IBM® SPSS® Amos™ 28

The following description of Bayesian imputation assumes that you have requested 7 completed datasets

and that the settings in the Options window have been left at their default values.

Amos's algorithm for Bayesian imputation uses an imputation workspace that has room for slightly more than 10,000 MCMC observations (10,000 being the value specified for Number of observations).

The actual size of the imputation workspace is determined as follows. First, the number of observations kept in the workspace is increased by the smallest amount necessary to make it an integral multiple of 7 (the Number of completed datasets). In this case the size of the imputation workspace is increased to 10,003 = 7 * 1429. After that, the size of the imputation workspace is increased further to make room for a small number of burn-in observations. The number of burn-in observations is either 6 or 7, chosen so that there will be an even number of MCMC observations in the imputation workspace. Here the final size of the imputation workspace is 10,010=10,003+7 observations.

When you click the Impute button, 10,010 MCMC observations are generated, filling up the imputation workspace. The autocorrelation function is then estimated for each parameter. If the autocorrelation for each parameter falls below the threshold specified by Maximum autocorrelation for some lag of 1428 or less, then observations 1436, 2865, 4294, 5723, 7152, 8581 and 10010 are considered to be effectively uncorrelated, and sampling terminates. If the 10,010 observations do not meet the autocorrelation criterion, every odd-numbered observation is discarded, leaving 5,005 observations. Sampling resumes, discarding one out of every two observations until until the number of observations in the imputation workspace again reaches 10,010. If the autocorrelation criterion is met at that point, sampling terminates. Otherwise, the odd-numbered observations are discarded and sampling resumes again (discarding three out of every four observations). The process of thinning out the workspace by discarding every odd numbered observation and then filling up the workspace by further sampling continues until the autocorrelation criterion is met.

After the autocorrelation criterion is met, the following observations (using the notation in How the MCMC algorithm works) are treated as uncorrelated.

.

Now write the mean and covariance matrix of the variables in the model as and so as to show that they are functions of the model parameters. Then from observation 1436 a completed dataset is created by setting and , and drawing at random from the conditional distribution of the unobserved values given the observed values. In the same way, a completed dataset is created from observation 2865, 4294, 5723, 7152, 8581 and 10010.