Table 2. Multilevel models for obesity.
Models 3 and 4 incorporate a random intercept per county/state, a random slope for year, and fixed effects for the FSA score and Fat and Sugar. A likelihood ratio test shows significant differences between the models: Model 1 vs Model 2: χ2(5) = 585.64, p < 0.001; Model 2 vs Model 3: χ2(1) = 23.91, p < 0.001; Model 3 vs Model 4: χ2(1) = 14.67, p < 0.001. For the fixed effects, the number in parenthesis shows the standard error.
| Model 1 | Model 2 | Model 3 | Model 4 | |
|---|---|---|---|---|
| Variance Components | ||||
| Var: county:State (Intercept) | 8.90 | 9.01 | 8.84 | 9.02 |
| Var: State (Intercept) | 4.87 | 5.35 | 5.28 | 5.31 |
| Var: Residual | 1.79 | 0.97 | 0.96 | 0.94 |
| Var: County:State Year | 0.09 | 0.09 | 0.09 | |
| Cov: County:State (Intercept) Year | -0.28 | -0.27 | -0.28 | |
| Var: State Year | 0.00 | 0.00 | 0.00 | |
| Cov: State (Intercept) Year | -0.04 | -0.04 | -0.04 | |
| Fixed Effects | ||||
| (Intercept) | 26.56*** (0.39) |
24.89*** (0.42) |
14.27*** (2.20) |
21.74*** (0.83) |
| Year | 0.30*** (0.03) |
0.31*** (0.03) |
0.32*** (0.03) |
|
| FSA score | 1.26*** (0.26) |
|||
| Fat/100g | 0.19* (0.08) |
|||
| Sugar/100g | 0.08* (0.03) |
|||
| AIC | 6796.61 | 6226.47 | 6205.44 | 6200.72 |
| BIC | 6818.30 | 6275.28 | 6259.68 | 6260.38 |
| Log Likelihood | -3394.31 | -3104.23 | -3092.72 | -3089.36 |
| Num. obs. | 1675 | 1675 | 1675 | 1675 |
| Num. groups: county:state | 311 | 311 | 311 | 311 |
| Num. groups: state | 47 | 47 | 47 | 47 |
Note:
*** p < 0.001,
* p < 0.05