Fixed Coefficients (generalized linear mixed models)

Figure 1. Fixed Coefficients view, table style
Fixed Coefficients view, table style
  1. Click the Fixed Coefficients view thumbnail.
  2. From the Style dropdown of the Coefficients view, select Table.
  3. In the parameter estimates table, click the Coefficient cell. This displays the standard error, t statistic, and confidence interval.

Compared to the parameter estimates for the linear mixed model, the significant teaching_method=0 effect indicates the experimental teaching method is indeed effective in both models, and we can expect a student taught by the new method to score 6 points higher than a student taught by the standard method, all other things being equal. This might imply that, regardless of the statistical superiority of the linear mixed model, it doesn't affect the school board's final decision to implement the new teaching method. However, there are a few important differences between the two models.

  • First, the standard error for the effect of the teaching method is too small in the linear regression model, resulting in an overly optimistic 95% confidence interval of [−6.324, −5.743]. The "honest" estimate from the linear mixed model is [−7.510, −4.883] more properly reflects the uncertainty in size of the effect of the experimental teaching method.
  • Next, the coefficient estimates for all other effects are very different between the two models, so the interpretation of these effects is different. In particular, the effects School type (school_type) and Gender (gender) are statistically significant in the linear mixed model but not the linear regression, and Number of students in classroom (n_student) is significant in the linear regression but not the linear mixed model.
  • Lastly, the large and significant variance estimates for the two random intercepts (17.219 and 7.793) indicate that heterogeneity among schools and among classes should not be ignored, and make the standard errors of the coefficients larger, especially those corresponding to school-level and class-level predictors, including the teaching method (to come back to the first point).