These functions compute residual covariances, variance-standardized
residual covariances, and normalized residual covariances
for the observed variables in a structural-equation
model fit by sem.
# S3 method for sem
residuals(object, ...)
# S3 method for msem
residuals(object, ...)# S3 method for sem
standardizedResiduals(object, ...)
# S3 method for msem
standardizedResiduals(object, ...)
# S3 method for objectiveML
normalizedResiduals(object, ...)
# S3 method for objectiveGLS
normalizedResiduals(object, ...)
# S3 method for msemObjectiveML
normalizedResiduals(object, ...)
Each function returns a matrix of residuals.
an object inheriting from class sem or msem returned by the sem function.
not for the user.
John Fox jfox@mcmaster.ca
Residuals are defined as \(S - C\), where \(S\) is the sample covariance matrix of the observed variables and \(C\) is the model-reproduced covariance matrix. The standardized residual covariance for a pair of variables divides the residual covariance by the product of the sample standard deviations of the two variables, \((s_{ij} - c_{ij})/(s_{ii}s_{jj})^{1/2}\). The normalized residual is given by $$\frac{s_{ij}-c_{ij}} {[(c_{ii}c_{jj}-c_{ij}^2)/N^{*}]^{1/2}}$$ where \(N^{*}\) is the number of observations minus one if the model is fit to a covariance matrix, or the number of observations if it is fit to a raw moment matrix.
Bollen, K. A. (1989) Structural Equations With Latent Variables. Wiley.
sem