Growth Curve Episode 3: A Multilevel Modeling Framework
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- Опубліковано 13 чер 2024
- In an earlier episode of Office Hours, Patrick addressed the question, “What are growth curve models”. In this episode he explores how a growth curve model can be estimated within the multilevel linear modeling (MLM) framework....
Patrick begins by reviewing the assumption of independence in the general linear model and how this is violated when data are nested (e.g., children nested within classrooms). He then describes how the MLM allows for the direct modeling of nested behavior, and how this framework can be extended to estimate growth models in which repeated measures are nested within individual. He examines the unconditional growth model, the incorporation of time-invariant and time-varying covariates, and expanding the MLM growth model to include additional levels of nesting.
Extremely talented instructor! I've gone through many papers and lectures on MLM and LGCM and this video/explanation has been the best I've seen so far. It's nice to see the use of a whiteboard!
No! Thank you very much for YOUR TIME!
This is truly the best explanation i have found about MLM. I have perused different courses, books, papers, workshops, repositories, other youtube videos and more, and while every one of those sources is good, this video has the best knowledge per minute ratio. It's really wonderful not because of the specific statistical technique (even if i'm truly grateful you chose to explain this topic), but because of the extremely clear explanation.
This video is a pedagogical gem.
SAME!
Wonderful lecture, wonderful teacher !!!!
I just came across this and I really want to thank you for explaining this and other topics in such an understandable way. It really helps :)
Thanks for the positive comments!
Thank you so much for the clear, coherent, and logical instruction!!!
Like it. it blows my mind. I guess, to some degree, you even give me direction about my dissertation.
Thank you very much, Dr. Curran~~~ You explained most of my questions!
Super amazing discussion and presentation. God Bless you Professor Curran
Thank you so much for the kind words -- I hope these are in some way helpful in your work. Take care and stay safe -- patrick
Super clear explanation ! Thanks a million!
Thanks so much Curran. Your explanation eliminated all the doubts I had about the fomulation of my model.
Thank you very much for your amazing explanation 👍👍👍
Many Thanks! Great clarify with an imaginable picture.
After watching your video, it feels like I have read 10 books... awesome! Thank you so much!
Hi Longzhu -- thanks for your nice words. Dan and I really appreciate it. Good luck with your work -- patrick
I later noticed that you are Patrick Curran :) You are the man in statistics, I admire you, professor!
Clear explanation, thanks!
A great deal of information here - taking the algebra to a three level model and describes a fascinating Army example with 5 levels!
Thanks! You saved my day! :)
very helpful. thanks
Great video
Thank you
I am so lucky to one of the 9316 viewers!
great as usual - interested in how you describe the level 1 subscripts sounds like 'ser' I ? Just wondered if it was a americanism:)
haha - Americans!
Great lecture. So what is the difference between the mixed model implemented in R lme4 package using the lmer() command and the Growth Curve you explain in this video?
thanks for your nice comments -- the lme4 package and lmer function jointly allows for the estimation of a general class of mixed effects models, including the growth models described here.
@@centerstat Thank you.
Leaving aside lmer(), what is the fundamental theoretical difference between the mixed effects models and the growth models described here?
@@OmarRafique-op7bv there is no difference -- they are one in the same. You estimate a growth model using a mixed effects framework. If you're interested, this might help:
Curran, P. J., Obeidat, K., & Losardo, D. (2010). Twelve frequently asked questions about growth curve modeling. Journal of cognition and development, 11(2), 121-136.
Is time itself a level-1 or level-2 factor?
Hi! tahnk you very much!
I have a question. Why when you added the second level "j" you didn´t add it to Age, in the level 1 model?
Hi Chem -- thanks for your note. You ask a great question -- the reason that "age" is entered at the level-1 part of the model with a subscript of both "t" and "i" is that the value of age differs for each child at each assessment (e.g., the child is 6, 7, 8, and 9 years of age over four time points -- that is indicated by "t"), but that different children can have different ages (e.g., 6, 8, 9, and 11 -- that is indicated by "i"). So age is allowed to vary over both time and person and this is entered at level 1. I hope this helps -- patrick
thank you for the prompt answer. Yes I understood that part, because of that, around the minit 20, he added a third level (class). Then in the first level formula he added the "class" level (j), but it wasn´t added for Age. I expected that it was the Age of the "i" child from de "j" class and I don't know if there is a mathematical reason for don't add the "j"
ahhhh....sorry, I misunderstood your initial question. Yes -- you could indeed include "j" on age; I was just writing on the fly and didn't add it in the full equation. But if you were to fully write out the 3-level growth, you would indeed have age_tij.
ok perfect! thank you very much for sharing your knowledge!
