Fixed Effect vs Random Effect Models Can anyone tell me what is Fixed effect and Random effect models? How to make out that when to use fixed effect and random effect model? What algorithms are the examples of fixed effect and Random effect models?
 A: Both models assume that there are certain parameters that determine the distribution of the observations.  Those parameters determine the "effects":  For example, there might be 3 groups of observations, and the means for each group are assumed to be the same for every observation in each group, but different between groups.  The "effect" of groups is a measure of the differences between those means.
Random effect models make the additional assumption that those parameters are themselves random variables drawn from some distribution, which may have its own parameters (sometimes called "hyperparameters").  This assumption gains you the ability to make predictions about unobserved groups.  In a fixed effect model, all you know is that the new group would have some mean, but you don't know anything about it.  In a random effect model, you can assume that new mean would be similar to the other means because it is drawn from the same distribution.
Depending on how they are analyzed, sometimes the estimates for each group will change between random effect models and fixed effect models.  This reflects the fact that the means are assumed to come from the same distribution, so estimates get pulled towards the overall mean.
The last part of your question doesn't really make sense.  Models are models, and algorithms are algorithms.  An algorithm can't be an example of a model.  If you really meant "what algorithms are used with each type of model", it would make more sense, but it's too big a question to really answer.  There are many algorithms for estimating the parameters of a model, and many more algorithms for computing things from those estimates.  
