Multiple population covariance structure analysis under arbitrary distribution theory

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.

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.

Analysis of Covariance Structures and Probabilistic Binary Choice Data

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.

AimLarge carnivore populations in Europe are expanding into new areas. This generates opportunities to improve their conservation status, but also creates a need to address new conflicts with humans. Species management units are constrained by administrative boundaries, but effective conservation and conflict management require a continental‐scale perspective on the opportunities and limitations for expanding populations. We assessed the conservation applicability and the uncertainties of transferring and up‐scaling local habitat suitability models from multiple populations in support of large‐scale, transboundary species conservation.LocationEurope.MethodsWe evaluated the accuracy of local population models to predict European brown bear (Ursus arctos) distribution patterns in other populations and at the continental scale. We also assessed the benefits of combining predictions from multiple local population models, and we evaluated the limitations of transferring models among populations and environmental settings. Last, we estimated the availability of unoccupied suitable habitats in Europe for colonization by expanding populations.ResultsWe found that integrating habitat predictions from multiple populations outperformed predictions from most individual populations. Results showed that about 37% of potentially suitable brown bear habitat in Europe remains unoccupied. As a synthesis of our results, we provide a set of predictive maps for the expansion of brown bears at the continental scale, including predictions from individual habitat models and a multimodel predictive map.Main conclusionsWe show that integrating habitat models from multiple populations provides richer and more reliable information on the distribution of suitable habitats in data deficient areas. This integration yields more reliable predictions compared to those based on individual populations and has important implications to manage species expansions and the associated conflicts. We also identified major limitations in transferring predictions among habitats; therefore, it is critical to enhance the reproducibility of habitat suitability models to apply local‐scale habitat studies to broader‐scale conservation practice.

Working within the framework of a confirmatory factor analytic (CFA) model, this study adds another dimension to construct validation of both the Beck Depression Inventory-II (BDI-II; Beck, Steer, & Brown, 1996) and a Chinese version of the BDI-II (C-BDI-II; Chinese Behavioral Sciences Society, 2000). Specifically, we tested for measurement equivalence of the C-BDI-II with the original BDI-II across Hong Kong (N = 1771) and American (N = 501) adolescents, respectively. Provided with evidence of measurement equivalence, we then tested for differences in the latent factor means (i.e., subscale levels) of three first-order factors of negative attitude, performance difficulty, and somatic elements and one second-order factor of general depression. All procedures were based on analyses of mean and covariance structures (MACS) that took into account both the incompleteness and non-normality of the data. Findings revealed sound evidence of measurement equivalence of the C-BDI-II and BDI-II factorial structures, and latent factor means that pointed to higher levels of depressive symptoms for Hong Kong adolescents than for their American counterparts.

This research expands the study of political skill, a construct developed in North America, to other cultures. We examine the psychometric properties of the Political Skill Inventory (PSI) and test the measurement equivalence of the scale in a non-American context. Respondents were 1511 employees from China, Germany, Russia, Turkey, and the United States. The cross-cultural generalizability of the construct is established through consistent evidence of multi-group invariance in an increasingly stringent series of analyses of mean and covariance structures. Overall, the study provides systematic evidence that political skill can be treated as a stable construct among diverse cultural groups. Furthermore, our findings demonstrate that translated PSI measures operationalize the construct similarly. With some exceptions, the item loadings and intercepts are invariant for the US and non-US responses, suggesting partial measurement equivalence. After verifying the accuracy of item translation, we conclude that any differences can be explained by variation in the cultural value of uncertainly avoidance and cultural differences on a low-to-high context continuum. Detected dissimilarities are addressed, and some suggestions regarding the correct use across borders of the instrument by managers and researchers are provided.

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.

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