Pairwise deletion for missing data in structural equation models: Nonpositive definite matrices, parameter estimates, goodness of fit, and adjusted sample sizes

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Abstract
The use of sample covariance matrices constructed with pairwise deletion for data missing completely at random (SPW) is addressed in a simulation study based on 3 sample sizes (n = 200, 500, 1,000) and 5 levels of missing data (%miss = 0, 1, 10, 25, and 50). Parameter estimates were unbiased, parameter variability was largely explicable in terms of the number of nonmissing cases, and no sample covariance matrices were nonpositive definite except when %miss was 50 and the sample size was 200. However, nominal χ2 test statistics (and, thus, fit indices based on χ2s) were substantially biased by %miss and its interaction with N. Corrected χ2s based on the minimum, mean, and maximum number of nonmissing cases per measured variables and cases per covariance term (NPC) reduced but did not eliminate the bias. Empirically derived power functions did substantially better but may not generalize to other situations. Whereas the minimum NPC (the default in the SPSS version of LISREL) is probably better than most simple alternatives in many applications, the problem of how to assess fit for models fit to SPWS has no simple solution; caution is recommended, and there is need for further research with more suitable methods for this problem.