solve function).Matrixpls estimates models where sets of indicator variables are combined as weighted composites. These composites are then used to estimate a statistical model describing the relationships between the composites and composites and indicators. The most typical use for these method is approximating structural equation models with latent variables.
The estimation algoritm consists of two steps. In the first step the indicators are combined as weighted composites and in the second step the composites are used to estimate a statistical model. The indicator weights are determined with the following iterative algorithm.
S,
estimation weight matrix W, and composite variable model matrix inner.mod.
The function returns an inner weight matrix E.
Outer Outer estimation function is applied to the data covariance matrix S,
estimation weight matrix W, inner weight matrix W, and weight model matrix W.mod.
The function returns a weight matrix W.
Convergence Convergence check function is applied to the weight matrix W before and
check after outer estimation. This function returns a scalar that is compared
against the tolerance value. If the scalar is smaller than the tolerance
value, the algorithm converges. Otherwise, a new iteration is started.
}
After the weights have been calculated, the parameter estimator function is applied to the data covariance matrix S, the weight matrix W, and model object.
The parameter matrices are constructed in such a way that they can be interpreted either as a set of multiple regression equations where the variables on rows are regressed on variables on columns or as covariance matrices.
S k x k Covariance matrix of the observed variables.
W l x k Outer weight matrix. Returned by outer estimator.
E l x l Inner weight matrix. Returned by inner estimator.
Covariance matrix of the composites formed by combining
C l x l the observed variables into weighted composites using the
weight matrix W. Calculated as W %*% S %*% t(W).
Covariance matrix between composites and indicators.
IC l x k Calculated as W %*% S after outer estimation or
as IC <- E %*% W %*% S after inner estimation.
}
Where k is the number of observed variables and l is the number of composites.
Dijkstra, T. K. (1983). Some comments on maximum likelihood and partial least squares methods. Journal of Econometrics, 22(1-2), 67–90.
Lohmöller, J. B. (1989). Latent variable path modeling with partial least squares. Physica-Verlag.
Hwang, H., & Takane, Y. (2004). Generalized structured component analysis. Psychometrika, 69(1), 81–99. doi:10.1007/BF02295841
Rönkkö, M., & Evermann, J. (2013). A Critical Examination of Common Beliefs About Partial Least Squares Path Modeling. Organizational Research Methods, 16(3), 425–448. doi:10.1177/1094428112474693
plspm, sempls,
sim