residuals.matrixpls: Residual diagnostics for matrixpls results

In matrixpls: Matrix-Based Partial Least Squares Estimation

Description

The matrixpls method for generic function residuals computes the residual covariance matrix and various fit indices.

Usage

## S3 method for class 'matrixpls'
residuals(object, ..., observed = TRUE)

Arguments

object	matrixpls estimation result object produced by the matrixpls function.
...	All other arguments are ignored.
observed	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.

Details

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 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 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.

Value

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.

References

Henseler, J., Dijkstra, T. K., Sarstedt, M., Ringle, C. M., Diamantopoulos, A., Straub, D. W., … Calantone, R. J. (2014). Common Beliefs and Reality About PLS Comments on Rönkkö and Evermann (2013). Organizational Research Methods, 17(2), 182–209. doi: 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), 1–55.

Lohmöller J.-B. (1989) Latent variable path modeling with partial least squares. Heidelberg: Physica-Verlag.

See Also

Other post-estimation functions: ave(), cei(), cr(), effects.matrixpls(), fitSummary(), fitted.matrixpls(), gof(), htmt(), loadings(), predict.matrixpls(), r2()

matrixpls documentation built on April 28, 2021, 5:07 p.m.