Fixed Effect Model
In this model, the investigator or researcher is concerned to draw inferences about ‘t” the treatments involved in the experiment. It is the appropriate model to use if the interest of the researcher, inference-wise, is in the ‘t’ treatments only.
In simple words, if the researcher is confined to the effect of pre-selected treatment, it is called a fixed-effect model.
If we run an experiment with the objective of comparing the yield performance of three varieties of wheat and wish to make inferences on these three varieties only, then, we will use the fixed-effect model.
Random Effect Model
This model is suitable for an experiment in which a researcher is interested to draw inferences about the population of treatments of which only a random sample of “t” treatments is selected.
If a breeder is interested in assessing the performance of certain varieties, then these varieties have to be taken as a random sample as they have come from a population of varieties.
The random effect can belong to a finite or infinite population. In this model, the main emphasis is on estimating and testing the variability among the effects of different treatments.
This model is suitable for CRD and can be extended to other designs.
The random effect model is often appropriate for data arising from survey-type investigations where a number of areas or units are sampled from which inference is made concerning the entire population of area are units.
Mixed Effect Model
If both the fixed and random effect models are involved, it will be called a mixed effect model. In this model, at least one variable is random and at least one variable is constant or fixed.
The mixed-effect model is used in factorial experimental combinations.
The method that describes a situation in which the treatments are the only treatments of interest is called the fixed model.
If we assume the treatments are randomly selected from a population of treatments and we are interested in making statistical inferences about the population of treatments, this is called a random model.
And a mixed model is one with fixed factors and random factors.