Log odds to odds interpretation with LGM
Message/Author
 Janet Audrain-McGovern posted on Monday, November 11, 2002 - 7:34 am
I have a question about the interpretation of the log odds to odds transformation (exponentiation) when dealing with exogenous variables. I regressed the slope (trend) of my ordered categorical outcome variable on the exogenous variable subs ("substitutes"). The slope from the exogenous variable to the trend factor was -.652, indicating that the log odds of my trend factor decreased by .652 for every unit increase in subs. I understand that part. However, I exponentiated this value and got 1.92. Does this mean that the odds of progressing to a higher level of my ordered categorical variable decreased by 92%? I'd appreciate your help vastly.
 bmuthen posted on Monday, November 11, 2002 - 1:43 pm
I would just say that the odds is 1.92 times lower when increasing subs by 1 unit. See Hosmer-Lemeshow (2000), p. 63, or Agresti (1990), p. 322.
 Leah Rohlfsen posted on Tuesday, May 20, 2008 - 11:28 am
I have a question about interpreting the effect of covariates on the slope in growth curve modeling when the outcome is binary (for example, binge drinking). Is the effect of the covariate interpreted in reference to the positive linear trend specified in the model or in reference to the mean slope obtained from the output under 'intercepts'? For example, the mean slope in the model is negative and the effect of a binary covariate (1=females) on the slope is negative. Would I interpret this as a) females have smaller (lower) increase in the log odds of binge drinking over time compared to males (using the positive trend specified in the model as the reference), or b) females have smaller rate of decline in the log odds of binge drinking over time compared to males (using the negative slope mean as the reference)?

Similarly, if the effect of gender on the slope coeffeicient were positive, it would mean a) females have larger increase in the log odds of binge drinking over time, or b) females have larger decrease in the log odds of binge drinking over time?
Am I even close at all? I understand that log odds arent' very intuitive, so will exponentiate and change to probabilies, but want to get the basics down first.
Thank you
 Bengt O. Muthen posted on Wednesday, May 21, 2008 - 11:21 am
You mention "the mean slope obtained...under intercept". The intercept is not the mean of the slope growth factor (the mean is influenced by the covariate as well) - you find its mean in Tech4.

You seem to say that you have a positive slope mean since you talk about a "positive trend". If that's the case, your interpretation a) is correct - the negative effect of female on the slope pulls the slope downwards.
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