In simple terms, how would you explain (perhaps with simple examples) the difference between fixed effect, random effect and mixed effect models?
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Blogger Andrew Gelman says that the terms 'fixed effect' and 'random effect' have variable meanings depending on who uses them (link). Perhaps you can pick out which one of the 5 definitions applies to your case. In general it may be better to either look for equations which describe the probability model the authors are using (when reading) or write out the full probability model you want to use (when writing). |
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Fixed effect: Something the experimenter directly manipulates and is often repeatable, e.g., drug administration - one group gets drug, one group gets placebo. Random effect: Source of random variation / experimental units e.g., individuals drawn (at random) from a population for a clinical trial. Random effects estimates the variability Mixed effect: Includes both, the fixed effect in these cases are estimating the population level coefficients, while the random effects can account for individual differences in response to an effect, e.g., each person receives both the drug and placebo on different occasions, the fixed effect estimates the effect of drug, the random effects terms would allow for each person to respond to the drug differently. General categories of mixed effects - repeated measures, longitudinal, hierarchical, split-plot. |
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The distinction is only meaningful in the context of non-Bayesian statistics. In Bayesian statistics, all model parameters are "random". |
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Not really a formal definition, but I like the following slides: Mixed models and why sociolinguists should use them (mirror), from Daniel Ezra Johnson. A brief recap' is offered on slide 4. Although it mostly focused on psycholinguistic studies, it is very useful as a first step. |
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@Andrew. These terms are very common in the context of meta-analysis and elsewhere. Let me explain in simple and non-technical way. The fixed-effects assumption is popular in case of what has come to be christianed as traditional Anova. The effect-size does not change (folloing repetitive measurements for a specific sample-size). A change in sample-size will change the sampling error and there will be no change in the effect-size! The observed effect-size will undergo a change. The observed effect-size embodies (true)effect-size as well as sampling error and presumablly no other effects such as moderator effects. The random=effects assumption is a little technical. It trusts in a number of possibilities ie a number of (observed) effect-sizes are feasible for a single-sample size. In the sense of what I have said, the mixed model |
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