A Multivariate Multilevel Gaussian Model with a Mixed Effects Structure in the Mean and Covariance Part A Multivariate Multilevel Gaussian Model with a Mixed Effects Structure in the Mean and Covariance Part Baoyue Li, Luk Bruyneel and Emmanuel Lesaffre Biostatistics department, Erasmus MC Bayes 2013 May 23, 2013 EMC-Logo Bayes 2013 May 23, 2013 1 / 17
A Multivariate Multilevel Gaussian Model with a Mixed Effects Structure in the Mean and Covariance Part Outline Data description and research questions Multivariate multilevel factor model Bayesian estimation and identification issue Application to RN4CAST data Some future work EMC-Logo Bayes 2013 May 23, 2013 2 / 17
A Multivariate Multilevel Gaussian Model with a Mixed Effects Structure in the Mean and Covariance Part Data description and research questions The RN4CAST project Registered Nurse Forecasting project Nurse survey across Europe (2009-2011) 33,731 nurses in 2,169 nursing units in 486 hospitals in 12 countries Study the impact of system-level features of nursing care on nurse wellbeing and patient safety outcomes Burnout, job satisfaction, turnover, etc. EMC-Logo Bayes 2013 May 23, 2013 3 / 17
A Multivariate Multilevel Gaussian Model with a Mixed Effects Structure in the Mean and Covariance Part Data description and research questions Three dimensions of burnout Emotional exhaustion (EE) Depersonalization (DP) Reduced personal accomplishment (PA) Measured using the 22-item Maslach Burnout Inventory Q: ”I feel emotionally drained from my work” A: 0-never; 1-a few times a year or less; ...; 6-every day Sum of all items within each dimension as the outcome EMC-Logo Bayes 2013 May 23, 2013 4 / 17
A Multivariate Multilevel Gaussian Model with a Mixed Effects Structure in the Mean and Covariance Part Data description and research questions 30 50 25 40 Reduced personal accomplishment 40 Emotional exhaustion 20 Depersonalization 30 30 15 20 20 10 10 10 5 0 0 0 BE UK FI DE GR IE NO PL ES CH NL BE UK FI DE GR IE NO PL ES CH NL BE UK FI DE GR IE NO PL ES CH NL Figure : Distribution of burnout at each country EMC-Logo Bayes 2013 May 23, 2013 5 / 17
A Multivariate Multilevel Gaussian Model with a Mixed Effects Structure in the Mean and Covariance Part Data description and research questions Some covariates: Working experience (yrs) Work environment Hospital size and nursing unit size Teaching hospital, technology hospital Type of nursing unit (surgical or medical) EMC-Logo Bayes 2013 May 23, 2013 6 / 17
A Multivariate Multilevel Gaussian Model with a Mixed Effects Structure in the Mean and Covariance Part Data description and research questions Research questions: Relationship of burnout and covariates at different levels If the correlations among the 3 burnout dimensions remain the same (check for inter cultural differences) At each level For different levels of covariates EMC-Logo Bayes 2013 May 23, 2013 7 / 17
A Multivariate Multilevel Gaussian Model with a Mixed Effects Structure in the Mean and Covariance Part Multivariate multilevel factor model Basic idea: combining two models: Gaussian multivariate mixed model: to estimate the mean structure Factor model: rebuild COV via the factor loadings Add covariates Add random effects EMC-Logo Bayes 2013 May 23, 2013 8 / 17
A Multivariate Multilevel Gaussian Model with a Mixed Effects Structure in the Mean and Covariance Part Multivariate multilevel factor model The 2-level single-factor model: y ij = β 0 + β 1 x ij + u j + δ ij , δ ij = ( β ∗ 0 + β ∗ ij + u ∗ j ) F ij + ε ij 1 x ∗ u j ∼ N ( 0 , Σ u ) , j ∼ N ( 0 , Σ ∗ u ) , u ∗ F ij ∼ N ( 0 , 1 ) , ε ij ∼ N ( 0 , Σ ε ) The conditional COV (on random effects): j ) T Σ = Σ ε + ( β ∗ 0 + β ∗ ij + u ∗ j )( β ∗ 0 + β ∗ ij + u ∗ 1 x ∗ 1 x ∗ EMC-Logo Bayes 2013 May 23, 2013 9 / 17
