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Psychology 290 Special Topics Study Course: Advanced Meta-analysis

Psychology 290 Special Topics Study Course: Advanced Meta-analysis. February 26 , 2014. Overview. Some issues related to the homework Border conditions X’WX ( cf /inverse in SAS) Discussion of REML Iteratively reweighted maximum likelihood Simulation Assessing convergence

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Psychology 290 Special Topics Study Course: Advanced Meta-analysis

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  1. Psychology 290Special Topics Study Course: Advanced Meta-analysis February 26, 2014

  2. Overview • Some issues related to the homework • Border conditions • X’WX (cf /inverse in SAS) • Discussion of REML • Iteratively reweighted maximum likelihood • Simulation • Assessing convergence • Efficiency • Leading to homework 3

  3. Iterative reweighting • MLEs can be obtained by calculating an estimate of the variance component and weighting: • The estimate of the variance component is recalculated, and the process iterates until there is no change.

  4. The REML estimate • Restricted maximum likelihood (REML) works similarly… • …but bias in the variance component estimate is corrected by an adjustment for the number of parameters in the regression model.

  5. REML • The adjusted estimate looks like this: • (Illustration in R.)

  6. REML (cont.) • Note that the correction factor changes when the number of predictors changes. • This means that the model with fewer predictors is not truly nested within the more complex model. • Hence, likelihood ratio tests are not valid.

  7. Simulation • Assessing convergence • Demonstration of CLT in R • Considerations related to efficiency • Efficient and inefficient ways to do the same thing • Using R functions • Preference for vector and matrix operations

  8. Simulation (cont.) • Designing a simulation • Crossing cells • Variance reduction • Homework related to Q between vs. LR tests

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