matrixpls method for generic function residuals computes the residual
covariance matrix and various fit indices.
"residuals"(object, ..., observed = TRUE)matrixpls function.TRUE (default) the observed residuals from the outerEstim.model regressions
(indicators regressed on composites) are returned. If FALSE, the residuals are calculated
by combining inner, reflective, and formative as a simultaneous equations
system and subtracting the covariances implied by this system from the observed covariances.
The error terms are constrained to be uncorrelated and covariances between exogenous observed
values are fixed at their sample values.inner, outer, and indices elements
containing the residual covariance matrix of regressions of composites on other composites,
the residual covariance matrix of indicators on composites, and various indices
calculated based on the residuals.
reflective and inner models) as presented by Lohmöller (1989, ch 2.4) or
model implied residuals calculated by subtracting model implied covariance matrix from the
sample covariance matrix as done by Henseler et al. (2014). The root mean squared residual indices (Lohmöller, 1989, eq 2.118) are calculated from the
off diagonal elements of the residual covariance matrix. The
standardized root mean squared residual (SRMR) is calculated based on the standardized residuals
of the reflective model matrix.
Following Hu and Bentler (1999, Table 1), the SRMR index is calculated by dividing with $p(p+1)/2$, where $p$ is the number of indicator variables. In typical SEM applications, the diagonal of residual covariance matrix consistes of all zeros because error term variances are freely estimated. To make the SRMR more comparable with the index produced by SEM software, the SRMR is calculated by summing only the squares of off-diagonal elements, which is equivalent to including a diagonal of all zeros.
Two versions of the SRMR index are rovided, the traditional SRMR that includes all residual covariances, and the version proposed by Henseler et al. (2014) where the within-block residual covariances are ignored.
Hu, L., & Bentler, P. M. (1999). Cutoff criteria for fit indexes in covariance structure analysis: Conventional criteria versus new alternatives. Structural Equation Modeling: A Multidisciplinary Journal, 6(1), 1–55.
Lohmöller J.-B. (1989) Latent variable path modeling with partial least squares. Heidelberg: Physica-Verlag.
ave,
cr, effects.matrixpls,
fitSummary, fitted.matrixpls,
gof, htmt,
loadings, predict.matrixpls,
r2