|
Structural equation modeling (SEM) refers to a diverse set of unrelated computer algorithms and statistical methods that fit networks of constructs to data. SEM includes confirmatory factor analysis, path analysis, partial least squares path analysis, LISREL and latent growth modeling. The term should not be confused with Structural Modeling in economics. Structural equation models are often used to assess unobservable 'latent' constructs. They often invoke a measurement model that defines latent variables using one or more observed variables, and a structural model that imputes relationships between latent variables. The links between constructs of a structural equation model may be estimated with independent regression equations or through more involved approaches such as those employed in LISREL. Use of SEM is commonly justified in the social sciences because of its ability to impute relationships between unobserved constructs (latent variables) from observable variables. To provide a simple example, the concept of human intelligence cannot be measured directly as one could measure height or weight. Instead, psychologists develop theories of intelligence and write measurement instruments with items (questions) designed to measure intelligence according to their theory. They would then use SEM to test their theory using data gathered from people who took their intelligence test. With SEM, "intelligence" would be the latent variable and the test items would be the observed variables. A simplistic model suggesting that intelligence (as measured by five questions) can predict academic performance (as measured by SAT, ACT, and high school GPA) is shown below. In SEM diagrams, latent variables are commonly shown as ovals and observed variables as rectangles. The below diagram shows how error (e) influences each intelligence question and the SAT, ACT, and GPA scores, but does not influence the latent variables. SEM provides numerical estimates for each of the parameters (arrows) in the model to indicate the strength of the relationships. Thus, in addition to testing the overall theory, SEM therefore allows the researcher to diagnose which observed variables are good indicators of the latent variables. Various methods in structural equation modeling have been used in the sciences, business, education, and other fields. Use of SEM methods in analysis is controversial because SEM methods generally lack widely accepted goodness-of-fit statistics and most SEM software offers little latitude for error analysis. This puts SEM at a disadvantage with respect to systems of regression equation methods, though the latter are limited in their ability to fit unobserved 'latent' constructs. == History == Structural equation modeling, as the term is currently used in sociology, psychology, and other social sciences evolved from the earlier methods in genetic path modeling of Sewall Wright. Their modern forms came about with computer intensive implementations in the 1960s and 1970s. SEM evolved in three different streams: (1) systems of equation regression methods developed mainly at the Cowles Commission; (2) iterative maximum likelihood algorithms for path analysis developed mainly at the University of Uppsala by Karl Gustav Jöreskog; and (3) iterative canonical correlation fit algorithms for path analysis also developed at the University of Uppsala by Hermann Wold. Much of this development occurred at a time that automated computing was offering substantial upgrades over the existing calculator and analogue computing methods available, themselves products of the proliferation of office equipment innovations in the late 19th century. The text ''Structural Equation Modeling: From Paths to Networks'', New York: Springer, 2015 provides a complete history of the methods (Westland, 2015) Loose and confusing terminology has been used to obscure weaknesses in the methods. In particular, PLS-PA (the Lohmoller algorithm) has been conflated with partial least squares regression PLSR, which is a substitute for ordinary least squares regression and has nothing to do with path analysis. PLS-PA has been falsely promoted as a method that works with small datasets when other estimation approaches fail. Westland (2010) decisively showed this not to be true and developed an algorithm for sample sizes in SEM. Since the 1970s the 'small sample size' assertion has been know to be false; e.g. see (Dhrymes, 1972, 1974; Dhrymes & Erlat, 1972; Dhrymes et al., 1972; Gupta, 1969; Sobel, 1982) Both LISREL and PLS-PA were conceived as iterative computer algorithms, with an emphasis from the start on creating an accessible graphical and data entry interface and extension of Wright’s (1921) path analysis. Early Cowles’ Commission work on simultaneous equations estimation centered on Koopman and Hood’s (1953) algorithms from the economics of transportation and optimal routing, with maximum likelihood estimation, and closed form algebraic calculations, as iterative solution search techniques were limited in the days before computers. Anderson and Rubin (1949, 1950) developed the limited information maximum likelihood estimator for the parameters of a single structural equation, which indirectly included the two-stage least squares estimator and its asymptotic distribution (Anderson, 2005) and Farebrother (1999). Two-stage least squares was originally proposed as a method of estimating the parameters of a single structural equation in a system of linear simultaneous equations, being introduced by Theil (1953a, 1953b, 1961) and more or less independently by Basmann (1957) and Sargan (1958). Anderson’s limited information maximum likelihood estimation was eventually implemented in a computer search algorithm, where it competed with other iterative SEM algorithms. Of these, two-stage least squares was by far the most widely used method in the 1960s and the early 1970s. Systems of regression equation approaches were developed at the Cowles Commission from the 1950s on, extending the transportation modeling of Tjalling Koopmans. Sewall Wright, and other statisticians attempted to promote path analysis methods at Cowles (then at the University of Chicago). University of Chicago statisticians identified many faults with path analysis applications to the social sciences; faults which did not pose significant problems for identifying gene transmission in Wright's context, but which made path methods such as PLS-PA and LISREL problematic in the social sciences. Freedman (1987) summarized these objections in path analyses': “failure to distinguish among causal assumptions, statistical implications, and policy claims has been one of the main reasons for the suspicion and confusion surrounding quantitative methods in the social sciences” (see also Wold’s (1987) response). Wright’s path analysis never gained a large following among U.S. econometricians, but was successful in influencing Hermann Wold and his student Karl Jöreskog. Jöreskog's student Claes Fornell promoted LISREL in the US. Advances in computers made it simple for novices to apply structural equation methods in the computer-intensive analysis of large datasets in complex, unstructured problems. The most popular solution techniques fall into three classes of algorithms: (1) ordinary least squares algorithms applied independently to each path, such as applied in the so-called PLS path analysis packages which estimate with OLS; (2) covariance analysis algorithms evolving from seminal work by Wold and his student Karl Jöreskog implemented in LISREL, AMOS, and EQS; and (3) simultaneous equations regression algorithms developed at the Cowles Commission by Tjalling Koopmans. SEM path analysis methods are popular in the social sciences because of their accessibility; packaged computer programs allow researchers to obtain results without the inconvenience of understanding experimental design and control, effect and sample sizes, and numerous other factors that are part of good research design. Supporters say that this reflects a holistic, and less blatantly causal, interpretation of many real world phenomena – especially in psychology and social interaction – than may be adopted in the natural sciences; detractors suggest that many flawed conclusions have been drawn because of this lack of experimental control. Direction in the directed network models of SEM arises from presumed cause-effect assumptions made about reality. Social interactions and artifacts are often epiphenomena – secondary phenomena that are difficult to directly link to causal factors. An example of a physiological epiphenomenon is, for example, time to complete a 100 meter sprint. I may be able to improve my sprint speed from 12 seconds to 11 seconds – but I will have difficulty attributing that improvement to any direct causal factors, like diet, attitude, weather, etc. The 1 second improvement in sprint time is an epiphenomenon – the holistic product of interaction of many individual factors. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「structural equation modeling」の詳細全文を読む スポンサード リンク
|