Hi Sunethra,

I am assuming that by covariate pattern model you are implying a Generalized Estimating Equations approach (GEE). The GEE approach will account for the correlation within your data and provide you with population average estimates (accounting for the correlation). However you cannot make any inferences about the reasons for this variation at the cluster level and will not be able to calculate cluster specific effects. However the fixed effect estimates from a random effects model for a continuous outcome will be very similar to the GEE estimates. So if your research question involves evaluation of cluster specific effects, you should explore mixed-effects models. However if you only are interested in population average effects of clustered data for a linear or log-linear outcome, you can use either of the approaches, although GEE is computationally less intensive.

 A good discussion of these approaches is here:

To GEE or Not to GEE: Comparing Population Average and Mixed Models for Estimating the Associations Between Neighborhood Risk Factors and Health, Hubbard et al. Epidemiology, Volume 21(4), July 2010, pp 467-474

What do you mean by covariates? Some people use covariate to mean the thing you are testing. Others use covariate to mean something you analyze but don't control/care about. 

In Designed Experiments, a covariate is something you recorded but could not change, like ambient temperature, lot number of solution, etc. In this case, the covariate is usually though of as a random variable. The factors in the designed experiments are fixed effects. This gives you a mixed model.

In an observational data set, I will add covariates, which are things I think have an effect on my outcome but were not part of the original model. 

If I want to extend my models to encompass more than what I tested, like in a gage R&R study, I can make my model a random model.

What do you plan to do for with the results of your data?   

Thanks for the response .

I actually mentioned a covariance pattern model which is one kind of generalized mixed model in which you specify a structure(compound symmetric, AR, heterogeneous and etc)  to the covariance matrix of the residuals.

Im having an observational data set that in which the i individuals show up a clustering via the geographical area they lived in. I want o model their survival times constraint on the clustered setting.

Hi, Sunethra

Good Afternoon,

I have attached one pdf related to your question.  But, it is in the clinical trial.  Kindly go through it.  I hope its very much useful for you.  see the attachment.

Hi Sunethra,

I am assuming that by covariate pattern model you are implying a Generalized Estimating Equations approach (GEE). The GEE approach will account for the correlation within your data and provide you with population average estimates (accounting for the correlation). However you cannot make any inferences about the reasons for this variation at the cluster level and will not be able to calculate cluster specific effects. However the fixed effect estimates from a random effects model for a continuous outcome will be very similar to the GEE estimates. So if your research question involves evaluation of cluster specific effects, you should explore mixed-effects models. However if you only are interested in population average effects of clustered data for a linear or log-linear outcome, you can use either of the approaches, although GEE is computationally less intensive.

 A good discussion of these approaches is here:

To GEE or Not to GEE: Comparing Population Average and Mixed Models for Estimating the Associations Between Neighborhood Risk Factors and Health, Hubbard et al. Epidemiology, Volume 21(4), July 2010, pp 467-474

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.

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

Data Manual supplement for MLwiN Version 2.14