Asymptotic Covariance Matrix

Figure 1. Asymptotic covariance matrix
Asymptotic covariance matrix

As a by-product of the iteration process, the maximum likelihood methods provide this table containing the asymptotic variance-covariance matrix of the variance estimates. The asymptotic variance-covariance matrix can be used to calculate confidence intervals and to test hypotheses about the variance components. In this example, the variance for the estimated Var(STOREID) is 65787.226. The positive square root of this number gives the standard error for Var(STOREID), which is 256.49. Now you can calculate the 95% confidence interval. The upper confidence interval value is Var(STOREID)+1.9600 x standard error of Var(STOREID), or 670.469 + (1.96 x 256.49) = 1173.19 The lower confidence interval value is Var(STOREID) - 1.96 x Standard error of Var(STOREID), or 670.469 - (1.96 x 256.49) = 167.75. Therefore, the 95% asymptotic confidence interval for Var(STOREID) is (167.75, 1173.19).

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