Two Recommended Solutions for Missing Data: Multiple Imputation and Maximum Likelihood

Two methods for dealing with missing data, vast improvements over traditional approaches, have become available in mainstream statistical software in the last few years.

Both of the methods discussed here require that the data are missing at random–not related to the missing values. If this assumption holds, resulting estimates (i.e., regression coefficients and standard errors) will be unbiased with no loss of power.

The first method is Multiple Imputation (MI). Just like the old-fashioned imputation methods, Multiple Imputation fills in estimates for the missing data.  But to capture the uncertainty in those estimates, MI estimates the values multiple times. Because it uses an imputation method with error built in, the multiple estimates should be similar, but not identical.

The result is multiple data sets with identical values for all of the non-missing values and slightly different values for the imputed values in each data set. The statistical analysis of interest, such as ANOVA or logistic regression, is performed separately on each data set, and the results are then combined. Because of the variation in the imputed values, there should also be variation in the parameter estimates, leading to appropriate estimates of standard errors and appropriate p-values.

Multiple Imputation is available in SAS, S-Plus, R, and now SPSS 17.0 (but you need the Missing Values Analysis add-on module).

The second method is to analyze the full, incomplete data set using maximum likelihood estimation. This method does not impute any data, but rather uses each cases available data to compute maximum likelihood estimates. The maximum likelihood estimate of a parameter is the value of the parameter that is most likely to have resulted in the observed data.

When data are missing, we can factor the likelihood function. The likelihood is computed separately for those cases with complete data on some variables and those with complete data on all variables. These two likelihoods are then maximized together to find the estimates. Like multiple imputation, this method gives unbiased parameter estimates and standard errors. One advantage is that it does not require the careful selection of variables used to impute values that Multiple Imputation requires. It is, however, limited to linear models.

Analysis of the full, incomplete data set using maximum likelihood estimation is available in AMOS. AMOS is a structural equation modeling package, but it can run multiple linear regression models.  AMOS is easy to use and is now integrated into SPSS, but it will not produce residual plots, influence statistics, and other typical output from regression packages.

Schafer, J. Software for Multiple Imputation
Hox, J.J. (1999) A Review of Current Software for Handling Missing Data, Kwantitatieve Methoden, 62, 123-138.
Allison, P. (2000). Multiple Imputation for Missing Data: A Cautionary Tale, Sociological Methods and Research, 28, 301-309.


Approaches to Missing Data: the Good, the Bad, and the Unthinkable
Learn the different methods for dealing with missing data and how they work in different missing data situations.

Reader Interactions


  1. Lau says

    Hi Karen,

    I have the same problem as LF. I’m doing an Exploratory Factor Analysis and just 27 of all 198 participants completed every item. So I did a multiple imputation. But now I’m struggeling how to run the factor analysis.

    For any advice I would be very very thankful!!

    • Karen Grace-Martin says

      Hi Lau,

      You don’t need Multiple Imputation for a factor analysis as factor analysis has no p-values, and that is where MI shines.

      I would do an EM estimate of the correlation matrix, then base the factor analysis on this matrix, rather than the raw data. This is something we show step-by-step in our Factor Analysis workshop, but it is a lot to explain. It’s easier in some software than others.

  2. hosein says

    hello – i am working in mineral exploration field -Do Cohen likelihood maximum Method for censored (missing) data replacement use for Geochemical data Now?

  3. Emily Stone says

    Hello! I am doing Asymptotically distribution free estimation in AMOS due to a data set that is not normal and has ordinal data. I am trying to determine how to handle missing data with this type of estimation in AMOS. Can you do multiple imputation in AMOS? Thank you so much!

  4. LF says

    Thanks Karen. Any help to the above question about the difference in MPlus and AMOS is much appreciated.

    I am struggling with dealing with missing data and doing an Exploratory Factor Analysis with a complete dataset. I thought perhaps I could do Multiple Imputation in SPSS and do the EFA there but I don’t think it is one of the supported analyses for pooled data. Any suggestions how to use MI in an EFA in SPSS or do I have to switch to another software? Any help is much appreciated.

    Thank you.

  5. LF says

    Hello Karen,
    In AMOS, when you use ML estimation with missing data, it says that the full sample is used. I’ve recently tried using MPlus and when it runs there, it says it takes out those cases from the analysis that doesn’t have any data on those variables. If it’s the same estimation method for missing data between the two packages, then why would it come out different. Is AMOS doing the same just not telling us it’s based on part of the sample?

    Thank you.

    • Karen says

      Hi LF,

      I don’t know MPlus, so I’m not sure what it is doing. AMOS isn’t dropping cases for having some missing data. I would suggest looking into the defaults in MPlus. Perhaps you just need to change an option.

      Any Mplus users want to chime in?

  6. Michael says

    Thanks Karen for the R free resource website..
    Hi Peng, If you are looking for some case studies in R with real world proven examples you can try for some free classes at
    there are practice tests also available to self assess your knowledge.

  7. kaushal Chaudhary says

    Hi Karen,

    SAS also used ml (maximum likelihood) or reml (restricted maximum likelihood) method for parameter estimation. Does this mean it also impute missing values in the data? So, if there are missing observartions, we do not have to impute. Thanks for your clarification.

    • Karen says

      Hi Kaushal,

      ML isn’t imputing. But yes, you can use SAS proc calis for missing predictors in a linear model or proc mixed for missing outcome values in a multilevel model.

  8. Dong says

    I am looking into how to run an MLE. Can SPSS 20 run an MLE in it’s easy-to-use pull-down menus or can this only be done via syntax? Thank you!

  9. peng says

    hi friends,
    I am new to R.I would like to know R-PLUS.Does any know where can I get the free training for R-PLUS.


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