*3.4. Modeling Results*

The first log-linear model for Latino men assumed that the three risk behaviors were mutually independent of one another with a goodness of fit of χ<sup>2</sup> (3) = 5.0, *p* = 0.17. The final (best fit) log-linear model containing smoking, fruit and vegetable intake, physical activity, the fruit and vegetable intake by physical activity interaction and the fruit and vegetable intake by smoking interaction had an improved goodness of fit of χ<sup>2</sup> (1) = 0.11, *p* = 0.74. The most significant interaction term in the final model was the low physical activity by consuming <5 servings/day of fruits and vegetables interaction (*p* = 0.08), which corresponded to the most frequent cluster in the overall sample (28%). For Latino men in general, of the individuals who had less than 5 servings of fruit and vegetables per day (*n* = 188), 40% smoked and 49% did not engage in physical activity, while of the individuals who had 5 or more servings of fruit and vegetables per day (*n* = 15), 13% smoked and 20% did not engage in physical activity. Table 3 presents the observed frequencies and the expected frequencies under the independence and final models.

For Puerto Rican men, the mutually independent model had a goodness of fit of χ<sup>2</sup> (4) = 10.1, *p* = 0.039. For the final (best fit) log-linear model containing smoking, fruit and vegetable intake, and physical activity, the fruit and vegetable intake and physical activity interaction and the fruit and vegetable intake and smoking interaction had an improved goodness of fit of χ<sup>2</sup> (2) = 1.6, *p* = 0.45. The most significant interaction term in the final model was the smoking and consuming <5 servings/day of fruits and vegetables interaction (*p* = 0.04), which corresponded to the most frequent cluster in the Puerto Rican sample (28%). Of the individuals who had less than 5 servings of fruit and vegetables per day (*n* = 95), 45% did not engage in physical activity and 51% smoked, while of the individuals who had 5 or more servings of fruit and vegetables per day (*n* = 9), 22% did not engage in physical activity and 0% smoked. Table 4 presents the observed frequencies and the expected frequencies under the independence and final models.

For Mexican men, the mutually independent model had a goodness of fit of χ<sup>2</sup> (3) = 3.6, *p* = 0.21. For the final (best fit) log-linear model containing smoking, fruit and vegetable intake, and physical activity, the fruit and vegetable intake and physical activity interaction had an improved goodness of fit of χ<sup>2</sup> (2) = 1.6, *p* = 0.46. The most significant term in the final model was the low physical activity and consuming <5 servings/day of fruits and vegetables interaction (*p* = 0.21), which corresponded to the most frequent cluster in the Mexican sample (33%). For Mexican men, of the individuals who had less than 5 servings of fruit and vegetables per day (*n* = 93), 54% did not engage in physical activity, while of the individuals who had 5 or more servings of fruit and vegetables per day (*n* = 6), 17% did not engage in physical activity. Table 5 presents the observed frequencies and the expected frequencies under the independence and final models.
