A comparison of inclusive and restrictive strategies in modern missing data procedures.

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(08/05/2024, 18:14:58)

“Two classes of modern missing data procedures, maximum likelihood (ML) and multiple imputation (MI), tend to yield similar results when implemented in comparable ways.” (Collins et al., 2001, p. 330)

“A simulation was presented to assess the potential costs and benefits of a restrictive strategy, which makes minimal use of auxiliary variables, versus an inclusive strategy, which makes liberal use of such variables. The simulation showed that the inclusive strategy is to be greatly preferred.” (Collins et al., 2001, p. 330)

“Missing data may bias parameter estimates, inflate Type I and Type II error rates, and degrade the performance of confidence intervals.” (Collins et al., 2001, p. 330)

“We do not consider ad hoc procedures such as listwise or pairwise deletion, substitution of means, regression predictions, or other forms of single imputation, which have been conclusively shown to perform poorly except under very restrictive or special conditions (Little & Rubin, 1987).” (Collins et al., 2001, p. 330)

“The attractive theoretical properties of these procedures, however, do not necessarily translate into good performance in real data analyses if they are poorly applied or if the mechanisms generating either the data or the missing values depart substantially from the underlying statistical assumptions.” (Collins et al., 2001, p. 330)

“The theoretical foundations of ML and MI share two common themes. First, they both regard the unknown data values as a source of random variation to be averaged over.” (Collins et al., 2001, p. 331)

“Second, ML and MI are both fully parametric, relying on joint probability models for the observed and unobserved data.” (Collins et al., 2001, p. 331)

“Despite the operational differences between ML and MI, there are many situations in which they lead to similar results.” (Collins et al., 2001, p. 336)

“To illustrate this point, we performed a preliminary study where we drew samples of X and Y and imposed missing values on Y in an MCAR fashion at rates of 25% and 50%. From each sample, we then calculated estimates and standard errors by an ML and an MI procedure. In ML, we maximized the bivariate normal likelihood based on X and the observed values of Y and obtained standard errors by inverting the observed information matrix (see Little & Rubin, 1987, Sections 6.2 and 6.3.1). In MI, we first created M = 10 imputations using the data augmentation procedure described by Schafer (1997, chapter 5) as implemented in NORM with the default noninformative prior; we then calculated parameter estimates and standard errors from each imputed data set by maximum likelihood based on the observed and imputed data and combined the results using Rubin's (1987) rules.” (Collins et al., 2001, p. 340)

“The results of this preliminary study are displayed in Table 1. The upper half of the table reports the standardized bias and RMSE of the parameter estimates, and the lower half reports the simulated coverage and average width of the nominal 95% intervals.” (Collins et al., 2001, p. 340)

“the RMSE and the average interval width both increase, reflecting the natural loss of information that occurs with higher rates of missing data.” (Collins et al., 2001, p. 340)

“Correspondence Between Maximum-Likelihood (ML) and Multiple Imputation (MI) When Data in Y Are Missing Completely at Random” (Collins et al., 2001, p. 341)

“Standardized bias and root-mean-square error” (Collins et al., 2001, p. 341) need to include this in simulation study

“ML and MI, we find the two methods practically indistinguishable. With 50% missingness, we see that the interval estimates from ML are slightly narrower, suggesting that ML is slightly more efficient than MI because the simulation aspect of MI introduces a minor amount of additional error. If the number of imputations were increased (e.g., to M = 20), these minor differences would vanish.” (Collins et al., 2001, p. 341)

“Whenever ML and MI use the same input data and model, the results from the two methodologies are practically indistinguishable. Differences do arise if the inputs vary. For example, if missing values are generated under one of the MAR mechanisms, and the cause of missingness, Z, is added to the imputation procedure but not to the ML procedure, then MI may tend to outperform ML. But this is less a comparison of MI versus ML than a comparison between an inclusive missing data strategy versus a restrictive one.” (Collins et al., 2001, p. 341)