9:45 PM
Path Analysis with Latent Variable
Unregarded Lives
Since the early 1970s path analysis and causal modeling have gained acceptance in educational research as well as in research in the social and behavioral sciences. The procedures employed have been developed to incorporate three main problems. First, in educational situations there are many outcomes as well as many explanatory factors to be considered. The analysis of the measures employed to represent these outcomes and explanatory constructs is confounded by problems of multicollinearity, measurement error, and validity. Measurements made on variables gain in strength and consistency if they are combined as related indicators of an underlying latent construct. Second, theory in educational research has advanced during the latter half of the twentieth century so that it is now possible to develop strong models that can be submitted to examination, and the estimation of the magnitude of the parameters of such models is of considerable theoretical interest and practical significance. Third, it is widely recognized that not only should the direct effects of explanatory variables be taken into consideration, but the mediating and moderating effects of such variables, as well as spurious and disturbance effects, should be examined. Those three issues have led to the development of latent variable path analysis and structural equation modeling (see Path Analysis and Linear Structural Relations Analysis).
Two general approaches have emerged in this field for the examination of models advanced from theoretical considerations. The first builds on the use of least squares regression analysis to predict and explain the effects of variables on one or more criteria. The emphasis in this approach is prediction and to maximize the amount of variance of the criteria explained by the predictors. The second approach builds upon maximum likelihood estimation procedures. This involves obtaining estimates of free parameters of a model, subject to specified constraints imposed by the fixed parameters, so that the covariance matrix derived from the estimations made is as close as possible to the covariance matrix based on the hypothesized model. Thus, the estimates obtained of the free parameters of the model are such that the difference between the covariance matrices of the observed data and the model are minimized. In this second approach the methods of parameter estimation employed distinguish between procedures that are dependent on the assumption of multivariate normality and those that are not. Normal theory estimation is associated primarily with the LISREL series of programs that employ both maximum likelihood estimation procedures and generalized and weighted least squares procedures (see Path Analysis
and Linear Structural Relations Analysis) and the work of Jöreskog and Sörbom (1989).
Asymptotic distribution free estimation is employed when the data are not multivariate normal and is associated with the work of Browne (1982, 1984) and Muthén (1984, 1987). This entry restricts itself to consideration of the approach that employs partial least squares (PLS) regression analysis to maximize prediction and the explanation of variance which was developed by Wold (1977, 1982). This approach is less well-known than the other approaches outside of continental Europe, with the developmental work having been carried out in Sweden and Germany. It has the clear advantages that no assumptions need be made about the shape and nature of the underlying distributions of the observed and latent variables. This permits the analysis of data of dichotomous variables that are not associated with an underlying continuous distribution, which is a distinct advantage for a variable such as sex of student, or for the use of variables to represent countries in cross-national comparative studies. Furthermore, the approach recognizes that nearly all data employed in educational research involve the use of complex cluster sample designs. As a consequence, procedures of statistical significance, that are heavily dependent on testing for statistical significance with assumptions of simple random sampling and multivariate normal distributions, are largely inappropriate. Least squares regression procedures are known from extensive experience to be robust. However, there is no proof, beyond very simple models which are equivalent to principal components analysis and canonical correlation analysis, that convergence in the iterative procedures employed is complete. There is the everpresent danger of a false minimum in the test for the iterative procedure, and thus an erroneous solution in the estimation process. Consequently, some form of testing by replication would appear to be essential to validate the solutions obtained with partial least squares analysis.
It should be noted, however, that partial least squares path analysis as a technique is quick in analysis, and convergence generally takes place rapidly; is flexible in use in the testing of complex models; and is relatively easy for a novice, but who has sound theoretical perspectives, to employ. Furthermore, while greater stability of the solution is attained with large samples, it does not demand large samples for effective operation, as is explained below. The maximum likelihood estimation approach is considered elsewhere (see Path Analysis and Linear Structural Relations Analysis). Full Reading ...
Technorati Tags: SPSS, multivariate, statistics, path analysis with latent variableTwo general approaches have emerged in this field for the examination of models advanced from theoretical considerations. The first builds on the use of least squares regression analysis to predict and explain the effects of variables on one or more criteria. The emphasis in this approach is prediction and to maximize the amount of variance of the criteria explained by the predictors. The second approach builds upon maximum likelihood estimation procedures. This involves obtaining estimates of free parameters of a model, subject to specified constraints imposed by the fixed parameters, so that the covariance matrix derived from the estimations made is as close as possible to the covariance matrix based on the hypothesized model. Thus, the estimates obtained of the free parameters of the model are such that the difference between the covariance matrices of the observed data and the model are minimized. In this second approach the methods of parameter estimation employed distinguish between procedures that are dependent on the assumption of multivariate normality and those that are not. Normal theory estimation is associated primarily with the LISREL series of programs that employ both maximum likelihood estimation procedures and generalized and weighted least squares procedures (see Path Analysis
and Linear Structural Relations Analysis) and the work of Jöreskog and Sörbom (1989).
Asymptotic distribution free estimation is employed when the data are not multivariate normal and is associated with the work of Browne (1982, 1984) and Muthén (1984, 1987). This entry restricts itself to consideration of the approach that employs partial least squares (PLS) regression analysis to maximize prediction and the explanation of variance which was developed by Wold (1977, 1982). This approach is less well-known than the other approaches outside of continental Europe, with the developmental work having been carried out in Sweden and Germany. It has the clear advantages that no assumptions need be made about the shape and nature of the underlying distributions of the observed and latent variables. This permits the analysis of data of dichotomous variables that are not associated with an underlying continuous distribution, which is a distinct advantage for a variable such as sex of student, or for the use of variables to represent countries in cross-national comparative studies. Furthermore, the approach recognizes that nearly all data employed in educational research involve the use of complex cluster sample designs. As a consequence, procedures of statistical significance, that are heavily dependent on testing for statistical significance with assumptions of simple random sampling and multivariate normal distributions, are largely inappropriate. Least squares regression procedures are known from extensive experience to be robust. However, there is no proof, beyond very simple models which are equivalent to principal components analysis and canonical correlation analysis, that convergence in the iterative procedures employed is complete. There is the everpresent danger of a false minimum in the test for the iterative procedure, and thus an erroneous solution in the estimation process. Consequently, some form of testing by replication would appear to be essential to validate the solutions obtained with partial least squares analysis.
It should be noted, however, that partial least squares path analysis as a technique is quick in analysis, and convergence generally takes place rapidly; is flexible in use in the testing of complex models; and is relatively easy for a novice, but who has sound theoretical perspectives, to employ. Furthermore, while greater stability of the solution is attained with large samples, it does not demand large samples for effective operation, as is explained below. The maximum likelihood estimation approach is considered elsewhere (see Path Analysis and Linear Structural Relations Analysis). Full Reading ...
