Negative Covariate on Negative Slope
Message/Author
 anonymous posted on Monday, August 04, 2008 - 12:21 pm
Hello,
I'm attempting to interpret the effect of family distress (high scores mean more family distress) on a decreasing linear slope in agressive symptoms (the linear slope mean is negative). The standardized regression coefficient of family distress on the linear slope factor is also negative. Would this indicate a slower decline in aggressive symptoms if there is high family distress? A faster decline? Or would this change the direction of the slope (i.e.,high family distress increases aggression over time?)
 Bengt O. Muthen posted on Monday, August 04, 2008 - 5:44 pm
A negative influence on a slope factor implies that it is lower when the influence is higher, no matter the mean of the slope. So here it implies that the slope has a larger negative value, that is, aggression goes down faster for higher family distress.
 anonymous posted on Monday, August 04, 2008 - 6:36 pm
This seems a little odd. Could it possibly be a regression to the mean effect? That is, the higher in family distress you are (and if family distress is positively correlated with aggression at baseline), the more you can decline over time in aggression?
 Bengt O. Muthen posted on Monday, August 04, 2008 - 6:44 pm
Perhaps.
 anonymous posted on Tuesday, August 05, 2008 - 1:42 pm
Thanks very much for your help! So, given this, does a positive beta coefficient to a slope (with a mean negative value) indicate that the effect of family distress increases the rate of aggression over time? That is, aggression increases faster for higher family distress?
 Bengt O. Muthen posted on Tuesday, August 05, 2008 - 6:44 pm
The value of the aggression slope may still be negative - so increasing family distress makes it less negative.
 Gabriela Roman posted on Friday, February 11, 2011 - 4:37 am
Hi, I think this might be incorrect. If the slope is negative, it means:
- if the correlation with item *a* (distress) is positive, then the larger the *a*, the larger/more abrupt the slope is. So the for a positive correlation, the more distress, the bigger the slope of the aggression scores (i.e., aggression goes down faster)
- if the correlation with item *a* is negative, then the higher the value if *a*, the less abrupt the slope is. In this case, the higher the distress, the smaller the slope of aggression scores (i.e. aggression goes down slower)

Am I right?

Thank you,
Gabriela
 Bengt O. Muthen posted on Friday, February 11, 2011 - 10:30 am
I would say the opposite in both cases. A simple picture to have in mind is a clock face where the clock hand (say the minute hand) represents the slope. The clock hand can move clock-wise or counter clock-wise. For an increasing covariate value:

- a positive slope for the covariate moves the hand counter clock-wise

- a negative slope moves the hand clock-wise

The initial position of the clock hand is for covariate value of zero, so that it's position is determined by the slope intercept. So a large negative intercept for the slope (slope value at x=0) means that the clock hand points to say 5 o'clock. With a positive slope, increasing x increases the value of the slope, and therefore will move the clock-hand up to say 4 o'clock, so still a negative slope. A bigger change in x can give a positive slope, say at 2 o'clock.
 Gabriela R posted on Saturday, February 12, 2011 - 3:31 am
Dear Dr Muthen,

Thank you for the very fast reply. This will be very helpful, since I am investigating predictors of a negative slope.

Best wishes,
Gabriela
 Jaci posted on Friday, May 06, 2011 - 6:35 am
I have a similar question, but instead I use my slope as a predictor. I have a negative slope, and this negative slope has a positive effect on another variable. So that means that a more negative slope leads to a lower score on the outcome, and a less negative slope leads to a higher score on the outcome, am I correct?
 Bengt O. Muthen posted on Friday, May 06, 2011 - 9:33 am
Yes. Just think in terms of the predictor value increasing or decreasing, which with a positive slope gives an increase or a decrease in the DV.
 Ryan Marek posted on Thursday, August 20, 2015 - 10:13 am
I have a question similar to those discussed in this trend. I have a sample of spine surgery patients who are evaluated on a disability index at three time points: pre-surgery (T1), 5 months post-op (T2), and 12 months post-op (T3). The disability index is a score of 0-100, with higher scores indicating worse disability. They are also assessed for somatization (high scores mean patients are more prone to somaticize) prior to surgery, which is being used as a predictor of poorer outcomes.

In my LGCA, I have a linear negative slope for the disability index (i.e., patients are improving as expected because their scores are going down). Therefore, the slope is a negative value. I'm hypothesizing that patients who tend to somaticize report greater disability at the 12-month outcome and also have a slower rate of change across time. Somatizatin is also positively correlated with the means at all time points, indicating that the more the patient somaticizes, the higher their disability scores tend to be at all time points as compared to patients who don't somaticize.

With the intercept centered at baseline, I have a positive coefficient between somatization and the slope. Does this indicate that the more a patient is somatizing at baseline, the faster they are improving across time? Or does this indicate that they are changing the least since the prediction coefficient is positive, but the slope is negative?
 Bengt O. Muthen posted on Friday, August 21, 2015 - 1:47 pm
The positive effect from somatization implies that the negative slope gets less negative as somatization increases, which is what you expect.
 Ryan Marek posted on Friday, August 21, 2015 - 4:46 pm
Thanks so much, Dr. Muthen!
 Robert Ciuchita posted on Friday, April 15, 2016 - 8:24 am
Hello,

I am modeling growth in the average usage of an innovation in the first four weeks after its introduction. I find a positive significant intercept and a negative, significant slope. The first and second periods are set at 0 and 1 while the third and fourth periods are freely estimated.

I then use the intercept and slope to predict users' usage of the innovation one year after the introduction. I expect that the higher their average usage during the first week and the less steeper their change from the first to the second week the more they will be using the innovation one year later. Indeed, I find positive, significant effects from both the intercept and the slope on usage one year later.

What I'm having difficulties with is interpreting the positive coefficient of the negative slope. Since both coefficients are positive it means that an increase in the intercept and an increase in the slope will lead to an increase in the average usage one year later. Is then the logic that an increase in the negative slope implies that the slope becomes less negative?! In other words a less negative change in the innovation usage from the first to the second week leads to more average usage one year later?

Thank you for considering my question!

Best regards,

Robert
 Bengt O. Muthen posted on Friday, April 15, 2016 - 4:05 pm
Q1-Q2. Yes.
 Robert Ciuchita posted on Sunday, April 17, 2016 - 3:45 am
Dear Dr. Muthen,

Thank you for your reply and for the comprehensive resources you provide us!

Best regards,

Robert
 steve posted on Wednesday, November 22, 2017 - 10:28 am
I have a related question: my slope (health behavior) is negative and used for predicting mortality. This main effect is negative.

Is my interpretation correct that negative change in the slope/health behavior is associated with lower mortality (which would be odd)? Or is it about the lower rate of negative change that is associated with lower mortality?

Thanks!
 Bengt O. Muthen posted on Wednesday, November 22, 2017 - 3:38 pm
An increase in the health behavior slope decreases mortality. Or, equivalently, a decrease in the health behavior slope (that is, having it even more negative) gives an increase in mortality.
 steve posted on Thursday, November 23, 2017 - 2:37 am
Thank you very much, Dr. Muthen. May I ask a follow-up question to see if I understand correctly:

Consequently, the logic is the same as in regression. A 1-unit increase in the slope is associated with an increase in the outcome, not matter the mean of the slope. That is, even if the average growth in health behavior declines over time, I would interpret the effect of this slope on mortality as if there is a 1-unit increase in health behavior.