Structural Equation Modeling (SEM) Overview
Structural Equation Modeling (SEM) is a family of statistical techniques that incorporates and integrates path analysis and factor analysis. It has proven useful in solving many substantive research problems in the social and behavioral sciences (Jöreskog & Sörbom, 1989). These models have been utilized in the study of consumer behavior, studies of genetic and cultural effects, racial discrimination in employment, housing and earnings, evaluation of social programs, intergenerational occupational mobility and many other social and behavioral phenomena.
Many researchers consider SEM to be a second generation statistical tool following multiple regression, factor analysis, and path analysis. Goldberger (1973) outlined three situations in which multiple regression falls short of structural equations:
- when the observed variables contain measurement errors and the interesting relationship is among the true variables
- when there is interdependence or simultaneous causation among the observed response variables, and
- when important explanatory variables have not been included in the analysis
Experimentation in the social and behavioral sciences is rarely performed under controlled situations. Causal relationships may be established as null and alternative hypotheses, but may not be proven. Theories may be formulated in terms of theoretical constructs that are not directly measurable or observable. It may be more plausible to employ a number of indicators or symptoms to study these theoretical constructs. For example, the construct ability may not be directly observable, but may be measured indirectly by scores on standardized reading and math tests.
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SEM Model
SEM can accommodate issues of measurement and complex causal relationships. The model consists of two parts: the measurement model and the structural equation model. The measurement model specifies how the latent variables or hypothetical constructs are measured in terms of the observed variables. It also describes the measurement properties, the validities and reliabilities, of the observed variables. The structural equation model specifies the causal relationships among the lateen variables and describes the underlying effects and the amount of unexplained variance.
Structural Equation Modeling is best explained through an example. The model below tests whether the influence of college on locus of control for young American men has changed in the twenty years between the high school graduating class of 1972 and the high school class of 1992 (Wolfle & List, 2004).
FIGURE 1 Structural equation model of stability and change in locus of control.
Background
People who are self-directed and perceive themselves as the primary determiners of their own fate are said to hold internal control expectancies, whereas those who see chance as the primary determiners of their destiny are said to be externally controlled. These are the dimensions of a scale well known as locus of control (Lefcourt, 1976; Rotter, 1966).
Although locus of control is fairly stable over time, it has been found to change in experimentally induced settings as well as some naturally occurring situations. One of the most influential natural interventions is the attainment of higher status (Harvey, 1971). Another has been the acquisition of higher education. There is ample evidence, reviewed by Pascarella and Terenzini (1991), that locus of control increases during college; that is, expectancies become more internalized.
A structural equation model identical for both cohorts (high school seniors in 1972 and 1992) was employed. Of primary interest is the stability of the social-psychological construct of locus of control, and whether or not attendance at a postsecondary institution increases internal expectancies. For this part of the model, measures of locus of control prior to high school graduation were incorporated into the model, along with the subjects’ attendance at a postsecondary educational institution, followed by another measure of locus of control obtained after high school graduation. It is not enough, however, to examine the effects of prior measures of locus of control and the influence of postsecondary attendance without controlling for other antecedent variables. Thus, we introduced into the model two exogenous variables, ability and the educational level of parents. Both of these exogenous variables have been shown to influence education (e.g., Duncan, Featherman, & Duncan, 1972). Moreover, abil- ity is known to influence locus of control (Crandall, Katkovsky, & Crandall, 1965; Crandall, Katkovsky,&Preston, 1962), as is socioeconomic status of parents (Battle & Rotter, 1963; Franklin, 1963; Stephens & Delys, 1973; Strodtbeck, 1958). Ability and parental education were considered to be exogenous and were hypothesized to be causally prior to and predictive of locus of control measured before high school graduation, prior to attendance at a postsecondary institution, and locus of control measured subsequent to graduation from high school. The earlier measure of locus of control was hypothesized to influence college attendance and to influence the later measure of locus of control. College attendance, measured in a 4-year span for the 1972 class but only a 2-year span in 1992, was hypothesized to have a positive effect on the later measure of locus of control, reflecting a move toward more internal control expectancies.
These relations are shown in Figure 1, in which variable names enclosed in ellipses are latent constructs, such as locus of control, and capitalized variable names shown in rectangles are manifest variables. Thus, the latent construct considered to be parental education (ParEduc) is indexed by two manifest measures of father’s educational attainment (FAED) and mother’s educational attainment (MAED). Ability is shown to be the factor underlying manifest scores on a reading (READ) and mathematics (MATH) test. Locus of control was measured twice (Locus1 and Locus2) with three identically worded items at the two administrations. Postsecondary attendance (PSA) was a so-called dummy variable that was set to one if the respondent attended college and zero otherwise.
These 11 manifest variables and four latent constructs delimit the model, and the Relations among them are shown in Figure 1, in which straight arrows flow from antecedent variables to the variables they influence, and curved, double-headed arrows indicate covariances.
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