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# topic9 - Statistics 512 Applied Linear Models Topic 9 Topic...

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Statistics 512: Applied Linear Models Topic 9 Topic Overview This topic will cover Random vs. Fixed Effects Using E ( MS ) to obtain appropriate tests in a Random or Mixed Effects Model. Chapter 25: One-way Random Effects Design Fixed Effects vs Random Effects Up to this point we have been considering “fixed effects models”, in which the levels of each factor were fixed in advance of the experiment and we were interested in differences in response among those specific levels. Now we will consider “random effects models”, in which the factor levels are meant to be representative of a general population of possible levels. We are interested in whether that factor has a significant effect in explaining the response, but only in a general way. For example, we’re not interested in a detailed comparison of level 2 vs. level 3, say. When we have both fixed and random effects, we call it a “mixed effects model”. The main SAS procedure we will use is called “ proc mixed ” which allows for fixed and random effects, but we can also use glm with a random statement. We’ll start first with a single random effect. In some situations it is clear from the experiment whether an effect is fixed or random. However there are also situations in which calling an effect fixed or random depends on your point of view, and on your interpretation and understanding. So sometimes it is a personal choice. This should become more clear with some examples. Data for one-way design Y , the response variable Factor with levels i = 1 to r Y i,j is the j th observation in cell i , j = 1 to n i A balanced design has n = n i 1

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KNNL Example KNNL page 1036 ( knnl1036.sas ) Y is the rating of a job applicant Factor A represents five different personnel interviewers (officers), r = 5 levels n = 4 different applicants were randomly chosen and interviewed by each interviewer (i.e. 20 applicants) (applicant is not a factor since no applicant was interviewed more than once) The interviewers were selected at random from the pool of interviewers and the appli- cants were randomly assigned to interviewers. Here we are not so interested in the differences between the five interviewers that happened to be picked (i.e. does Joe give higher ratings than Fred, is there a difference between Ethel and Bob). Rather we are interested in quantifying and accounting for the effect of “interviewer” in general. There are other interviewers in the “population” (at the company) and we want to make inference about them too. Another way to say this is that with fixed effects we were primarily interested in the means of the factor levels (and the differences between them). With random effects, we are primarily interested in their variances .
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topic9 - Statistics 512 Applied Linear Models Topic 9 Topic...

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