Covariance structure analysis in experimental research: Comparing two word translation models

The asymptotically distribution free (ADF) method is often used to estimate parameters or test models without a normal distribution assumption on variables, both in covariance structure analysis and in correlation structure analysis. However, little has been done to study the differences in behaviors of the ADF method in covariance versus correlation structure analysis. The behaviors of 3 test statistics frequently used to evaluate structural equation models with nonnormally distributed variables, χ2 test TAGLS and its small-sample variants TYB and TF(AGLS) were compared. Results showed that the ADF method in correlation structure analysis with test statistic TAGLS performs much better at small sample sizes than the corresponding test for covariance structures. In contrast, test statistics TYB and TF(AGLS) under the same conditions generally perform better with covariance structures than with correlation structures. It is proposed that excessively large and variable condition numbers of weight matrices are a cause of poor behavior of ADF test statistics in small samples, and results showed that these condition numbers are systematically increased with substantial increase in variance as sample size decreases. Implications for research and practice are discussed.

In this chapter, we bring together the notions of measurement error discussed in Chaps. 3 and 4 with the structural modeling of simultaneous relationships presented in Chap. 6. We demonstrate that a bias is introduced when estimating the relationship between two variables measured with error if that measurement error is ignored. We then present a methodology for estimating the parameters of structural relationships between variables that are not observed directly: analysis of covariance structures. We focus on the role of the measurement model as discussed in Chap. 4 with the confirmatory factor analytic model.

Keeping track of patients' medication histories is an important component of pharmacy practice. In this study, we conducted a questionnaire survey on medication histories among pharmacists and performed covariance structure analysis to investigate pharmacists' attitudes toward medication histories. The survey was conducted among pharmacists who work at pharmacies. With regard to the questions on medication histories, factor analysis and covariance structure analysis were performed to create a path diagram. The response rate to the questionnaire was 97.0%. The factor analysis revealed six factors, including: "patient assessment", "learning attitude", "practicing the recording of medication histories", "conscious effort to improve medication histories", "uniformity in medication histories" and "issues regarding medication histories". Meanwhile, covariance structure analysis revealed that the five-factor model excluding "issues regarding medication histories" was the best-fitted model. According to this model, it was clear that the pharmacists were extremely conscious about introducing improvements to the content of medication histories. In this study, covariance structure analysis enabled the effective analysis of the attitudes of pharmacists toward medication histories. We believe that creating and conducting a training program to clarify and resolve issues related to medication histories and then reviewing the outcome of such a training program will lead to quality improvement and standardization of the future management of medication histories.

PurposeThe aim is to evaluate the performance of symmetric and asymmetric ARCH models in forecasting both the one‐day‐ahead Value‐at‐Risk (VaR) and the realized intra‐day volatility of two equity indices in the Athens Stock Exchange.Design/methodology/approachTwo volatility specifications are estimated, the symmetric generalized autoregressive conditional heteroscedasticity (GARCH) and the asymmetric APARCH processes. The data set consisted of daily closing prices of the General and the Bank indices from 25 April 1994 to 19 December 2003 and their intra day quotation data from 8 May 2002 to 19 December 2003.FindingsUnder the VaR framework, the most appropriate method for the Bank index is the symmetric model with normally distributed innovations, while the asymmetric model with asymmetric conditional distribution applies for the General index. On the other hand, the asymmetric model tracks closer the one‐step‐ahead intra‐day realized volatility with conditional normally distributed innovations for the Bank index but with asymmetric and leptokurtic distributed innovations for the General index.Originality/valueAs concerns the Greek stock market, there are adequate methods in predicting market risk but it does not seem to be a specific model that is the most accurate for all the forecasting tasks.

The region which discharges pollution from the production processes is not necessarily coincident with the region which suffers from this pollution. This kind of problem is often called a transboundary pollution problem (TBP problem). Many articles which deal with TBP problems have been written since 1990. In this paper, we will survey these preceding articles by contrasting the symmetric two-region model with the asymmetric one, where in our model, “asymmetric two-region” means that region 1 derives less satisfaction from consuming the good but cares more about the pollution stock and the welfare of the coming generation than does region 2. In the symmetric model, the steady state of the pollution stock is always less under cooperative pollution control than in the non-cooperative case in which a Markov-perfect strategy is supposed, but the converse is possible in the asymmetric model. In the analyses of TBP model, we usually employ Hamilton-Jacobi-Bellman equation (H-J-B equation). Therefore, based on the “principle of optimality” in dynamic programming, we have established the H-J-B equation as a general formula applicable to TBP problems.

Traditionally, two approaches have been employed for structural equation modeling: covariance structure analysis and partial least squares. A third alternative, generalized structured component analysis, was introduced recently in the psychometric literature. The authors conduct a simulation study to evaluate the relative performance of these three approaches in terms of parameter recovery under different experimental conditions of sample size, data distribution, and model specification. In this study, model specification is the only meaningful condition in differentiating the performance of the three approaches in parameter recovery. Specifically, when the model is correctly specified, covariance structure analysis tends to recover parameters better than the other two approaches. Conversely, when the model is misspecified, generalized structured component analysis tends to recover parameters better. Finally, partial least squares exhibits inferior performance in parameter recovery compared with the other approaches. In particular, this tendency is salient when the model involves cross-loadings. Thus, generalized structured component analysis may be a good alternative to partial least squares for structural equation modeling and is recommended over covariance structure analysis unless correct model specification is ensured.

