Christian's book recommendation is a good one.

Most of what you'll find with only three time points is some form of trajectory modeling. Trajectory (or growth) modeling is essentially a data reduction technique -- how can you summarize an individual's change over the three points? It also will give you a summary (usually mean) trajectory.

The most common and straightforward is using latent growth modeling, a type of mixed-effect or random-effect model, to treat each respondent's change as linear growth with respect to time. AMOS can handle that easily, as can any SEM software. But linear is not the only functional form. You can use any curve that can be characterized by only two parameters (degrees of freedom issue).

I think the most contemporary recommendations are to use theory to identify a functional form if possible, and eyeballing individual change plots from the raw data if it's not. For example, I can imagine that an exponential decay (with respect to time) might be a better fit to your data than straight lines, and it can be done with two parameters (respondent-specific starting points and rates of decay), and any SEM software that allows nonlinear constraints on parameters (not sure about AMOS).

More general proportional change models may also serve you well -- McArdle and colleagues have led the way on those, and AMOS should be able to handle it just fine.

Hi, you can use software like EQS, LISREL, AMOS or R with the relevant packages to analyze longitudinal data. I would recomend the new book of Todd Litte (Little, T.D. (2013). Longitudinal Structural Equation Modelling. New York: Guilford Press.) as very good overview in the field of longitudinal analyses using SEM. KR, Christian

Thanks Christian Rietz

Christian's book recommendation is a good one.

Most of what you'll find with only three time points is some form of trajectory modeling. Trajectory (or growth) modeling is essentially a data reduction technique -- how can you summarize an individual's change over the three points? It also will give you a summary (usually mean) trajectory.

The most common and straightforward is using latent growth modeling, a type of mixed-effect or random-effect model, to treat each respondent's change as linear growth with respect to time. AMOS can handle that easily, as can any SEM software. But linear is not the only functional form. You can use any curve that can be characterized by only two parameters (degrees of freedom issue).

I think the most contemporary recommendations are to use theory to identify a functional form if possible, and eyeballing individual change plots from the raw data if it's not. For example, I can imagine that an exponential decay (with respect to time) might be a better fit to your data than straight lines, and it can be done with two parameters (respondent-specific starting points and rates of decay), and any SEM software that allows nonlinear constraints on parameters (not sure about AMOS).

More general proportional change models may also serve you well -- McArdle and colleagues have led the way on those, and AMOS should be able to handle it just fine.

Thanks Patrick Malone for very detailed answer. please clarify two things you mentioned (1) use theory to identify a functional form, and (2) general proportional change models. Thanks again

Naeem,

"Functional form" refers to the shape of the curve with respect to time. For example, linear, exponential decay, etc. If you have a priori reason to believe one or another, start with that, instead of something data-driven. Though you are still limited to curves that can be described by two parameters in this approach, so there aren't many to try.

Proportional change models are a different approach to the more common (at least in my field) polynomial trajectory models (e.g., linear, quadratic, cubic). Polynomial models have the time-specific values as indicators of the person-level values of intercept, linear slope, and so on. Proportional change models (again, see J. J. "Jack" McArdle's body of work, and more recent papers led by his co-authors) model the change (decline?) from occasion to occasion as a function of the previous level. There are lots of variations of both, and ways to do some of the same models in both, but that might get you started.

Hope that helps,

Pat

Thanks, Patrick

Latent Growt Curve Modeling via SEM is not the only alternative.

You could also try Hierachical Lineal Models, using specialized software, like HLM, or using special modules for Lineal Mixed Models, as those available in SPSS, STATA, SAS, etc

In this models, the diferent measures (time) would be nested within persons

This article is about SPSS:

http://ehp.sagepub.com/content/32/3/207.abstract

I have uploaded the following how-to-do it book on random-effects (HLM) modelling to Research Gate along with the data – there are two chapters on longitudinal data analysis

Developing multilevel models for analysing contextuality, heterogeneity and change using MLwiN, Volume 2

https://www.researchgate.net/publication/260772180_Developing_multilevel_models_for_analysing_contextuality_heterogeneity_and_change_using_MLwiN_Volume_2?ev=prf_pub

If you are a Stata user you can run MLwin via runmlwin

http://www.bristol.ac.uk/cmm/software/runmlwin/

and if you are a R user; you can use R2MLwiN

http://www.bristol.ac.uk/cmm/software/r2mlwin/

Book Developing multilevel models for analysing contextuality, he...

Any softwares such as AMOS, R, EQS and LISREL, with the relevant packages can be used to analyze longitudinal data.

Good article, Andres!

Attached is the actual article that Andres Burga referred to. If you follow his link you will be directed only to the abstract,and will have to pay for access to the article.

Latent growth analysis is the best techniques