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I'm just wondering what is the difference between empirical = TRUE or FALSE when simulating normally distributed multivariate. Is it that when empirical = TRUE every simulated data will indicate the identical preset covariance matrix?

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    $\begingroup$ You could generate a tiny dataset and check in less time that you will have to wait for an answer... $\endgroup$
    – whuber
    Jun 2 at 15:13
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    $\begingroup$ Hi Whuber, thanks for your suggestion! I just forgot this very simple option ... I tried both argument settings. When empirical = TRUE, the generated dataset will exactly replicate the specified covariance matrix. When empirical = FALSE, the generated dataset would contain more or less sampling error as noted by Billy. But many thanks for all of the answers! $\endgroup$
    – Bo WANG
    Jun 3 at 15:20

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"If true, mu and Sigma specify the empirical not population mean and covariance matrix." (from mvrnorm documentation)

Meaning that if TRUE, the covariance matrix would be as specified

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  • $\begingroup$ A covariance must always be specified (this is the Sigma argument). The documentation just specifies that when empirical = TRUE then the provided mean and covariance matrix are sample-based estimates (i.e., derived empirically) whereas when empirical = FALSE the mean and covariance matrix are treated as known/true population parameters estimated without sampling error $\endgroup$
    – Billy
    Jun 2 at 22:39
  • $\begingroup$ Would you want to make that an answer and I can delete mine copied from the documentation? $\endgroup$
    – pep
    Jun 3 at 1:14
  • $\begingroup$ These answers are all valuable! I would rather retain all of them for those who may have similar questions. Many thanks to both of you! $\endgroup$
    – Bo WANG
    Jun 3 at 15:24

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