Now I have longitudinal data (two waves), all exposures and outcomes were measured at time 1 and time 2. I primarily want to test the temporal relationship between exposures and outcomes, and then test the mediation effects using the third variables which were also measured at both times.
I know that there are GEE, multilevel model, and SEM can be used to analyze longitudinal data.
But how to use these methods to test the mediation effects?
Thanks.
Hi,
Mediation models for longitudinal data have much to offer for improving statistical inference and for allowing the examination of intra individual variation. This choice of medication models to use longitudinal data adds considerable complexity. Three important issues are there, to consider for mediation models using longitudinal data. Two of these issues are common to any longitudinal model but the third is specific to longitudinal mediation models.
1. The first issue relates to the theory of change. This was explained by Collins et. al ie., whether the variables in the model are expected to change, in what ways the variables are expected to change, and what the possible determinants of change. Refer also Ram & Gerstorf et al for this issue. The theory of change should inform the mediation model we choose.
2. The second issue is the important role of time in any model. This applies to choosing the period, or time of interest in the life of the participants; choosing the span of the study, or length of time that participants will be followed; as well as the lag, or the amount of time that will elapse between adjacent measurements.
3. The third issue is one of multiple types of indirect effects possible when using longitudinal data. Contrary to the three-variable mediation models for cross-sectional data in which only one indirect effect is examined, mediation models for longitudinal data often have multiple indirect effects and even different types of indirect effects. It is important to consider whether and how to summarize these multiple indirect effects.
Next we examine, the aforementioned issues in the context of three mediation models for longitudinal data: You can use the following models like: cross-lagged panel model, a latent growth curve model, and a latent difference score model.
References:
1. Collins, L. M. Analysis of longitudinal data: The integration of theoretical model, temporal design, and statistical model. Annual Review of Psychology 2006; 57, p: 505–528.
2. Ram, N. & Gerstorf, D. Methods for the study of development – developing methods: Introduction to a special issue of Research in Human Development. Research in Human Development; 2009; Vol. 6(2–3); p: 61–73.
Hi,
Mediation models for longitudinal data have much to offer for improving statistical inference and for allowing the examination of intra individual variation. This choice of medication models to use longitudinal data adds considerable complexity. Three important issues are there, to consider for mediation models using longitudinal data. Two of these issues are common to any longitudinal model but the third is specific to longitudinal mediation models.
1. The first issue relates to the theory of change. This was explained by Collins et. al ie., whether the variables in the model are expected to change, in what ways the variables are expected to change, and what the possible determinants of change. Refer also Ram & Gerstorf et al for this issue. The theory of change should inform the mediation model we choose.
2. The second issue is the important role of time in any model. This applies to choosing the period, or time of interest in the life of the participants; choosing the span of the study, or length of time that participants will be followed; as well as the lag, or the amount of time that will elapse between adjacent measurements.
3. The third issue is one of multiple types of indirect effects possible when using longitudinal data. Contrary to the three-variable mediation models for cross-sectional data in which only one indirect effect is examined, mediation models for longitudinal data often have multiple indirect effects and even different types of indirect effects. It is important to consider whether and how to summarize these multiple indirect effects.
Next we examine, the aforementioned issues in the context of three mediation models for longitudinal data: You can use the following models like: cross-lagged panel model, a latent growth curve model, and a latent difference score model.
References:
1. Collins, L. M. Analysis of longitudinal data: The integration of theoretical model, temporal design, and statistical model. Annual Review of Psychology 2006; 57, p: 505–528.
2. Ram, N. & Gerstorf, D. Methods for the study of development – developing methods: Introduction to a special issue of Research in Human Development. Research in Human Development; 2009; Vol. 6(2–3); p: 61–73.
Jibin,
Senthilvel's answer has quite a lot of good information. The impression I have from your question, though, is that much of it is too late for your current study.
The theory of change Senthilvel discusses is critical to any modeling of indirect effects, regardless of the number of times of observation. If you can justify your assumed theory of change, there's nothing magical about two- or three-wave data compared to even cross-sectional (once you get beyond three, there's much more you can do with the statistical modeling).
In any measurement situation, you need to justify the assumptions you build into your model. With longer panel designs, it's typially easier to make those justifications, but it's not any different philosophically.
Note, though, that statistical methods rooted in the causal inference literature, such as instrumental variable approaches, can strengthen these justifications.
Pat
I would with only two waves go even simpler and use standard OLS models in which the response for now ( the output variable) is regressed on the predictor which is simply the past value (the input variable) - you are then modelling change or progress or decline or whatever it is. This model focuses on change and is considered by Gelman and Hill (2007) Data analysis and multivel models, pages 177-178 - they also explain why this is preferable to using the response as the difference in the input and output values (a gain score).
I typically mean centre the predictor so that the intercept will give you the response output value for a person with a typical value of the input score. You can then add into this model any moderating or mediating values that you wish to consider and consider how the coefficients change.
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