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.