolution is influenced by interactions among multiple bubbles in a given tissue. Two-region models that are incorrectly applied in such cases yield results that may be reinterpreted in terms of their three-region model equivalents but only if the parameters in the two-region model transform into consistent values in the three-region model. When such transforms yield inconsistent parameter values for the three-region model, results may be qualitatively correct but are in substantial quantitative error. Obviation of these errors through appropriate use of the different models may improve performance of probabilistic models of DCS occurrence that express DCS risk in terms of simulated in vivo gas and bubble dynamics.     

Dynamic Field Test, System Identification, and Modal Validation of an RC Minaret: Preprocessing and Postprocessing the Wind-Induced Ambient Vibration Data

The investigation of dynamic response for civil engineering structures largely depends on a detailed understanding of their dynamic characteristics, such as the natural frequencies, mode shapes, and modal damping ratios. Dynamic characteristics of structures may be obtained numerically and experimentally. The finite-element method is widely used to model structural systems numerically. However, there are some uncertainties in numerical models. Material properties and boundary conditions may not be modeled correctly. There may be some microcracks in the structures, and these cracks may directly affect the modeling parameters. Modal testing gives correct uncertain modeling parameters that lead to better predictions of the dynamic behavior of a target structure. Therefore, dynamic behavior of special structures, such as minarets, should be determined with ambient vibration tests. The vibration test results may be used to update numerical models and to detect microcracks distributed along the structure. The operational modal analysis procedure consists of several phases. First, vibration tests are carried out, spectral functions are produced from raw measured acceleration records, dynamic characteristics are determined by analyzing processed spectral functions, and finally analytical models are calibrated or updated depending on experimental analysis results. In this study, an ambient vibration test is conducted on the minaret under natural excitations, such as wind effects and human movement. The dynamic response of the minaret is measured through an array of four trixial force-balanced accelerometers deployed along the whole length of the minaret. The raw measured data obtained from ambient vibration testing are analyzed with the SignalCAD program, which was developed in MATLAB. The employed system identification procedures are based on output-only measurements because the forcing functions are not available during ambient vibration tests. The ModalCAD program developed in MATLAB is used for dynamic characteristic identification. A three-dimensional model of the minaret is constructed, and its modal analysis is performed to obtain analytical frequencies and mode shapes by using the ANSYS finite-element program. The obtained system identification results have very good agreement, thus providing a reliable set of identified modal properties (natural frequencies, damping ratios, and mode shapes) of the structure, which can be used to calibrate finite-element models and as a baseline in health monitoring studies.