53 3 users to completely specify their own model, taking all facets and levels into account. Estimation in OpenBUGS is done with a Markov chain Monte Carlo (MCMC) procedure. The script for the estimation of the overall model (without any added effects, equation 1) is provided in Appendix B. The MCMC sampling procedures in the application were run with over 24000 iterations for each of two chains. Each chain had a burn-in of 10000 iterations. These large numbers were chosen to ensure convergence and small estimation errors. The sampling procedures were checked for convergence by visual inspection of the trace plots, by comparing the estimates of the two chains and by checking whether the MCMC errors were acceptably small (< 5% of estimated standard deviation; Lunn et al., 2012). 3.3.9 Model comparisons A more complex model proved to fit the data better than a simpler model. But at some point, adding more complexity destroys the interpretability and reliability of the analyses (Akaike, 1974). Therefore, the model fit was evaluated by using a methodology for the evaluation of model fit that condemns overly complex models. The f irst model was the full model, where differences between students, teachers, measurement timings and interactions between these variance components were included. In the second model, the interaction between time and teachers was removed. Model three was a linear regression model, to analyse teachers’ growth curve over time. The models were compared with each other by calculating the deviance information criterion (DIC; Spiegelhalter et al., 2002) provided by the OpenBUGS software. The DIC is the sum of two components: the expected deviance, denoted by %a.%-'%>!>%8#(*-%=!>%*)'%>!K9! =!(*>!'<#-%!'0% .%*(6'9!:)&!'0%!*,+K%&!):!.(&( +)>%6=!>%*)'%>!K9 2!D!6)<%&!"cW!8(6,%!#$!(*!#*>#-('#)*!):!K%''%&!+)>%6!:#'2! ;2?&K%80-$8& I=N=<)W".0,)("23+&-$"#$) (*(69$%$2! ;(K6%!I2N W".0,)("23+&-$"#$)'$-#6)%;0)K1! I"/%- QR)%1$%/& J%G.(#1% P%#(-$9&7"*&$'%& #0A6%*&"7& )(*(A%$%*8&.#& $'%&A"/%- , and twice the penalty for the number of parameters in the model, denoted by +)>%6=!>%*)'%>!K9 2!D!6)<%&!"cW!8(6,%!#$!(*!#*>#-('#)*!):!K% ;2?&K%80-$8& I=N=<)W".0,)("23+&-$"#$) (*(69$%$2! ;(K6%!I2N W".0,)("23+&-$"#$)'$-#6)%;0)K1! I"/%- QR)%1$%/& J%G.(#1% P%#(-$9&7"*&$'%& #0A6%*&"7& )(*(A%$%*8&.#& $'%&A"/%- . A lower DIC value is an indication of better model f it. 3.4 RESULTS 3.4.1 Model comparisons Results of the model comparisons are given in Table 3.4. It can be seen that the full model has the best fit, as the DIC value is the lowest there. Therefore, this model was used for further analyses.
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