It depends. See the notes at the following link. Best wishes, David Booth

https://www.stat.ncsu.edu/people/davidian/courses/st790/notes.html

My dissertation work used mixed models. I copied the below from my methods chapter briefly summarizing the advantages of longitudinal multilevel modeling (MLM). I highly recommend Lesa Hoffman's book " Longitudinal Analysis: Modeling Within-Person Fluctuation and Change ".

"The primary advantage of a longitudinal study lies in its capacity to inform about within-person in addition to between-person relationships. The use of MLM in analyzing longitudinal data allows the examination of both between- and within-person relationships at different levels of analysis simultaneously. Many benefits have been reported of the use of MLM over traditional general linear models in analyzing longitudinal data.

With repeated measurements, strong correlations (or dependency) are expected between the individual’s responses over time, which violates the assumption of independence of data that is required for repeated measures analyses of variance and regression analyses. Multilevel models overcome this shortcoming by partitioning the outcome’s residual variance into a within-person component (the variance of the time-level or level 1 residuals) and a between-person component (the variance of the person-level or level 2 residuals). The covariance between residual components at each level in the hierarchy and between hierarchies is therefore explored to identify sources of dependency and accurately distinguish individual and time-specific differences (Hoffman, 2015; Hox, 2010). Furthermore, MLM handles missing and unbalanced data while preserving statistical power and the generalizability of results, which overcomes the problem of listwise deletion with general linear models. "

Many thanks dear David Booth & Nour Alayan for the very important resources you shared me! One more request though: if you can find me recent article(s) published comparing the two?

Have a very pleasant time!

I think it is important to realize that they are different models and not just different estimation proecdures. And for me the Mixed/ Random/ Multilevel approach is more general and flexible in that you can derive the cluster-specific and population average estimates from the mixed model but only the latter ones from the GEE model.

There is a lot about the difference in this

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

and this a long previous post on the topic

Revised version as of 20th July 2014

There are two types of models when dealing with a panel study where occasions are nested within individuals, subjects or clusters; that is there is dependency or autocorrelation over time in the response variable. This has particular importance for discrete outcomes eg predicted probability having a disease or not (say) from an estimated model.

The two approaches to within subject variation are: 1) Marginal i.e. Population average models: estimated by GEE estimation: the estimated slope is the effect of change in the whole population if everyone’s predictor variable changed by one unit 2) Conditional: cluster specific, mixed or multilevel: the slope is the effect of change for a particular ‘individual’ or subject of a unit change in a predictor.

Marginal estimates should not be used to make inferences about individuals (committing ecological fallacy), while conditional estimates should not be used to inferences about populations (atomistic fallacy). The population average approach underestimates the individual risk & vice-versa . Importantly, GEE estimation is robust to assumptions about the higher level, between- subject distribution; gives correct SE for fixed part and gives the Population average value. But GEE does not give the higher-level variance, it is not extendible to random slopes and 3 level models etc; and does not give & cannot derive the cluster-specific estimates. All things that you get with the mixed, multilevel random-effects approach. Moreover, it has been argued by Gary King that using robust SE's is like taking a canary down the mine; if the robust SE's give different results , there is something wrong with the model, it is not OK to interpret it. For what it is worth I agree with him and thus I think it is better to have an explicit model that does take the dependency into account and not just treat as a nuisance to be corrected.

http://gking.harvard.edu/publications/how-robust-standard-errors-expose-methodological-problems-they-do-not-fix

Consequently I believe, contra Hubbard et al, that random effects analysis is the more generally useful method - To GEE or Not to GEE: Comparing Population Average and Mixed Models for Estimating the Associations Between Neighborhood Risk Factors and Health, Epidemiology, Volume 21(4), July 2010, pp 467-474

Indeed, population-averaged values can be obtained from random effects model in the MLwiN software via simulating predicted probabilities (but not vice versa), see below In practice there has to be a lot of difference between individuals and therefore (equivalently) a lot of similarity over time within subjects for there to be a difference between the two estimates. Thus when a fixed estimate is -1.5 on the logit scale, and the between variance is 1.0 (ie some 23 percent of the variance lies at the occasion level; with the level 1 within person variance of a standard logistic being constrained always to 3.29), the cluster specific result is a probability of 0.18 while the population average value is 0.22 .

However if the between variance on a logit scale is 3 (so that 48% of the total variance lies at the occasion level) , the cluster specific result remains a probability of 0.18 while the population average value is now 0.27. The GEE approach treats this clustering as a nuisance and does not give an estimate of the higher-level variance.

The mixed random effects model treats the clustering as of substantive interest and you do get an estimate of its size and nature – but this generally requires distributional assumptions about the higher-level random effects; although non-parametric random effects procedures are possible. There is more on mixed modelling for longitudinal analysis here, and a long chapter considers diiferent types of dependency over time such as the Toeplitz model and the unstructured model in the random effcets model. The essence of this is the random intercepts model may not be complex enough to capture the nature of the dependence as it assumes that the autocorrelation between any two time points is the same (ie compound symmetry assumption). The unstructured model estimates different degree of dependence between each and every time period - this is flexible but not parsimonious as the number of parameters grows rapidly. The Toeplitiz model is quite flexible and quite parsimonious as it assumes equal autocorrleation for periods the same lag apart - all of this is detailed in the following

Developing multilevel models for analysing contextuality, heterogeneity and change using MLwiN, Volume 2 Kelvyn Jones, VS Subramanian ; available from

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

And the MLwin procedure for getting both population average and cluster-specific estimates via simulation post estimation is documented here

https://www.researchgate.net/publication/234015221_Manual_supplement_for_MLwiN_Version_2.14?ev=prf_pub

Apologies for going on at length and re-using some material from previous posts.

Dear Kelvyn Jones, thank you so much for the very important & extensive explanation to my question. Hopefully, others will also share helpful resources on this topic!

Many thanks again,

Berhanu

It depends on several factors and the research question (level of complexity of the model you want) including the number of levels to be considered, whether only random intercept or both random intercept & slope is to be considered, missing data assumptions, etc.

In most cases, I would prefer the mixed-effects/random coefficients analysis than GEE as it provides a more general and flexible modeling. Mixed model with a random intercept (the simpler mixed-effects model) is something equivalent to GEE with exchangeable correlation. However, in mixed-effects you can model more complex assumptions including random slopes, multiple levels of clusters, with different options for the covariance between the random intercepts & slope. The mixed model also enables you to estimate both population average & cluster specific estimates whereas GEE provides only population average estimates as it uses a semiparametric approach for specifying the clustering of measurements. With missing data, mixed-effects model assumes MAR (missing at random) & GEE assumes MCAR (missing completely at random) where the latter is a more stringent assumption to meet in real data. One thing important in mixed model is that validity of inference can be affected if your data deviated from model assumptions. Below are some of the important reference for both analysis approaches.

Jos Twisk. Applied Longitudinal Data Analysis for Epidemiology.

Garrett Fitzmaurice et al. Applied Longitudinal Analysis.

Peter Diggle. Analysis of Longitudinal Data.

Thank you so much dear Alemayehu for your contribution!