Multilevel modelling and time series analysis in ... - ERSO - Swov

Chapter 2• Click on “Add Term”, select “Previously” as a predictor, select “not testedpreviously” as reference category• Click on “Add Term”, select “Probability” as a predictor; select “very low” asreference category• Click on “Add Term”, select “Previously” as a predictor, select “Age16-25” asreference categoryEstimationIn the binomial distribution it is assumed that the variance is equal to the oddsratio,π ji (1- π ji ). To test this assumption, first estimate a model assuming anextra-Binomial distribution, where the variance is left free to vary.• Click on “Notation” at the bottom of the “Equations” window again• Select “extra Binomial” in the top row• Leave the other two options at their default value (1 st order linearization andMQL as estimation type)• Click “Done”• Press “Start” to start the estimation procedure.Once the estimation procedure has converged (i.e. all blue numbers turnedgreen)• Click on “Notation” at the bottom of the “Equations” window again• Select “2 nd order” under “Linearization”• Select “PQL” under “Estimation type”• Press “Done”• Press “More” to continue the estimationIn the estimation procedure, the nonlinear link function is linearized byapproximating it with a Taylor Series expansion. A Taylor series consists of aninfinite number of terms and the more of them are used, the closer theapproximation. The first choice is whether only the first (1 st order linearization)or the first two are used (2 nd order linearization). The other choice concerns thevalues that the Taylor series expansion is based on: During each iteration theTaylor series is calculated on the basis of the currently estimated parametervalues. In the Marginal Quasi Likelihood method (MQL) only the fixedparameters are included, in the Penalized Quasi Liklihood method (PQL) theresiduals are included as well. Generally speaking, 2 nd order linearization andPQL are more accurate but computationally intensive and more prone toconvergence problems. The 1 st order MQL estimates on the other hand areknown to be biased downwards. It is therefore suggested to use 1 st orderlinearization and MQL to get rough starting values on which the final estimationusing 2 nd order linearization and PQL is based. For more information seeGoldstein (2003) or Hox (2002). With these methods, slight variations in theestimated values are to be expected.