# Correction for measurement errors in the covariance matrix

The next step is the computation of the correction of the covariances for common method variance. As before, this will be done for the variables sharing the same method. The coefficients that should be corrected for common method variance are highlighted in the following table.

Table 6.2: The covariance matrix between the observed variables of ESS Round 6 for Great Britain indicating the correlations that had to be corrected for measurement error

The starting point for the computations of these corrections is the cmv of the standardized variables computed above in Table 4.4 and reproduced here in Table 6.3.

Table 6.3: Correction for common method variance for the standardized variables

To obtain the common method variance for the same unstandardized variables, these cmv have to be multiplied by the standard deviations for the specific variables.

 Unstandardized cmv = (Standardized cmv) sisj equation 6.1

From the data, we get:

sSatdem = 2.152, sFree = 1.879, sCritic = 1.946, sEqual = 2.768, sLRplace = 1.813, sInc = 2.986

The result of this computation is the common method variance of the unstandardized variables, which has to be subtracted from the estimated covariances for the same variables to obtain the corrected covariances. The different steps are presented in Table 6.4.

Table 6.4: Correction for common method variance for unstandardized variables

These results are introduced in the proper place in the covariance matrix. The resulting matrix is presented in Table 6.5.

Table 6.5: Covariance matrix corrected for common method variance

The last step is to correct the variances for all variables for measurement errors. This is done by substituting the originally estimated variances of all variables by the variances corrected for measurements errors. The variance coefficients that should be corrected in this case are highlighted in the following table.

Table 6.6: The covariance matrix between the observed variables of ESS Round 6 for Great Britain only corrected for common method variance and indicating the correlations to be corrected for measurement errors

Because 1-q2 is the proportion of error variance in the observed variables, the variances corrected for errors can be computed by multiplying the variances by the quality (from Table 3.3) of the variables. The result of these steps is presented in Table 6.7.

Table 6.7: Correction of the variances for measurement errors

The results are introduced in the diagonal in the covariance matrix. The result is presented in Table 6.8.

Table 6.8: Covariance matrix corrected for common method variance and random errors

Now that the covariance matrix has been corrected, the analysis with correction for measurement errors can start.

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