Anonymous posted on Monday, November 14, 2005 - 7:03 am
I'm using Mplus to estimate level and a linear trend (T1=@0 T2=@1 T3=@2) of self and peer-perceptions in the peer context, and predicting these growth components with perceptions of the self and others in the family context, assessed only at T1. Both growth models fit well, there is individual variation in both growth components, and a negative correlation between the level and the trend (mean for the trend positive and significant)in the self and peer perceptions curves.
I'm getting a consistent pattern of findings indicating theoretically meaningful relationships between the predictor variables and the level (e.g., debilitated perception of self in the family context predicts low levels of self regard in the peer context), but the opposite pattern occurs in terms of the linear trend, e.g., debilitated coping predicts a growing trend of the self-perception positively rather than negatively. These are very consistent findings accross a bulk of predictors. Could this be related to the fact that there is an inverse relationship, i.e., significant negative correlation, between the level (=intercept) and trend of the self-perception in the peer context over time, suggesting that the lower the overall level of self-perception, the higher are the increases in self-regard over time?
The predictors and outcomes are measured with likert scales (scores ranging from 1 to 4), and include some values between these scores due to missing data imputation. I have so far used MLM and MLR estimators, are there something else that I could do/check in Mplus for not obtaining a negative correlation between the intercept and the slope of change? If not, or this really is the phenomennon in empiria, do I still have a valid case to say that the given predictors predict the outcome measures also over time (when there in fact are significant betas in response the slope), and just note that the signs change from positive to negative due to the inverse relationship between the intercept and the slope)? Even with this complexity, I wouldn't want to go to traditional SEM models due to the strong stability of the outcome measures over a short period of time.
Thanks so much, Anonymous
bmuthen posted on Monday, November 14, 2005 - 5:50 pm
A negative correlation between intercept and slope is quite alright and may have an interesting substantive interpretation. It could also point to the more mundane reasons of the outcome scale showing ceiling or floor effects such that if a person starts high he/she cannot growth as much.
I would first fit the "unconditional" model without predictors and make sure that the negative correlation shows up here too.
Yes, if intercept and slope are negatively correlated, I think it can make sense that the influence of predictors on them have different signs.
Anonymous posted on Wednesday, November 16, 2005 - 9:24 am
Thanks for clearing that out! Still a quick question: If there is a highly significant, inverse relationship between the level and the slope, does the "sign change" in any effect hold even when the covariate in question is unrelated to the level (=beta close to zero), but predicts the slope significantly? For instance, let say a theory predicts a positive relationship between a covariate and the outcome, and variable A has a positive effect on the level, but a negative effect on the slope (covariate-slope relation is then interpreted to reflect the inverse relationship between the level and slope), but a variable B has only a positive relationship with the slope (as predicted by theory in the first place). Does the effect of B support the theory (as one would interpreted without considering the relationship between the level and the slope), or does the effect in fact go against the theory, even if it's effect on the level is close to zero (might have a negative sign though)?
Thank you again, Anonymous
bmuthen posted on Wednesday, November 16, 2005 - 4:47 pm
Dear Prof. Muthén, We modeled individual differences in competence development by using LGC with 3 time points. Time was coded with 0, 1, 2; Measurement error was set equal. The input-syntax was: i by T1@1 T2@1 T3@1; s by T1@0 T2@1 T3@2; i with s*; T1 T2 T3(1); [i* s*]; [T1@0 T2@0 T3@0]; Model results indicate a strong positive correlation between the intercept and slope of about .7; However, when we looked at the estimated data for individual subjects, it turns out that students with identical competence values at time one receive higher intercept estimates if their slope value is stronger and vice versa. Therefore I wonder if this positive correlation is an artificial one? For example Student 1: Empirical values: T1=37.91 T2=41.85 T3=43.63 Estimated Intercept: 38.60 Estimated Slope: 3.96 Student 2: Empirical values: T1=37.91 T2=43.71 T3=56.69 Estimated Intercept: 42.46 Estimated Slope: 5.03 Is it okay to interpret the positive correlation between the model based intercept and slope? From your paper (Muthén & Khoo, 1998, p.92) I learned that such an interpretation is possible, but I am not quite sure if it is appropriate for our data.
Thank you very much for your quick response. Unfortunately I'm not quite sure what you mean by "intercept growth factor mean"? Am I supposed to assume zero variance for the intercept (i@0;)? It would be much appreciated if you could send me the syntax command.