Multiple imputation on the other hand can include auxiliary variables that are not part of the analysis, in the imputation model. If the missingness depends on observed variables outside the multilevel model, the MAR assumption is violated for the specific analysis and valid results can no longer be guaranteed.
THREEWAY ANOVA SPSS CODE FULL
However, structural equation modeling is not the most obvious choice for carrying out ANOVA.Ī consequence of this limitation of full information maximum likelihood is that it will only be guaranteed to provide unbiased results if the missingness depends on variables within the multilevel model. An exception to this is full information maximum likelihood in a structural equation modeling context, in which auxiliary variables may be used as saturated correlates (see, Graham, 2003). Moreover, a disadvantage of full information maximum likelihood is that for handling the missing data it normally cannot include variables outside the multilevel model. It frequently happens that researchers are interested in mean differences among the different sexes, different SES’s, or different ethnicities. However, ANOVA is used in non-experimental research as well. The necessity of Multiple imputation in an ANOVA context may thus not seem obvious at first. In a repeated-measures ANOVA design missing data may be more common due to attrition but in this context researchers usually handle the missing data using multilevel with full information maximum likelihood (e.g., Hox, 2002 Snijders & Bosker, 1999). ANOVA is often used in experimental settings where a researcher has control over the situation, so that missing data will not occur frequently. Even SPSS 19.0, which performs Multiple imputation and pools results from multiply imputed data sets for several statistical techniques, does not provide pooled F-tests for any type of analysis of variance.Ī possible reason for this is that Multiple imputation may not often be considered necessary in ANOVA. For example, if people with high incomes tend to leave more questions open on the other variables than people with low incomes, people with the same income have the same probability of missing data on the other variables, and income is observed for all respondents, then the missingness for these questions is said to be missing at random (MAR), provided that income is included in the imputation modelĬombination Rules for (Repeated-Measures) ANOVAĪ problem of Multiple imputation in the context of analysis of variance is that to our knowledge the rules for pooling the significance tests of the M analyses of the completed data sets have never been explicitly discussed in the literature. In this case the missing data are considered to have occurred at random conditional on one or more observed variables. While Listwise deletion requires the data to be MCAR in order to obtain valid inferences, Multiple imputation will also lead to valid results if the missing data are missing at random (MAR Little & Rubin, 2002, p. Secondly, Multiple imputation makes less stringent assumptions about the missingness mechanism. Firstly, unlike Listwise deletion, Multiple imputation uses all available data and does not throw away any information. Multiple imputation has several advantages over Listwise deletion.