Chapter 6 Supplement 1 - Mixed Models
Baseline Model for Maladaptive Exercise
\[ Maladaptive\ Exercise_{ij} = b_{0j} + e_{ij}\\ b_{0j} = \gamma_{00} + u_{0j} \]
Step 0: Age Effect Model
\[ Maladaptive\ Exercise_{ij} = b_{0j} + b_1Age + e_{ij} \\ b_{0j} = \gamma_{00} + u_{0j} \]
The model including the random effect of time also serves as the baseline model for Exercise for Weight Loss, as the ordinal package requires at least one random effect predictor in a model
\[ Exercise\ for\ Weight\ Loss_{ij} = b_{0j} + b_1Age + e_{ij}\\ b_{0j} = \gamma_{00} + u_{0j} \] Step 1 Covariates: Main Effects of Parent SES and BMI at age 13
\[ Maladaptive\ Exercise_{ij} = b_{0j} + b_1Age + b_2ParentSES + b_3BMI13 + e_{ij} \\ b_{0j} = \gamma_{00} + u_{0j} \]
\[ Exercise\ For\ Weight\ Loss_{ij} = b_{0j} + b_1Age + b_2ParentSES + b_3BMI13 + e_{ij} \\ b_{0j} = \gamma_{00} + u_{0j} \]
Step 2 Covariates: Main Effects of Parent SES, BMI at age 13, and eating disorder cognition variables at age 14
\[ Maladaptive\ Exercise_{ij} = b_{0j} + b_1Age + b_2ParentSES + b_3BMI13 + b_4TI14 + b_5BodyDissat14 + b_6FearWt14 + e_{ij} \\ b_{0j} = \gamma_{00} + u_{0j} \]
\[ Exercise\ For\ Weight\ Loss_{ij} = b_{0j} + b_1Age + b_2ParentSES + b_3BMI13 + b_4TI14 + b_5BodyDissat14 + b_6FearWt14 + e_{ij} \\ b_{0j} = \gamma_{00} + u_{0j} \] Step 3 Covariates: Time x Predictor Interactions
\[ Maladaptive\ Exercise_{ij} = b_{0j} + b_1Age + b_2ParentSES + b_3BMI13 + b_4TI14 + b_5BodyDissat14 + b_6FearWt14 + \\ b_7Age\ X\ BMI13 + b_8Age\ X\ TI14 + b_9Age\ X\ Body Dissat14 + b_{10} Age\ X\ FearWt14 + e_{ij} \\ b_{0j} = \gamma_{00} + u_{0j} \] \[ Fear\ of\ Weight\ Gain_{ij} = b_{0j} + b_1Age + b_2ParentSES + b_3BMI13 + b_4TI14 + b_5BodyDissat14 + b_6FearWt14 + \\ b_7Age\ X\ BMI13 + b_8Age\ X\ TI14 + b_9Age\ X\ Body Dissat14 + b_{10} Age\ X\ FearWt14 + e_{ij} \\ b_{0j} = \gamma_{00} + u_{0j} \]