52 Factors associated with differences in digitally measured student perceptions of teaching quality To study the associations of potentially related factors at the student, classroom and teacher levels (see Table 3.2) with differences in the student Impact! ratings, the effects of these factors were separately added to equation 2. For example, the main effect of student gender, teacher gender and the interaction effect is given by: 44 !"# residual ~ 50, ! 4 "#6 To study the associations of potent ally related factors at the student, class oom and teacher levels (see Table 3.2) with differences in the student Impact! ratings, the effects of these factors were separately added to equation 2. For example, the main effect of student gender, teacher gender and the interaction effect is given by: !"# = " + " / + # + !" 4 + " !" /4 + !|" + "# + !#|" . (3) The interpretation and the distribution of these random effects from equation 3 are given in Table 3.3. It was decided to eliminate variables that did not significantly correlate with the dependent variable (bottom-up) instead of adding all possible variables into the model and then removing the ones that do not correlate (top-down). This bottom-up approach resulted in adding several variables that are possibly related to the dependent variable, based on the theoretical framework of this study. . (3) The interpretation and the distribution of these random effects from equation 3 ar given in Table 3.3. It was decided to eliminat variables that did not significantly correlate with the dependent vari ble (b ttom-up) instead of adding all possible variables into the model and then removing the ones that do not correlate (top-down). This bottom-up approach resulted in adding several variables that are possibly related to the dependent variable, based on the theoretical framework of this study. Table 3.3 Generalizability theory model with main effects of student and teacher gender and the interaction between those two: parameters, interpretation and distributions Parameter Interpretation Distribution 3.3.8 Estimation method The combined models were estimated in a Bayesian framework using OpenBUGS (Lunn et al., 2009). The reason for this choice rather than traditional standard software for latent variable modelling is that Open Bugs allows its Table 3.3 Generalizability theory model with main effects of student and teacher gender and the interaction between those two: parameters, interpretation and distributions Parameter Interpretation Distribution " main effect teacher ~ (0,1) # growth coefficient ~ (0, # 4 ) "# interaction teachers and time points ~ (0, " 4 # !|" effect students nested within teachers ~ (0, ! 4 |") (!|")# interaction student effects and time points ~ (0, ( 4 !|")#) !"# residual ~ (0, ! 4 "#) / main effect gender teacher ~ (0, / 4 ) 4 main effect gender student ~ (0, 44 ) /4 interaction genders teacher and student ~ (0, /4 4) 3.3.8 Estimation Method main effect teacher growth coefficient interaction teac r d time points ffect students t ithin teachers interaction student eff cts and time points residual main effect gender teacher main eff ender student interaction ge teacher and student
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