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I did notice that in the following example, I obtained a insignificant main effect for treatment when including interaction, although the treatment is clearly effective. Any intuitive explanation?

with interaction in the model:

Source DF Type III SS Mean Square F Value Pr > F 
treat 1 1.13373175 1.13373175 1.01 0.3155 
BASE 1 43.14496711 43.14496711 38.51 <.0001 
BASE*treat 1 4.39447963 4.39447963 3.92 0.0488

without interaction:

Source DF Type III SS Mean Square F Value Pr > F 
treat 1 97.54885862 97.54885862 86.00 <.0001 
BASE 1 42.28030383 42.28030383 37.27 <.0001
kjetil b halvorsen
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hehe
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  • But how does it follow from the question body that Type III _is not recommended_? Any source, citations? – ttnphns Sep 28 '21 at 21:12
  • Type III is the senate. Type II is the house of representatives. Go with weights that are proportional to sample size. Seldom use type III . – Frank Harrell Sep 28 '21 at 22:49
  • @ttnphns https://en.wikipedia.org/wiki/Principle_of_marginality $\qquad$ https://www.stats.ox.ac.uk/pub/MASS3/Exegeses.pdf – Glen_b Sep 28 '21 at 23:37
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    @Glen_b, thank you. I've read the paper before. The topic of Type SS, and, particularly, Type III, is highly philosophical and opinion-laden. I personally think that III has its right. But my comment to the question was pointed to that the OP did not discuss the topic, limiting themselves to a mere example. – ttnphns Sep 29 '21 at 00:05
  • @ttnphns I saw this comment from some lecture slides. My understanding is that Type III SS leads to a test that compares a full model with a model without the last added variable, which is a model with interaction but without the main effect. Therefore, it seems a bit strange. The result from this example is supportive. It seems difficult to interpret the main effects based on type III SS if there is interaction in the model. However, for balanced design, there is no problem since all types of SS are the same. – hehe Sep 29 '21 at 17:31
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    Hehe, type III tests only unique portions of all the effects in the model, it doesn't depend on the sequence the effects enter it. It is true that under balancedness types SS don't differ - because then the effects don't overlap. – ttnphns Sep 29 '21 at 18:32
  • Dr Harrell, do you recommend to use type II SS? Actually I cannot think of a case where type III SS is more useful than type II. – hehe Sep 29 '21 at 18:35
  • @ttnphns thanks. Just feel that the unique portion of main effects excluding interaction is difficult to interpret. For instance, the main treatment effect in the example in the question. type II also does not depend on sequence. – hehe Sep 29 '21 at 18:37
  • Only type I depends on sequence. – ttnphns Sep 29 '21 at 18:41

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