Interpreting Linear and Quadratic Slope PreviousNext
Mplus Discussion > Growth Modeling of Longitudinal Data >
 anonymous posted on Friday, February 29, 2008 - 6:55 am
I have run a time-invariant 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!
 Linda K. Muthen posted on Friday, February 29, 2008 - 8:05 am
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 alcohol-related problems from ages 18 to 37 in a U.S. national sample. Journal of Studies on Alcohol, 61, 290-300.
 Kathryn Modecki posted on Sunday, August 12, 2012 - 2:23 am
Dear Dr. Muthén-
I have a LGM with gender and pubertal timing (grade 8) predicting intercept (grade 8) and linear slope (grades 8-10) of risk behavior. Risk intercept and slope in turn predict grade 11 cyber-bullying. Similar to your article above (Muthén & Muthén, 2000), I then re-centered 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 non-significant. 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.
 Linda K. Muthen posted on Sunday, August 12, 2012 - 9:35 am
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.
 Kathryn Modecki posted on Sunday, August 12, 2012 - 6:06 pm
Thanks, that makes sense. So this would only make sense for predicting the intercept at different time points, then.
 Linda K. Muthen posted on Monday, August 13, 2012 - 9:52 am
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.
 Kathryn Modecki posted on Monday, August 13, 2012 - 10:55 pm
Sorry-yes, they are predicting cyber-bullying. 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.
 Linda K. Muthen posted on Tuesday, August 14, 2012 - 12:08 pm
Yes, that is true.
 Andrea Norcini Pala posted on Friday, November 14, 2014 - 10:07 am
Dear Professors,
I am running a Growth Model (MLR estimator) with Binary outcomes (3 time points). I obtain a standardized Slope means greater than |1|. Is it possible or is it an error?
Thank you for you help,
 Bengt O. Muthen posted on Friday, November 14, 2014 - 1:10 pm
That is ok. The slope scale is not in probability metric. The slope is a continuous predictor of the binary outcome.
 Andrea Norcini Pala posted on Saturday, November 15, 2014 - 5:47 am
Thank you so much.
 Daniel Lee posted on Monday, December 05, 2016 - 7:02 am
To follow up on the question immediately above this one, I am running a growth model for binary (0= no, 1 = yes) outcome. The standardized slope is -1.354...I am having trouble interpreting this. I'm wondering if this is possible or an error, and how to interpret such a slope. I used WLSMV for estimator and parameterization theta.

Also, for these analyses (binary growth model), would I focus solely on standardized results and ignore unstandardized results?

Thank you!
 Bengt O. Muthen posted on Monday, December 05, 2016 - 5:50 pm
Perhaps you mean that -1.354 is the standardized mean of the slope growth factor. If so, it is in a standardized probit (z-score) metric and can well be greater than 1. I see no real use for a standardized slope growth factor mean. The best way to interpret the model may be the plot of the estimated growth curves and the (possibly standardized) slopes in the regressions of the growth factors on covariates.
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