residuals: Residual Covariances for a Structural Equation Model In sem1: Structural Equation Models

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

 ``` 1 2 3 4 5 6 7 8 9 10 11 12``` ```## S3 method for class 'sem' residuals(object, ...) standardized.residuals(object, ...) ## S3 method for class 'sem' standardized.residuals(object, ...) normalized.residuals(object, ...) ## S3 method for class 'sem' 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[ii] + 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.

Value

Each function returns a matrix of residuals.

Author(s)

John Fox [email protected]

References

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

`sem`
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68``` ``` ## Not run: # ------------- 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 ## End(Not run) ```