In this chapter, we use an example of panel data on the longitudinal development of reading in children to introduce the latent growth curve analysis. Latent growth modeling originates in a simple mapping of the standard multilevel model for change onto the general model available for covariance structure analysis (CSA). Here, we illustrate how the latent growth modeling approach can be enacted by using the CSA Y‐measurement model to contain the level‐1 individual growth model and the CSA structural model to contain the level‐2 model for interindividual differences in change. Because this mapping is possible, all fixed and random parameters in the multilevel model for change can be estimated by fitting the corresponding CSA model to data using standard structural equation modeling software (such as LISREL). Latent growth curve analysis is important because it capitalizes on the intrinsic flexibility of the general CSA model to test interesting and complex hypotheses about change, many of which are either more difficult or impossible to test using standard multilevel modeling approaches.

Indirect measures of psychological constructs are vital to clinical research. On occasion, however, the meaning of indirect measures of psychological constructs is obfuscated by statistical procedures that do not account for the complex relations between items and latent variables and among latent variables. Covariance structure analysis (CSA) is a statistical procedure for testing hypotheses about the relations among items that indirectly measure a psychological construct and relations among psychological constructs. This article introduces clinical researchers to the strengths and limitations of CSA as a statistical procedure for conceiving and testing structural hypotheses that are not tested adequately with other statistical procedures. The article is organized around two empirical examples that illustrate the use of CSA for evaluating measurement models with correlated error terms, higher-order factors, and measured and latent variables.

Analysis of Covariance Structures and Probabilistic Binary Choice Data

Analysis of covariance structures is the common term for a number of techniques for analyzing multivariate data in order to detect and assess latent (unobserved) sources of variation and covariation in the observed measurements. The techniques of covariance structure analysis are general and flexible in that they can handle many types of covariance structures useful especially in the behavioral and social sciences. Although these techniques can be used for exploratory analysis, they have been most successfully applied to confirmatory analysis where the type of covariance structure is specified in advance. A covariance structure of a specified kind may arise because of a specified substantive theory or hypothesis, a given classificatory design for the measures, known experimental conditions, or because of results from previous studies based on extensive data. Sometimes the observed variables are ordered through time, as in longitudinal studies, or according to linear or circular patterns, as in Guttman’s (1954) simplex and circumplex models, or according to a given causal scheme, as in path analysis.

This paper states and proves the asymptotic properties of constrained generalized least squares estimators in the analysis of covariance structures in multiple populations with arbitrary distributions of variables. Asymptotic chi-square tests are also presented to permit evaluation of the goodness-of-fit of models. The currently known results for multiple population models based on variables that are multivariate normally distributed are obtained as a special case.

As a semi-active hydraulic device, the magnetorheological (MR) damper's damping characteristics will be influenced by temperature. In addition, the MR damper with gas accumulator usually shows asymmetric loop characteristics. To capture the hysteretic characteristics of MR dampers accurately, a developed model considering the temperature effects and asymmetric characteristics is proposed and analyzed. A typical mono-tube MR damper with gas accumulator is designed and tested under different sinusoidal excitations, currents and temperatures for obtaining the temperature-dependent and asymmetric damping characteristics. Based on experimental results, the proposed asymmetric model and conventional symmetric model are compared. The accurately asymmetric model is identified to calculate coefficients of current and temperature. The MR systems with symmetric model considering temperature effects, asymmetric model independent with temperature and asymmetric model considering temperature effects are simulated and compared under an H∞ control strategy. Results show that the proposed model is the best in accuracy and can be used for semi-active control system.

Problem statement: This study examines several stylized facts (heavy-tailedness, leverage effect and persistence) in volatility of stock price returns exploiting symmetric and asymmetric GARCH family models for Saudi Arabia. Approach: This study is carried out using closing stock market prices over 15 years covering the period 1 January 1994 to 31 March 2009. The sample period is divided into three sub-periods according to the local crisis in 2006. Results: The results reveal that asymmetric models with heavy tailed densities improve overall estimation of the conditional variance equation. Moreover, we find that AR (1)-GJR GARCH model with Student-t outperform the other models during and before the local crisis in 2006, while AR (1)-GARCH model with GED exhibits a better performance after the crisis. Furthermore, the findings reveal the existence of leverage effect at 1 percent significance level. Conclusion/Recommendations: Finally, the volatility persistent in the samples during and after crises decreases in all models under various distribution assumptions.

This paper analyzed the relationship among the differential diagnosis, treatment, and results for allergic rhinitis using the covariance structural model. The data were collected from 274 patients with suspected allergic rhinitis who visited the Otorlaryngology Department of the Paik Hospital during 1991-1993. After each patient's characteristics was categorized and combined into several common factors, covariance structure analysis was performed to analyze the structural relationships among the differential diagnosis, treatment, and results of treatment using the significant factors obtained from discriminant analysis. The significant characteristics influenced the diagnosis were the results of skin test from mite/animal, and from mugworts, the results from laboratory tests, rhinorrhea and sneezing, and nasal polyps. The significant characteristics that influenced the method of treatment were: nasal polyps, headache/general symptom, family history/medication, and septal deviation. Headache/general symptom was the only significantly influencing factor for the treatment results.

This paper examines the problem of model modification in covariance structure analysis. Two methods of model modification are studied: the Modification Index (MI) which suggests modifications based on the largest drop in the overall value of the test statistic, and the Expected Parameter Change Statistic (EPC) which suggests modifications based on the removal of large and interesting specifications errors. Following a detailed discussion of the theory behind the MI and EPC, these methods are studied and applied to two specifications of the Wisconsin status attainment model. Additionally, a standardized version of the EPC statistic (SEPC) is proposed and applied to one of these models. Results indicate that the MI tends to suggest freeing substantively implausible parameters. The EPC and SEPC, by contrast, suggest freeing substantively interesting parameters. Results are discussed in terms of the practice of covariance structure modeling.