The EM algorithm and mixed (random effects) model approaches to missing values
Multivariate procedures usually only use complete cases giving an accompanying loss of power. There are two ways to address this: estimating missing values using existing data (e.g. using the variable means) or using random effect models.
Howell gives a comprehensive and accessible overview and illustration of all these techniques [http://www.uvm.edu/~dhowell/StatPages/More_Stuff/Missing_Data/Missing.html here.] This is well worth a read for getting a feel for the issues involved and how they can be addressed!
Howell, in particular, suggests that a better way to estimate missing values on a variable is by using a more complex approach than variable means, namely the EM algorithm. This can be used under analyse>missing value analysis from version 13 of SPSS or using PROC MI and PROC MIANALYSE in SAS or stand-alone freeware (NORM) which can be downloaded from [http://www.stat.psu.edu/~jls/misoftwa.html here.] The EM algorithm produces a 'filled in' (or imputed) data set with values estimated using the original data replacing the original missing values. The analysis can then be carried out using this filled-in data set. Note each missing data estimate in addition to using parameter estimates based on the original data also adds in a random error term which means we get different missing values each time we perform the estimation to account for sampling variability.
To account for sampling variability Howell points out that multiple imputations are required. In practice this means that multiple 'filled in' data sets (typically 3 to 5 data sets) should be analysed to assess the consistency of the results across missing value estimates. Howell illustrates using the NORM downloadable software to obtain an overall result for multiple regression coefficients pooling over 5 imputated data sets and suggests a similar pooled approach can be used for other estimates provided they have their standard errors. However he prefers using random effects models for missing values in analysis of variance and is not sure how to combine results from these. Part of the problem is that effects which do not have a single degree of freedom will be represented by more than one model estimate.
He does notice in a further example that the F tests on each of three imputed data sets from a repeated measures analysis of variance are very similar. PROC MIANALYSE in SAS also combines results from multiple imputations. There is no such facility for combining results in SPSS (upto version 16 at least).
Random effect models, unlike the standard 'fixed effects' analysis of variance, use all cases irrespective of whether they contain missing values and therefore have a unique solution. These are available for use in most statistical packages such as SPSS (MIXED), SAS (MIXED) and R (LME). They are particularly useful for analysis of variance where it is wished to generalise results from the factors considered.
In the unusual situation where missingness is due to an impossibility of an event occurring e.g. asking a person about their sibling's occupation when they have no siblings or are not 'in touch' with them then a more dummy adjustment procedure (Cohen and Cohen, 2003) may suffice (Allison, 2002). This procedure simply uses the variable mean to fill in the missing value but then includes a variable as a covariate in the analysis taking a value of 0 except where a missing value occurs where it takes a value of '1'.
References
Allison P (2002) Monograph on Missing Data (Sage paper # 136) .
Cohen, J and Cohen, P (2003) Applied Multiple Regression/Correlation Analysis for the Behavioral Sciences. Lawrence Erlbaum:London.
Graham, JW (2009) [attachment:graham.pdf Missing Data Analysis: Making It Work in the Real World] Annual Review of Psychology 60 pp. 549-576. A paper found to be very useful for explaining practical issues and implementation associated with missing values. This paper is also available for downloading from [http://arjournals.annualreviews.org/doi/abs/10.1146/annurev.psych.58.110405.085530 here.]
Howell, D.C. (2008) The analysis of missing data. In Outhwaite, W. & Turner, S. Handbook of Social Science Methodology. London: Sage.
Schafer and Olson (1998) Multiple imputation for multivariate missing-data problems: A data analyst’s perspective. Multivariate Behavioral Research, 33 545–571.