Performing Likelihood Ratio Tests with Multiply-Imputed Data Sets

Abstract

JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org.. Biometrika Trust is collaborating with JSTOR to digitize, preserve and extend access to Biometrika. SUMMARYExisting procedures for obtaining significance levels from multiply-imputed data either (i) require access to the completed-data point estimates and variance-covariance matrices, which may not be available in practice when the dimensionality of the estimand is high, or (ii) directly combine p-values with less satisfactory results. Taking advantage of the well-known relationship between the Wald and log likelihood ratio test statistics, we propose a complete-data log likelihood ratio based procedure. It is shown that, for any number of multiple imputations, the proposed procedure is equivalent in large samples to the existing procedure based on the point estimates and the variance-covariance matrices, yet it only requires the point estimates and evaluations of the complete-data log likelihood ratio statistic as a function of these estimates and the completed data. The proposed procedure, therefore, is especially attractive with highly multiparameter incomplete-data problems since it does not involve the computation of any matrices.

Alternative Multiple Imputation Inference for Mean and Covariance Structure Modeling

“…Second, even setting the cumbersomeness aside, the standard procedure does not provide an overall model fit statistic, which forms the basis of model fit assessment in mean and covariance structure modeling. Current suggestions (e.g., Allison, 2001;Meng & Rubin, 1992) are either not accurate enough (see e.g., Allison, 2003) or require computations that are cumbersome and nonstandard, at least insofar as mean and covariance structure modeling is concerned. Moreover, the performances of those suggestions have not been evaluated in the context of mean and covariance structure modeling.…”

Large tests of independence in incomplete two-way contingency tables using fractional imputation

“…proposed a Wald test statistic. Meng and Rubin (1992) proposed likelihood ratio tests with F reference distributions.…”

“…Since it is easy in these examples to create many more imputations than the dimension of the parameters, it is possible to conduct a Wald test based on the MI estimates of parameters and the MI estimate of the variance-covariace matrix for the estimates; see, for example, Meng and Rubin (1992). Meng and Rubin (1992) introduced a likelihood ratio based procedure and applied it to a three-way partially classified table of counts. introduced a procedure for combining results from either Wald test statistics or LRT statistics.…”

“…The third procedure requires only the test statistics from appling the test procedure separately to the multiply imputed tables. As such, it is expected that the third procedure will be less powerful than the others (Meng and Rubin, 1992). The second procedure requires a level of information between the other two.…”

Modeling Earnings Measurement Error: A Multiple Imputation Approach

“…al. (1991) and Meng and Rubin (1992) can be consulted for more accurate alternative approximations and test statistics for small values of M.…”