Analysis of Covariance Structures

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.

Covariance structure analysis is a statistical technique in which a theoretical model, or a covariance structure, is constructed, and the covariances predicted by the theoretical model are compared with those of the observed data. The adequacy of the model in reproducing the sample covariances is reflected by estimates of the parameters of the model and measures indicating the goodness of fit. Covariance structure analysis is frequently used for analyzing data obtained in nonexperimental or quasiexperimental research, but is seldom employed in experimental research. In this paper, the applicability of this technique in experimental research is discussed and illustrated by covariance structure analysis studies in which two models for word translation—the symmetrical model and the asymmetrical model—are described, refined, and contrasted.

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.

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.

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.

The principal aim of the book is an exposition of methods for the analysis of clustered observations; the secondary one is to provide substantive interest as a measure of uncertainty, quality, equity, or generally, as a summary of differences among experimental or observational units. Another goal is to make a balanced presentation of the advantages and limitations of these methods The examples used for illustration of methods are not drawn exclusively from the social sciences. Although models are motivated mainly by social science problems, they are applicable in a variety of situations involving (imperfect) replication, such as repeated measurements, repeated experiments, logitudinal analysis, and analysis of covariance structures in general.

ABSTRACTFocusing has been used in various fields. However, there are few studies on focusing in the field of sports. Correlations between focusing attitudes and psychological competitive abilities were investigated to provide psychological support for athletes by focusing. Public self-consciousness was considered a parameter mediating between focusing attitudes and psychological competitive abilities. University student-athletes (N = 180; 111 men and 69 women) completed three questionnaires. Path analysis was conducted using covariance structure analysis. Results suggested that focusing attitudes contributed to improving psychological competitive abilities. Regarding the correlation with public self-consciousness, it was predicted that acquiring an attitude of ‘keeping a distance from experiencing (a focusing attitude)’ would reduce anxiety and fear toward evaluation from others, leading to ‘mental stability and concentration (a psychological competitive ability).’ The results indicated that taking an attitude of ‘accepting and acting from experiencing (a focusing attitude),’ contributed to an improvement in ‘self-confidence (a psychological competitive ability),’ leading to positive effects on other factors related to psychological competitive abilities. Based on the above results, it was indicated that acquiring focusing attitudes would increase athletes’ self-confidence and contribute to improvements in overall psychological competitive abilities. The possibility of psychological support for athletes using focusing is suggested.

BackgroundOccupational mental health, work environment, sleep health, presenteeism, and loss of work productivity caused by health problems are all public health concerns. Although sleep affects mental health and presenteeism, the associations between sleep disturbance, job stressors, stress responses, and presenteeism have remained unclear. We hypothesized that job stressors affect the presenteeism of office workers through sleep disturbance and analyzed the association among these factors.Subjects and MethodsIn 2017, a cross-sectional survey of adult office workers was performed. A total of 2899 subjects who provided written consent were included in the analysis. The survey collected demographic information, as well as the Work Limitation Questionnaire (WLQ), Pittsburgh Sleep Quality Index (PSQI), and Brief Job Stress Questionnaire (BJSQ). Associations between each of the variables were analyzed by path analysis (covariance structure analysis). This study was approved by the Ethics Committee of Tokyo Medical University.ResultsThe path analysis demonstrated that job stressors, psychological and physical stress response (PPSR) in the BJSQ, and sleep disturbance in the PSQI had direct effects on presenteeism in the WLQ. Both job stressors and social support in the BJSQ indirectly affected presenteeism through effects on sleep disturbance and PPSR. Sleep disturbance indirectly affected presenteeism via PPSR. This model accounted for the variation of presenteeism (R2 = 0.322).ConclusionIn the workplace, job stressors and low social support increase presenteeism through psychological and physical stress responses, as well as sleep disturbance. Evaluating and resolving work problems and sleep disturbance would hence be beneficial from the aspects of public health and socioeconomics.

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.

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.

On asymptotic distributions of normal theory MLE in covariance structure analysis under some nonnormal distributions

A Bayesian approach to the testing of competing covariance structures is developed. The method provides approximate posterior probablities for each model under consideration without prior specification of individual parameter distributions. The method is based on ayesian updating using cross-validated pseudo-likelihoods. Given that the observed variables are the samefor all competing models, the approximate posterior probabilities may be obtained easily from the chi square values and other known constants, using only a hand calculator. The approach is illustrated using and example which illustrates how the prior probabilities can alter the results concerning which model specification is preferred.