This exercise considers growth in mathematics achievement over grades 7, 8, 9, and 10 in U.S. public schools for a sample of 3,102 students. The data are from the Longitudinal Study of American Youth (LSAY). The data structure is multilevel with students clustered within schools, but for the purpose of this assignment this complication can be ignored.
The research question is how the time-varying covariate of math course taking influences the math achievement growth. The variables in the attached LSAY data set are shown in the attached Mplus input for a BASIC analysis. Here, the math course taking variable is labeled mthcrs7-mthcrs10 and is recorded as follows:
mthcrs7-mthcrs12 = Highest math course taken during each grade ! (0 = no course, 1 = low, basic, 2 = average, 3 = high, ! 4 = pre-algebra, 5 = algebra I, 6 = geometry, ! 7 = algebra II, 8 = pre-calc, 9 = calculus)
For simplicity, this variable may be treated as continuous.
The exercise consists of using Mplus to find a good time-varying covariate growth model by exploring conventional approaches with fixed and random coefficients, as well as innovative alternatives. Individuals with little Mplus growth modeling experience may consult chapter 6 of the Mplus Version 5 Userís Guide (see www.statmodel.com).
Although it is not possible for the Mplus team to look at individual solutions, the Mplus course at Johns Hopkins University on Thursday August 21, 2008 will present several solutions for this exercise.
Scott Smith posted on Friday, October 18, 2013 - 1:13 pm
I am trying to model a growth curve model with a count dependent variable. I have four waves of data but I am using an accelerated cohort design. I already have my data wide. I want to use both time-varying and time-invariant covariates. I used example 6.10 as a guide. If I only have the time-invariant variable in the model (i.e. gender) the model will run. When I start to add the time-varying covariates (i.e. drug use at each time point) I get the following message:
*** ERROR There is at least one count variable that has only one unique value. Please check your data and format statement. *** ERROR One or more variables in the data set have no non-missing values. Check your data and format statement.
Don't use a missing data flag for the time-varying covariates; use some other number. If the tvs is missing at time t and the outcome at the corresponding time is missing, such timepoints still won't contribute to the likelihood computations. By not using a missing data flag, you avoid deleting subjects who have missing on any tvcs.
Scott Smith posted on Saturday, October 19, 2013 - 5:12 pm
That makes sense. I will give it a try. Thank you for your timely feedback.
I think I know well how latent growth modeling with TVC works, but I'm not sure how to interpret its meaning properly in research papers.
As the first post of this thread said, the research question is "how the time-varying covariate of math course taking influences the math achievement growth". Suppose that at each time point, course taking affect math achievement positively, how should I answer the research question? I don't think just say "time-varying course taking influence growth of math achievement positively" is enough. Can you propose an interpretation more in detail that can reflect some of the rationale of this model?
And, can I understand TVC model as an extension of LGM by adding TVCs as predictors of growth besides calendar time (i.e., growth is joint function of both time and tvc)? Or,the term "growth" has to be a function of time exclusively, and TVC is just a correlate of growth?
Some observations having missing values on all analysis variables. These are eliminated from the analysis. If you can't see the issue, send the data, output, and your license number to email@example.com.
For LGM with TVCs, is it possible to examine a factor (for example self-efficacy) as both a time variant and time invariant factor within a single model? By this I mean T1 self-efficacy can be used as both a predictor of the intercept and slope, but also as a direct predictor of the T1 outcome factor. The model converges, but I don't know if this makes theoretical sense.
I think it makes sense - you are not stating that the self-eff influences the factors at all time points - which would not be identified beyond its influence on intercept and slope - but influences the T1 outcome factor beyond the influence that goes through intercept and slope.