A Multivariate Multilevel Gaussian Model with a Mixed Effects Structure in the Mean and Covariance Part Multivariate multilevel factor model 5 0.90 4 Covariance Correlation 3 0.80 2 0.70 1 −2 −1 0 1 2 −2 −1 0 1 2 Covariate Covariate Figure : Relationship between covariance/correlation and covariate EMC-Logo Bayes 2013 May 23, 2013 10 / 17
A Multivariate Multilevel Gaussian Model with a Mixed Effects Structure in the Mean and Covariance Part Bayesian estimation and identification issue Frequentist method may not be efficient High dimensionality of random effects - Numeric problem for integration Lack of software/packages to model COV appropriately Bayesian method Avoid numeric problem by MCMC sampling Quite flexible for complex modeling EMC-Logo Bayes 2013 May 23, 2013 11 / 17
A Multivariate Multilevel Gaussian Model with a Mixed Effects Structure in the Mean and Covariance Part Bayesian estimation and identification issue Identification issue in Bayesian estimation ”flipping states” issue: Λ F ⇐ ⇒ ( − Λ)( − F ) A lesser problem for models without random effects ( u ∗ j ) in loadings This issue will be mixed up with the random effects, MCMC run will never converge Solution: assign a mixture normal distribution to the loadings EMC-Logo Bayes 2013 May 23, 2013 12 / 17
A Multivariate Multilevel Gaussian Model with a Mixed Effects Structure in the Mean and Covariance Part Bayesian estimation and identification issues 0.4 0.3 0.2 0.1 0.0 − β β * * 0 -6 -4 -2 0 2 4 6 0 0 = β + * * L u j 0 j x Figure : The 2 normal distributions that form the mixture distribution for the factor loadings EMC-Logo Bayes 2013 May 23, 2013 13 / 17
A Multivariate Multilevel Gaussian Model with a Mixed Effects Structure in the Mean and Covariance Part Application to RN4CAST data 3-variate 4-level factor model Include all covariates in both the mean and loadings Random intercept at each level in both the mean and loadings Computational details dclone package in R, 3 chains using 3 cores 70,000 burnin + 30,000 iterations Convergence: Brooks-Gelman-Rubin plots, Rhat < 1 . 1; MCMC error / SD < 5 % Model comparison: DIC (defined by Martyn Plummer) and PSBF EMC-Logo Bayes 2013 May 23, 2013 14 / 17
A Multivariate Multilevel Gaussian Model with a Mixed Effects Structure in the Mean and Covariance Part Application to RN4CAST data Better work environment, more working experience lead to less burnout Nurses working in a surgical nursing unit are more inclined to burnout than in a medical nursing unit. Adding covariates and random effects to COV improved the model fit largely COV is different among countries, hospitals and nursing units The more experienced the nurse is, the more correlation between EE and PA EMC-Logo Bayes 2013 May 23, 2013 15 / 17
A Multivariate Multilevel Gaussian Model with a Mixed Effects Structure in the Mean and Covariance Part Some future work Use the latent factor score for burnout instead of sum of the items Model COV at higher levels Relax some model assumptions: Correlated random effects in the mean and loadings Replace multivariate normal distribution of the random effects among the outcomes with multivariate t distribution EMC-Logo Bayes 2013 May 23, 2013 16 / 17
A Multivariate Multilevel Gaussian Model with a Mixed Effects Structure in the Mean and Covariance Part It is over!!! EMC-Logo Bayes 2013 May 23, 2013 17 / 17
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