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Therefore, to evaluate multiple pollutant exposures in one model, we used a multiple imputation approach to impute the missing exposure values (Royston and White 2011).
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].
This was essentially the approach used in Henry and Boscoe 2008 [33], applying a multiple imputation approach to estimate expected rates of imputing to the correct Census units.
Comparison of the multiple imputation approach and the simpler method of imputing missing values as sex specific means showed no qualitative difference in the interpretation of the results between the two methods.
A multiple imputation approach was then used to assign income quintile, taking the average of the multiple imputed values, [ 38] for all DAs that did not have missing information on one or more of these socio-demographic variables and for all individuals who did not have a missing postal code.
The multiple imputation approach created 20 copies of the data in which missing values were imputed by chained equations.
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A hybrid of predictive mean matching, referred to as posterior predictive mean matching, proceeds first by obtaining parameter draws using classical multiple imputation approaches.
Following Honaker and King (2010) and Honaker (personal communcation, June 2011) the first step is to bootstrap the PISA and TALIS concatenated data set to create m versions of the incomplete data, where m ranges typically from 3 to 5 as in other multiple imputation approaches.
Adjustments to variances were carried out using standard multiple imputation approaches.
The exception to this is in the first of two multiple imputation approaches used.
Along with multiple imputation approaches, FIML is recommended as one of the best approaches to handling missing data [ 23, 24].
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