MLR is similar to the full information maximum likelihood (FIML) method, in which missing data are not imputed, but parameters and standard errors are estimated directly using all the observed data [ 50].
Define (widehat {Y}_{i}^{(ell)}(mathcal {M}_{2}),i=11,ldots, n) to be the predicted outcomes computed in step (Q2) of the Q-learning algorithm using the ℓth imputed dataset and parameter (widehat {theta }_{2}^{(ell)}(mathcal {M}_{2})).
The mixed-effects models were fitted to the ten imputed datasets, and parameter estimates and standard errors were combined using the SAS function PROC_MIANALYZE.
Missing trait data (0 4.5% of data) were imputed by default parameter settings which uses an average of three nearest neighbor values.
Procedures that imputed catchability functional parameters from similar species were precise and median unbiased given the quantity and quality of data that are available for the Gulf of Mexico.
Thus, missing values were not imputed, while population parameters and standard errors were estimated based on the data available (e.g. Enders 2006).
39, 40 All the statistical analyses were performed within a structural equation modeling framework using the Mplus statistical package Version 6.12 with the standard MAR missing data method where missing values are not imputed, but instead parameters and standard errors are estimated from all available data.
The analytical strategy was implemented for two scenarios: cases with a complete response of the outcome parameter and, an imputed dataset in which missing values of the outcome parameter were imputed.
Since respondent age was missing for approximately 5% of the study sample, the logistic regression analyses were performed using a multiple imputation approach (10 imputed datasets constructed using Markov Chain Monte Carlo method) with parameter estimates adjusted using Rubin's rules [ 6].
Missing hourly data for PM2.5 and BC (but not other pollution or weather parameters) were imputed.
