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The column labeled Population gives the population parameter values
that are given in the MODEL command, the MODEL COVERAGE
command, or using the COVERAGE option of the MONTECARLO
command. The column labeled Average gives the average of the
parameter estimates across the replications of the Monte Carlo
simulation study. These two values are used to evaluate parameter bias.
To determine the percentage of parameter bias, subtract the population
parameter value from the average parameter value, divide this number by
the population parameter value, and multiply by 100. The parameter
bias for the variance of i would be
100 (.4969 - .5000) / .5000 = -0.62.
This results in a bias of -0.62 percent.
The column labeled Std. Dev. gives the standard deviation of the
parameter estimates across the replications of the Monte Carlo
simulation study. When the number of replications is large, this is
considered to be the population standard error. The column labeled S.E.
Average gives the average of the estimated standard errors across
replications of the Monte Carlo simulation study. To determine standard
error bias, subtract the population standard error value from the average
standard error value, divide this number by the population standard error
value, and multiply by 100.
The column labeled M.S.E. gives the mean square error for each
parameter. M.S.E. is equal to the variance of the estimates across the
replications plus the square of the bias. For example, the M.S.E. for the
variance of i is equal to 0.0704 squared plus (0.4969 - 0.5) squared
which is equal to 0.00497 or 0.0050. The column labeled 95% Cover
gives the proportion of replications for which the 95% confidence
interval contains the population parameter value. This gives the
coverage which indicates how well the parameters and their standard
errors are estimated. In this output, all coverage values are close to the
correct value of 0.95.
The column labeled % Sig Coeff gives the proportion of replications for
which the null hypothesis that a parameter is equal to zero is rejected at
the .05 level (two-tailed test with a critical value of 1.96). The statistical
test is the ratio of the parameter estimate to its standard error, an
approximately normally distributed quantity (z-score) in large samples.