If is not too much to ask, I'm working with longitudinal data (growth along time of plants) I have around 7 measures for each plant, but those aren´t at the same time for all the plants. The data is perfectly adapted to a 3p logistic curve (I need an asymptote), and I want to compare the growth curves of diferent groups of plants (if one group grows faster than other, etc). What will be your advise for comparing the curves between groups in all ways posible?
Thank you again
Thank you so much for this. I have a question.
@18:00 when you include B2i.QualityTi into the Level 1 equation does it still remain a growth curve model. Can't I also call it a Quality curve model with Age as another variable? Why do yo still call it a growth curve model.
Secondly, the graph you make is Agg vs Age, but after @18:00 it should be Agg vs Age(one independent axis) + Quality(another independent axis).
Thanks for your nice words. With a 2nd time-varying covariate in addition to your time metric, it is still a growth model but it can be interpreted in two ways. First, you can examine growth in the DV net the effects of the TVC (so you are looking at growth curves in the adjusted outcome); or second, you can examine the relation between the TVC and the outcome above and beyond the effect of the underlying growth trajectory. These are precisely the same model and simply give different interpretational priority depending on your theory. The same holds for the plotting of effects. Raudenbush and Bryk have a really nice section on this in their 2002 book on hierarchical linear modeling.
@@centerstat Sorry, could you please explain this again. Not a native speaker. What is the neaning of "net the effects" and "above abd beyond"?
@@user-mk9gx4hd2l of course -- it simply means the unique effect of each predictor while holding all other predictors constant. This is sometimes referred to as "controlling" for other predictors -- statistically, it's as if the only characteristic individuals varied on is the predictor of interest because all others are held constant.
Is "teacher quality" in this example a moderating variable, is this the way I test for moderatoring effects in a multi level growth curve model? Thank you! :)
Hi Svenja -- Thanks for the question. Yes....'teacher quality' could be considered a moderator of change over time. Dan and I have written a couple of papers on this that might be of interest to you. The cites are below. Good luck with your work -- patrick
Bauer, D.J., & Curran, P.J. (2005). Probing interactions in fixed and multilevel regression: Inferential and graphical techniques. Multivariate Behavioral Research, 40, 373-400.
Curran, P.J., Bauer, D.J., & Willoughby, M.T. (2004). Testing and probing main effects and interactions in latent curve analysis. Psychological Methods, 9, 220-237.
@@centerstat Great, thank you!!
Basic question here:
So how does nesting solve the correlation between observation problem of regression?
Hi -- by building a model that explicitly represents the two separate sources of variability (time within person, and between persons) then the conditional distributions among the residuals at level 1 are independent.
In the model @15:30 there is an interaction term introduced between gender and age. What if I do not want an interaction term and just the main effects for age and gender.
Thanks for the comment -- if you don't want a cross-level interaction with time, then you need only include your predictor in the intercept equation and not the slope equation. Then it will be a main effects-only model.
@@centerstat thank you for the reply.
But what is an intercept equation and what is a slope equation? And by predictor, do you mean Age or Gender?
@@OmarRafique-op7bv the intercept equation if B0 and the slope equation is B1; age would only enter at level 1 and gender at level 1.
What if I put gender into the level 1 equation @15:30.
unless gender varied with time (say self-reported variability in perceived gender) then you could enter this at level 1. However, if you treat a characteristic as immutable to the passage of time (say biological sex at birth) then it would go into level 2 given the values do not vary as a function of time.
Please, how can I carryout a Nonlinear Split-plot design model analysis using SAS? Using MLE, ANOVA and REML methods for the variance estimates for the WPE and SPE(EGLS), as well compare it to a Nonlinear SPD Model analysis using OLS method for the parameters estimates?