Sorry if this is a foolish question, I'm still fairly new to analyzing count data. I know that the intercept and slope values obtained in negative binomial LGMs must be exponentiated in order to be interpretable as means. However, I'm less clear about whether or not ALL of the other parameters in the model also need to be exponentiated when reporting results in manuscript tables (when one chooses to report exponentiated I and S values). I assume that I need to also exponentiate (please confirm):
1. the SEs for the growth factors (obviously, so that they are reported in the same scale) 2. Residual variance estimates for the intercept and slope and their SEs (Correct?) 3. estimates and SEs for the regressions of intercept and slope on covariates (Correct? This is the one that's least clear to me)
I am not a fan of exponentiating for this model. True, we model the log-mean and therefore the mean is obtained by exponentiating. There is, however, an advantage to staying in the log-mean metric because those coefficients are much closer to being normally distributed so that the symmetric CIs we usually compute as +-1.96*SE are relevant. When you exponentiate, you get a non-normally distributed estimate and you have to adjust to get the right CI. I would just look for sign and significance in the output that you get and report that.
To get a more tangible interpretation of the results I don't think a count mean says very much anyway. I don't have a good feel for how a negbin mean influences the counts. I would instead want to know the estimated probability distribution for the count outcomes 0, 1, 2,. ... Say at the first time point and the last, in order to gauge how much growth occurs.
But maybe there are books that show ways to report count growth models (none come to mind immediately) that would contradict me.
Thank you Bengt, very helpful. I see your point about not exponentiating, but unfortunately in applied journals editors and readers tend to want to see "real" numbers - how do effects translate into reductions or increases in the number of occurances. I will consider your viewpoint (and perhaps cite "personal communication") as I put my results tables together.
Would love to read other viewpoints on this issue.
A covariate effect on a growth factor can also be translated into an effect on the probabilities of the outcome categories. What I hear is that it would be good if Mplus could add a "calculator" similar to our new LTA calculator to compute covariate effects for count outcomes.
Yes, it would be good to hear about others' experiences and publications with count outcomes.
Brianna H posted on Thursday, December 13, 2012 - 4:19 pm
Hello Dr. Muthen, I have a related question about reporting the effects of covariates on the intercepts and slopes of a zero-inflated Poisson model for a count outcome. My model has a continuous covariate and a categorical (binary) covariate. In the Mplus Users Guide and in other areas of the Discussion Board, Dr. Muthen has recommended reporting STDYX for continuous covariates and STDY for binary covariates. When I examine the Model Results, STDYX, and STDY output, however, the significance level of the intercept and growth factors vary. For example, in the STDY output, the effect of the binary covariate on the slope of the inflation factor is significant, but in the Model Results, this is not significant. In contrast, the effect of the binary covariate on the intercept of the count growth curve is significant both in the Model Results and in STDY. Is it appropriate to report STDY for the effects of the binary covariate; STDYX for the continuous covariate; and to report overall results from the Intercepts section of the Model Results? Thank you.
Significance can be different for un-standardized and standardized estimates, in which case I would decide significance by the un-standardized ones.
I would report all unstandardized coefficients and their significance (SEs) and then also add the standardized - for which I would use STDY for binary and STDYX for cont's covariates. I don't think SEs and significance is really needed for standardized values.