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I have a problem with model structure because of the way factors are nested in a potentially non-hierarchical way. I'm not sure if I fully understand the issue but I can't find a way to specify the model which Minitab or R will process without error.

The design is fairly simple. I have one response variable Reject which is measured under two levels of a within-subjects factor Equal and under two levels of a between-subject factor Cost. I also want to include Gender as a factor. I account for the within subject design by including Individual as a random factor.

I think the problem is that Individual is nested under both Gender (because each individual has only one gender) and Cost (because that is a between-subject factor), but neither of Cost or Gender is nested in the other. So that perhaps makes any valid model non-hierarchical (that is in any case Minitab's complaint).

Has anyone got any tips for how to construct a valid model testing the significance of Equal, Cost, and Gender, implementable in R or Minitab?

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  • $\begingroup$ Gender is not a random effect since it has only two levels. $\endgroup$ Commented Dec 16, 2014 at 10:31
  • $\begingroup$ Correct. But I didn't write that it was. I wrote that individual is a random factor. Am I missing something? $\endgroup$ Commented Dec 16, 2014 at 13:27
  • $\begingroup$ In hierarchical model you estimate random effects for higher levels (e.g. schools) and lower level nested in higher level (e.g. pupils in schools). So if you don't have a higher level (Gender is not a random variable with multiple levels) then it is not hierarchical model. If your only random term are individual observations then you have a simple linear model where error term accounts for individual variance. $\endgroup$ Commented Dec 16, 2014 at 13:37
  • $\begingroup$ Thanks for explaining that. It was news to me that you can't have random effects nested in fixed factors. Unfortunately I do have to have Individual as a random factor, I can't just have the standard linear error term, because there is the within-subject factor Equal. Not including the term would be ignoring the non-independenceof the within subject measurements. Do you have a suggestion for a specific model specification that would make this work? $\endgroup$ Commented Dec 16, 2014 at 16:35
  • $\begingroup$ What is your Effect variable and how many categories does it have? $\endgroup$ Commented Dec 16, 2014 at 16:41

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