Hi, thanks for these great presentation, gained a lit from it. I have a quite similar example with 2 binary time-invariant covariates (TICs). So the interpretation is quite straightforward as you explained. Now I want to create a plot and face problems in doing. With 2 binary TICs I have 4 groups or different trajectories but I dont know how to combine the estimates (which is also showing my shortcomings in math). and: do I have to use the unstandardised or standardised estimations of my model? Maybe a paper on this issue would also help. Thanks for helpful comments and hints! BR Gert
Hi Dr. Curran! Thank you for all of these videos- I still use them all the time. One question- I am running a latent growth curve that has a quadratic slope. I have time-invariant predictors on the intercept, slope, and quadratic slope. I ran these in MPlus. Once I have run these contingent-LGCMs, does the interpretation of the intercept, slope, and quad slope (Under the "intercept" category in the mplus output) moot?
Thanks for your kind words -- I'm glad you have found these videos helpful. When you have TICs predicting the latent growth factors, the intercept terms of the latent factors are interpreted in the same way as a traditional regression -- that is, they are the model-implied means of the factors when all TICs are equal to zero. If that implied value has some meaning (say you mean-center your continuous predictors or have a binary predictor where a value of zero reflects a given group) then these may be meaningful to interpret. If zero values on your TICs are not interpretable (say you have a TIC that ranges from 1 to 5, so zero is not a valid value) then interpreting these can be quite misleading. I hope this helpful -- good luck with your work -- Patrick
great video. why don't intercept and slope covary directly anymore? and, how can I identify the variance of slope and intercept after adjusting for covariates in SEM? before integrating timeinvariant covariate, the double headed arrows back and to the slope/intercept were the variances. now these are just residual variances now if I understand correctly. Or do I still have to create separate latents for the residual variances, like you did?
Hi Leo -- thanks for the note. The intercept and slope continue to covary, either as an unconditional variance (if there are no TICs) or as a conditional or disturbance (if there are TICs). So that covariance is always there no matter what. If you only have TVCs, you can still interpret the latent intercept and slope variance as you would without the TVCs -- but in the TVC model they are simply growth trajectories in the *adjusted* repeated measures net the TVCs. If you also have TICs, then you can longer unambiguously interpret the variance of the growth factors because these are now residual variances. Hope that helps -- stay safe -- patrick
@@centerstat Hi Patrick, thank you very much. My concern, I think, is much more about parametrization, maybe I don't understand the different possible ways of showing the residuals. In this video, you draw a path from the residuals to the factors and let the residuals covary. The residuals in this case are standalone latents, right? What if I do not parametrize it this way, but rather just estimate the variance of each factor (intercept, slope) und let the factors covary normally (and then of course interpret the regular variances of these factor as residual variances)? I am talking about two headed arrows from and leading to the factors. This should get me the same estimates right?
@@leod1740 Hi Leo -- you're right....the residuals are often drawn as a one-indicator latent factor with a loading fixed to 1.0. However, as you suspect, these are simply typical residuals in the model parameterization -- you don't define any latent factor for them, and they are nothing more than a variance implied by the model net the joint effects of the predictors. As a side note, it's possible to create a thing called a "phantom variable" -- this term was first coined by David Rindskopf -- and you can "trick" the model into thinking the residual is an actual factor. The motivation for doing this is to then allow you access to the residual as a concrete part of the model -- you can predict it, or use it as predictor. But those models get a bit weird and are atypical in practice. Hope that helps -- patrick
@@centerstat okay now I get it... thank you very much! In fact, I have been using these phantom variables so far, as I've simply redrawn in my SEM program what I've seen in the path diagrams...
Thank you for a great series of lectures. Your lecture is so clear and concise.
These sounded strange the first time I watched. After reading and implementing their references, they now sound worldly.
Free valuable resources!
Wonderful video. Thank you.
