The matrixpls
method for generic function residuals
computes the residual
covariance matrix and various fit indices.
# S3 method for matrixpls
residuals(object, ..., observed = TRUE)
matrixpls estimation result object produced by the matrixpls
function.
All other arguments are ignored.
If 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.
A list with three elements: 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.
The residuals can be
either observed residuals from the regressions of indicators on composites and composites
on composites
(i.e. the reflective
and inner
models) as presented by Lohm<U+00F6>ller (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 (Lohm<U+00F6>ller, 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 consists 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.
Henseler, J., Dijkstra, T. K., Sarstedt, M., Ringle, C. M., Diamantopoulos, A., Straub, D. W., <U+2026> Calantone, R. J. (2014). Common Beliefs and Reality About PLS Comments on R<U+00F6>nkk<U+00F6> and Evermann (2013). Organizational Research Methods, 17(2), 182<U+2013>209. 10.1177/1094428114526928
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<U+2013>55.
Lohm<U+00F6>ller J.-B. (1989) Latent variable path modeling with partial least squares. Heidelberg: Physica-Verlag.
Other post-estimation functions:
ave()
,
cei()
,
cr()
,
effects.matrixpls()
,
fitSummary()
,
fitted.matrixpls()
,
gof()
,
htmt()
,
loadings()
,
predict.matrixpls()
,
r2()