Use of Multilevel Covariance Structure Analysis to Evaluate the Multilevel Nature of Theoretical Constructs
Farmer, G. Lawrence, Social Work Research
Hierarchical linear modeling (HLM) techniques have had significant impact on the evaluation of multilevel theoretical models in a variety of disciplines (that is, educational research, criminology, organizational psychology, economics, and family therapy; see Bryk & Raudenbush, 1987,1992; Draper, 1995; Hoeksma & Koomen, 1992; Hox & Kreft, 1994; Kreft & Leeuw, 1998; Moritz & Watson, 1998; Raudenbush, Brennan, & Barnett, 1995; Rogosa & Saner, 1995a, 1995b; Sampson, Raudenbush, & Earls, 1997; Thum, 1997; Vancouver, 1997). Despite its effect, HLM does not allow researchers to examine covariance structure models, such as factor analysis, path analysis, and structural equation models. Recognizing this limitation, researchers (for example, Harnqvist, 1978; Muthen, 1994; Muthen & Satorra, 1989) have extended HLM to the analysis of multilevel structural equation models, which is referred to as multilevel covariance analysis (MCA). This article illustrates the use of MCA by evaluating the multilevel nature of students' perceptions of school safety. The article provides readers with an overview of MCA, discuss its application to social work research, and demonstrates how Mplus 1.0, a structural equation model (SEM) program, can be used to analyze MCA models.
Multilevel Covariance Analysis--Definition and Uses
MCA represents an extension of hierarchical linear multivariate modeling to those situations that involve covariance structure models, such as factor analysis, path analysis, and structural equation modeling. The research and theory used to achieve this extension is based on the work of Muthen and colleagues (Muthen, 1994; Muthen & Muthen, 1998; Muthen & Satorra, 1989).
Given the hierarchical nature of social and organizational behavior, social workers have a keen interest in multilevel analysis techniques. For example, these techniques help social workers gain a better understanding of the effects of both community characteristics and individual characteristics on residents' perceptions of neighborhood safety (see, for example, Sampson et al., 1997).
MCA has several advantages and potential uses for social workers. Like HLM, the primary advantage is found in its ability to simultaneously estimate both within- and between-setting variance, and therefore more accurately estimate individual's outcomes within the setting (Muthen, 1994). MCA allows social workers to study the contribution to the variations in individuals' behavior that are associated with between-context variations and idiosyncrasies of individuals or their experiences. For example, it allows school social workers to examine the contribution that differences in school climate, compared to parent's cultural capital, play in student's academic progress. Like SEM, MCA makes use of two methodological traditions: Thurstonian factor analysis and simultaneous equation (path analytic) modeling (Kaplan & Elliott, 1997). These two methodologies allow social workers to develop statistical models that acknowledge the relationship among predictors and their direct and indirect relationships to outcome variables. In other words, MCA allows a social worker to examine the role that various community resources have on activism when both the relationships among community resources and individual's temperament are taken into account. In addition, MCA allows social workers to represent complex theoretical constructs as latent variables. For example, social workers studying sibling social behavior could represent social behavior as a latent variable, that is, composed of indicators of adaptive and maladaptive social functioning. In addition, the relationship among predictors of social functioning, for example, parental discipline and conflict resolution styles, could be studied.
Advantages of MCA
MCA seeks to incorporate SEM's ability to capture the complexity of multivariate relationships with HLM's ability to capture the nested nature of those relationships, both of which are needed to develop accurate statistical models of social phenomena. …