residuals.sem {sem}R Documentation

Residual Covariances for a Structural Equation Model

Description

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.

Usage

residuals(object, ...)

standardized.residuals(object, ...)

standardized.residuals(object, ...)

normalized.residuals(object, ...)

normalized.residuals(object, ...)

Arguments

object an object of class sem returned by the sem function.
... not for the user.

Details

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

(s_{ij} - c_{ij})/[(c_{ii}c_{jj} - c_{ij}²)/N]^{1/2}

where N is the number of observations.

Value

Each function returns a matrix of residuals.

Author(s)

John Fox jfox@mcmaster.ca

References

Bollen, K. A. (1989) Structural Equations With Latent Variables. Wiley.

See Also

sem

Examples

    
# ------------- assumes that Duncan, Haller and Portes peer-influences model
# -------------     has been fit and is in sem.dhp.1

residuals(sem.dhp.1)

##                  ROccAsp        REdAsp       FOccAsp        FEdAsp
##    ROccAsp  4.156103e-07 -2.896368e-07 -2.866110e-02  9.102874e-02
##    REdAsp  -2.896368e-07 -1.541581e-06 -1.094841e-02 -2.379215e-02
##    FOccAsp -2.866110e-02 -1.094841e-02 -3.740356e-06 -9.564103e-07
##    
##    . . .
##    
##                      FIQ       FParAsp
##    ROccAsp  3.467853e-02 -3.187309e-02
##    REdAsp   4.878970e-03 -4.443480e-02
##    FOccAsp -7.354686e-03  2.488120e-02
##    FEdAsp   1.124604e-02 -3.690078e-02
##    RParAsp  2.775558e-17  5.551115e-17
##    RIQ      2.220446e-16  6.938894e-17
##    RSES     0.000000e+00 -1.387779e-17
##    FSES     1.110223e-16 -2.775558e-17
##    FIQ      4.440892e-16  1.110223e-16
##    FParAsp  1.110223e-16  4.440892e-16

normalized.residuals(sem.dhp.1) 

##                  ROccAsp        REdAsp       FOccAsp        FEdAsp
##    ROccAsp  5.330519e-06 -4.455587e-06 -4.898232e-01  1.567678e+00
##    REdAsp  -4.455587e-06 -1.977191e-05 -1.857670e-01 -4.071582e-01
##    FOccAsp -4.898232e-01 -1.857670e-01 -4.797271e-05 -1.460881e-05
##    
##    . . .
##    
##                      FIQ       FParAsp
##    ROccAsp  6.080514e-01 -5.747909e-01
##    REdAsp   8.518738e-02 -8.007295e-01
##    FOccAsp -1.180429e-01  4.374639e-01
##    FEdAsp   1.832159e-01 -6.514685e-01
##    RParAsp  5.019082e-16  1.000322e-15
##    RIQ      3.818356e-15  1.252092e-15
##    RSES     0.000000e+00 -2.506364e-16
##    FSES     1.931472e-15 -5.029583e-16
##    FIQ      5.695780e-15  1.971289e-15
##    FParAsp  1.971289e-15  5.695780e-15
      
standardized.residuals(sem.dhp.1)

##                  ROccAsp        REdAsp       FOccAsp        FEdAsp
##    ROccAsp  4.156103e-07 -2.896368e-07 -2.866110e-02  9.102874e-02
##    REdAsp  -2.896368e-07 -1.541581e-06 -1.094841e-02 -2.379215e-02
##    FOccAsp -2.866110e-02 -1.094841e-02 -3.740356e-06 -9.564103e-07
##    
##    . . .
##    
##                      FIQ       FParAsp
##    ROccAsp  3.467853e-02 -3.187309e-02
##    REdAsp   4.878970e-03 -4.443480e-02
##    FOccAsp -7.354686e-03  2.488120e-02
##    FEdAsp   1.124604e-02 -3.690078e-02
##    RParAsp  2.775558e-17  5.551115e-17
##    RIQ      2.220446e-16  6.938894e-17
##    RSES     0.000000e+00 -1.387779e-17
##    FSES     1.110223e-16 -2.775558e-17
##    FIQ      4.440892e-16  1.110223e-16
##    FParAsp  1.110223e-16  4.440892e-16
    

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