

Interpreting Linear and Quadratic Slope 

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anonymous posted on Friday, February 29, 2008  6:55 am



Hello, I have run a timeinvariant conditional LGM of child problems with both a linear and quadratic slope. The model includes covariates (family problems) that are correlated. In the results, I find the regression of the slope functions on the covariates to be positive for the linear slope, but negative for the quadratic slope. Is this unusual? My understanding is that to interpet the effect of these covariates on the intercept and slope functions, it is necessary to consider both the linear and quadratic slope together. I am wondering if you can clarify exactly what equation I need to use to obtain mean scores for children at each time point. Also, is there an easier way to interpret the data (i.e., does Mplus calculate these scores?). Thank you! 


I don't think what you are reporting is unusual depending on the actual shape of the quadratic growth. For example, if you have a positive linear slope mean and a negative quadratic slope mean. The linear and quadratic growth factors should be interpreted together which is difficult to do. I would suggest centering at each time point and looking at the intercept growth factor only as was done in the following paper: Muthén, B. & Muthén, L. (2000). The development of heavy drinking and alcoholrelated problems from ages 18 to 37 in a U.S. national sample. Journal of Studies on Alcohol, 61, 290300. 


Dear Dr. Muthén I have a LGM with gender and pubertal timing (grade 8) predicting intercept (grade 8) and linear slope (grades 810) of risk behavior. Risk intercept and slope in turn predict grade 11 cyberbullying. Similar to your article above (Muthén & Muthén, 2000), I then recentered at each time point. In this case, the values for linear slope on the outcome (cyberbullying) vary at each centering point. Generally, as I move the centering point to higher grades, the effect of slope on the outcome becomes nonsignificant. I take this to mean that it is only the overall increase in risk across the three grades that affects the DV. Does this sound correct? Thanks very much. 


Because you change the centering point at each time point, the correlation between the intercept and slope growth factors changes making it difficult to make your interpretation. 


Thanks, that makes sense. So this would only make sense for predicting the intercept at different time points, then. 


From what you said earlier, I thought the intercept and slope growth factors are predictors of cyberbullying. Is this the relationship you are looking at? I am confused above where you say predict the intercept. 


Sorryyes, they are predicting cyberbullying. I mean that changing the centering is useful for questions that focus on the influence of covariates on the intercept, as per your 2000 paper. 


Yes, that is true. 

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