# [R] covariance estimate in function sem (Lavaan)

Luna czhangster at gmail.com
Mon Jul 30 23:00:56 CEST 2012

```Dear R users,
I have a hard time interpreting the covariances in the parameter estimates
output (standardized), even in the example documented (PoliticalDemocracy).
Can anyone tell me if the estimated covariances are residual covariances
(unexplained by the model), or the covariances of the observable variables?
I haved checked the data and it does not look like the covariances of the
observable variables, however when I tried to find out using simulated data
( with correlated residuals) the estimates did not seem to be the covariance
of the residuals either (much much underestimated). Can anyone help?

Below is the output:

lavaan (0.4-14) converged normally after 70 iterations

Number of observations                            75

Estimator                                         ML
Minimum Function Chi-square                   38.125
Degrees of freedom                                35
P-value                                        0.329

Parameter estimates:

Information                                 Expected
Standard Errors                             Standard

Estimate  Std.err  Z-value  P(>|z|)   Std.lv  Std.all
Latent variables:
Ind60 =~
x1                1.000                               0.670    0.920
x2                2.180    0.139   15.742    0.000    1.460    0.973
x3                1.819    0.152   11.967    0.000    1.218    0.872
Dem60 =~
y1                1.000                               2.223    0.850
y2                1.257    0.182    6.889    0.000    2.794    0.717
y3                1.058    0.151    6.987    0.000    2.351    0.722
y4                1.265    0.145    8.722    0.000    2.812    0.846
Dem65 =~
y5                1.000                               2.103    0.808
y6                1.186    0.169    7.024    0.000    2.493    0.746
y7                1.280    0.160    8.002    0.000    2.691    0.824
y8                1.266    0.158    8.007    0.000    2.662    0.828

Regressions:
Dem60 ~
Ind60             1.483    0.399    3.715    0.000    0.447    0.447
Dem65 ~
Ind60             0.572    0.221    2.586    0.010    0.182    0.182
Dem60             0.837    0.098    8.514    0.000    0.885    0.885

Covariances:
y1 ~~
y5                0.624    0.358    1.741    0.082    0.624    0.296
y2 ~~
y4                1.313    0.702    1.871    0.061    1.313    0.273
y6                2.153    0.734    2.934    0.003    2.153    0.356
y3 ~~
y7                0.795    0.608    1.308    0.191    0.795    0.191
y4 ~~
y8                0.348    0.442    0.787    0.431    0.348    0.109
y6 ~~
y8                1.356    0.568    2.386    0.017    1.356    0.338

Variances:
x1                0.082    0.019                      0.082    0.154
x2                0.120    0.070                      0.120    0.053
x3                0.467    0.090                      0.467    0.239
y1                1.891    0.444                      1.891    0.277
y2                7.373    1.374                      7.373    0.486
y3                5.067    0.952                      5.067    0.478
y4                3.148    0.739                      3.148    0.285
y5                2.351    0.480                      2.351    0.347
y6                4.954    0.914                      4.954    0.443
y7                3.431    0.713                      3.431    0.322
y8                3.254    0.695                      3.254    0.315
Ind60             0.448    0.087                      1.000    1.000
Dem60             3.956    0.921                      0.800    0.800
Dem65             0.172    0.215                      0.039    0.039

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