Worksheet Functions
Real Statistics Functions: The Real Statistics Pack provides the following array functions:
EM_MNORM_IMPUTE(R1, iter): outputs an array containing the data in R1 but with any missing data elements imputed.
EM_MNORM(R1, iter): outputs an array containing the covariance matrix and mean vector for the data in R1 where any missing data elements have been imputed.
iter = number iterations (default 200).
For Example 1 of Multivariate Normal Data with Multiple Missing Data Patterns, =EM_MNORM_IMPUTE(B4:D21) produces the output shown in CB4:CD21 of Figure 3 of Multivariate Normal Data with Multiple Missing Data Patterns. =EM_MNORM(B4:D21) produces a 4 × 3 array, the first three rows of which are the covariance matrix shown in range CF5:CH7 of Figure 3 on that webpage and the last row of which is the mean vector shown in CF3:CH3 of Figure 3 on that webpage.
Data Analysis Tool
Real Statistics Data Analysis Tool: The Real Statistics Resource Pack provides the EM for Missing Multivariate Normal Data data analysis tool.
To use this tool for Example 1 of Multivariate Normal Data with Multiple Missing Data Patterns, press Ctrl-m and select EM for Missing Multivariate Normal Data from the Misc tab (or from the menu of choices that appears if using the original user interface). Fill in the dialog box that appears as shown in Figure 1 and press the OK button.
Figure 1 – EM for Missing Multivariate Normal Data dialog box
The output is shown in Figure 2.
Figure 2 – Output from the data analysis tool
Examples Workbook
Click here to download the Excel workbook with the examples described on this webpage.
References
Efron and Hastie (2016) Computer age statistical inference. Cambridge University Press
Walczak, B., Massart, (2001) Dealing with missing data: Part II. Chemometrics and Intelligent Laboratory Systems 58 Ž2001. 29–42
https://www.academia.edu/59642526/Dealing_with_missing_data