R McDowell posted on Friday, December 01, 2017 - 5:51 am
Hello. I am working through the examples in the short course topic 3 relating to incorporating time varying covariates in growth models (Models M1-M3, slides 137 ff) and was hoping someone could clarify a couple of points for me.
In model M1, where there are fixed slopes for TVCs, varying across grade, the time-varying covariates mthcrs7-mthcrs10 do not covary with each other and with the latent growth factors. Although that could additionally be incorporated into the model by explicitly including terms for the means and variances for mthcrs7-mthcrs10 I wondered when this simpler approach as detailed in M1 would be adequate and/or appropriate.
In Model M2, the effect associated with crs on maths is allowed to have a distribution and its mean and variance are estimated. We also get covariances between stvc and the intercept/slope of the growth curves effects and I was wondering how you interpret these in layman's terms?. For example supposing the correlation of stvc with s was 0.7 and this was of statistical significance- does this mean that mothers whose crs scores increase over time tend to have maths scores which also increase over time, or something else?
In M1, the covariates are correlated as the default like all covariates are in regression settings - the parameters are just not part of the model because we condition on the covariates.
In M2, increasing stvc means that a larger amount of course taking at a certain time point increases the math performance. It would be natural to have that correlate positively with the growth slope s.
R McDowell posted on Monday, December 04, 2017 - 9:08 am
Thank you for replying and clarifying these points. I see that when Model M1 is fitted as per the handout, the time varying covariates do not covary with the growth factors by default.
Could you clarify for me please in M2, what the correlation/covariance between the intercept and stvc means? Thank you.
One way to interpret it is as follows. As the starting point (which is the intercept growth factor value) of the growth process increases, a larger amount of course taking at a certain time point has an increasing effect on the math performance.
R McDowell posted on Tuesday, December 05, 2017 - 12:05 am
Thank you for that interpretation, which is very helpful and spells out carefully what the meaning of the covariance I is.