The above results suggest that there are differences in the association of family background (education and social class) with obesity and being overweight compared to normal/healthy BMI. We can test these formally, by examining the overall effect of mother’s education using the ‘test’ command.
We can see that there is no significant difference between the association of when the participant’s mother left education and the participant’s own BMI in later life.
We can also test the overall influence of fathers social class using the ‘test’ command.
Here we see the overall influence of father’s social class on BMI category is statistically significant (chi-square = 15.79, pless than 0.05). (N.B. the commands numbered (1),(4),(7) and (10) in the above output are constrained as they are the baseline reference category, i.e. normal/healthy weight).
Focusing on our predictor of interest ‘general ability’, we can use predicted probabilities to help understand the relationship between ‘general ability’ and obesity, overweight and normal/healthy BMI in the model. In this example we want to calculate the predicted probability of the three BMI categories for a given score on the ‘general ability’ test. Predicted probabilities can be calculated using the ‘margins’ command. We create the predicted probabilities for values of the ‘general ability’ test (n920 which ranges from 0 to 79) from 10 to 80 in increments of 10. The values in the table are the average predicted probabilities calculated using the sample values of other predictor variables. The example below shows the predicted probability for healthy BMI given the ‘general ability’ test score.
The first part of the output tells us which row is associated with which ‘general ability’ test score. Row 1 (Expression = 1._at) relates to a test score of 10, while row 8 equal to a test score of 80. As the test score at age 11 increases, the probability of a healthy BMI at age 42 being a 1 is increasing from a probability of 0.421 to 0.526.
We can use the ‘marginsplot’ command to create a graph of the predicted probabilities and their confidence intervals for each of the BMI categories. We can also combine those graphs using the command ‘graph combine’. This last command has the option ‘ycommon’ which we will use to ensure the combined graphs have the same y axis.
The predicted probability of a normal weight (top left graph), overweight (top right graph) or obesity (bottom left graph) at age 42 is on the Y axis and the ‘general ability’ test score at age 11 is on the X axis. The fitted line increases from left to right, is flat and decreases from left to right for normal weight, overweight and obesity respectively as general ability scores increase.
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