0

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?

Amorphia
  • 591
  • 1
  • 3
  • 13
  • `Gender` is *not* a random effect since it has only two levels. – Tim Dec 16 '14 at 10:31
  • Correct. But I didn't write that it was. I wrote that individual is a random factor. Am I missing something? – Amorphia Dec 16 '14 at 13:27
  • 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. – Tim Dec 16 '14 at 13:37
  • 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? – Amorphia Dec 16 '14 at 16:35
  • What is your `Effect` variable and how many categories does it have? – Tim Dec 16 '14 at 16:41
  • Also check this link: http://conjugateprior.org/2013/01/formulae-in-r-anova/ – Tim Dec 16 '14 at 19:02
  • Sorry Tim, I don't follow you. I didn't say I have a variable called Effect - that would be really confusing. I have a continuous response variable called Reject, and I want to be able to test the main effects of a two-level within-subject factor Equal, a two-level between-subject factor Cost, and Gender. The problem is my models choke up because the random factor Individual needs to be nested in both Gender and Cost. – Amorphia Dec 16 '14 at 20:35
  • I meant Equal. Do you have balanced design? – Tim Dec 16 '14 at 22:13
  • Not perfectly balanced, but there is a lot of data in every cell. – Amorphia Dec 17 '14 at 07:54

0 Answers0