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.
 Yangjun Liu posted on Thursday, September 12, 2019 - 1:22 pm
Hi,

I am running the latent growth model (3 time-points) with binary outcome by using ML estimator, and I just want to check the interpretation of STDYX and STDY.
For Intercept regress on X, if the X is continous variable, could I interpret the STDYX coefficient(b) as with 1 SD increases in X, the log odds of outcome increase b SD? And if X is binary, then STDY coefficient(b)as with X changes from "0" to "1", the log odds of outcome increases b SD?

Thank you for your reply in advance!
 Bengt O. Muthen posted on Thursday, September 12, 2019 - 4:28 pm
By "intercept" I assume you mean the continuous intercept growth factor. If so, log odds would not be relevant because this DV is continuous.
 Yangjun Liu posted on Friday, September 13, 2019 - 2:03 pm
Thank you for the reply.However, I still feel confused. Here is my undestanding, for the latent growth model (LGM), the formula is:
log (odds Y) = t + lamda0j * intercept + lamda1j * slope + eij,
Intercept = b00 + b01 * Age + b02 * Sex + u0i; suppose slope does not regress on any variable and its variance is 0; then after the substitution, the formula becomes
log (odds Y) = t + lamda0j * (b01 * Age + b02 * Sex + u0i) + lamda1j (time) * b10 + eij;
lamda0j is specified as 1. lamda1j represents time and is specified as 0, 1 , 2. The formula becomes
log (odds Y) = t + b01 * Age + b02 * Sex + lamda1j (time) * b10 + u0i + eij .
For me, it looks like simple logistic regression formula.
The Age coefficient b01 comes directly from "intercept regress on age", but after the substitution, it is also the coefficient for "log odds regress on Age" as presented in the last formula. But why log odds is not relevant? Or the standardization process is different in LGM (estimator = ML) compared with the simple logistic model? Then how to interpret the STDYX coefficient in latent growth model? (estimator = ML),I thought if could be interpreted as 1 SD increase in X, log odds of Y increase b SD (esimator = ML). But it seems it is wrong.
 Bengt O. Muthen posted on Saturday, September 14, 2019 - 12:35 pm
You were asking about "Intercept regress on X" which has a continuous DV. But now it is clear that you are interested in the binary outcome regression - and for that logodds are correct.
 Yangjun Liu posted on Saturday, September 14, 2019 - 2:43 pm
Thanks a lot for your further reply. I have two further questions.

(1) I found that the standardized results (STDYX,STDY,STD) from "Estimator = ML; Link = Probit" are identical to the standardized results from "Estimator = ML; Link = Logit" in latent growth model. If the standardized results from "Estimator = ML; Link = Logit" could be interpreted as log odds, does it mean that the standaardized results from "Estimator = ML; Link = Probit" could also be interpreted as log odds? If not, why they are identical?

(2) I read the tutorial of the latent growth model in the Mplus website, and it recommended to use "Estimaor = WLSMV" to specify probit model, but its unstandardized coefficient * 1.81 is not approximate to the coefficient from "Estimaor = ML; Link = Logit". Is it the right case? However, the results from "Estimaor = ML, Link = Probit" is consistent with results from "Estimaor = ML, Link = Logit" (1.81-fold difference in unstandardized coefficients, and identicial standardized coefficients). I am wondering the reasons for these two unconsistent and consistent situations, and for me it seems that both "Estimaor = WLSMV" and "Estimaor = ML, Link = Probit" can specify probit model, what is the difference between them, and why the results from these two are different?

Many thanks for your help!
 Bengt O. Muthen posted on Monday, September 16, 2019 - 4:05 pm
Both of these outcomes are very unusual - are you sure you are looking at the output correctly? You can send relevant outputs to Support along with your license number.
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