Hi, thanks for these great presentation, gained a lit from it. I have a quite similar example with 2 binary time-invariant covariates (TICs). So the interpretation is quite straightforward as you explained. Now I want to create a plot and face problems in doing. With 2 binary TICs I have 4 groups or different trajectories but I dont know how to combine the estimates (which is also showing my shortcomings in math). and: do I have to use the unstandardised or standardised estimations of my model? Maybe a paper on this issue would also help. Thanks for helpful comments and hints! BR Gert
as always, great video professor!
Thanks a lot for such wonderful lecture
Hi Dr. Curran! Thank you for all of these videos- I still use them all the time. One question- I am running a latent growth curve that has a quadratic slope. I have time-invariant predictors on the intercept, slope, and quadratic slope. I ran these in MPlus. Once I have run these contingent-LGCMs, does the interpretation of the intercept, slope, and quad slope (Under the "intercept" category in the mplus output) moot?
Thanks for your kind words -- I'm glad you have found these videos helpful. When you have TICs predicting the latent growth factors, the intercept terms of the latent factors are interpreted in the same way as a traditional regression -- that is, they are the model-implied means of the factors when all TICs are equal to zero. If that implied value has some meaning (say you mean-center your continuous predictors or have a binary predictor where a value of zero reflects a given group) then these may be meaningful to interpret. If zero values on your TICs are not interpretable (say you have a TIC that ranges from 1 to 5, so zero is not a valid value) then interpreting these can be quite misleading. I hope this helpful -- good luck with your work -- Patrick
@@centerstat Thank you!! I did not center the TIC continuous variables and it led to a very confusing intercept! Thanks so much :)
great video. why don't intercept and slope covary directly anymore? and, how can I identify the variance of slope and intercept after adjusting for covariates in SEM?
before integrating timeinvariant covariate, the double headed arrows back and to the slope/intercept were the variances. now these are just residual variances now if I understand correctly. Or do I still have to create separate latents for the residual variances, like you did?
Hi Leo -- thanks for the note. The intercept and slope continue to covary, either as an unconditional variance (if there are no TICs) or as a conditional or disturbance (if there are TICs). So that covariance is always there no matter what. If you only have TVCs, you can still interpret the latent intercept and slope variance as you would without the TVCs -- but in the TVC model they are simply growth trajectories in the *adjusted* repeated measures net the TVCs. If you also have TICs, then you can longer unambiguously interpret the variance of the growth factors because these are now residual variances. Hope that helps -- stay safe -- patrick
@@centerstat Hi Patrick, thank you very much. My concern, I think, is much more about parametrization, maybe I don't understand the different possible ways of showing the residuals. In this video, you draw a path from the residuals to the factors and let the residuals covary. The residuals in this case are standalone latents, right? What if I do not parametrize it this way, but rather just estimate the variance of each factor (intercept, slope) und let the factors covary normally (and then of course interpret the regular variances of these factor as residual variances)? I am talking about two headed arrows from and leading to the factors. This should get me the same estimates right?
@@leod1740 Hi Leo -- you're right....the residuals are often drawn as a one-indicator latent factor with a loading fixed to 1.0. However, as you suspect, these are simply typical residuals in the model parameterization -- you don't define any latent factor for them, and they are nothing more than a variance implied by the model net the joint effects of the predictors. As a side note, it's possible to create a thing called a "phantom variable" -- this term was first coined by David Rindskopf -- and you can "trick" the model into thinking the residual is an actual factor. The motivation for doing this is to then allow you access to the residual as a concrete part of the model -- you can predict it, or use it as predictor. But those models get a bit weird and are atypical in practice. Hope that helps -- patrick
@@centerstat okay now I get it... thank you very much! In fact, I have been using these phantom variables so far, as I've simply redrawn in my SEM program what I've seen in the path diagrams...
Hi,
What if the covariates are not normally distributed? Should I transform them?
Curran-Bauer Analytics Thank you so much! I haven’t seen many applications transform dependent variables either.