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Date:         Wed, 7 Oct 2009 09:51:24 -0700
Reply-To:     Dale McLerran <stringplayer_2@YAHOO.COM>
Sender:       "SAS(r) Discussion" <SAS-L@LISTSERV.UGA.EDU>
From:         Dale McLerran <stringplayer_2@YAHOO.COM>
Subject:      Re: Appropriate model for intra-class correlation coefficient
In-Reply-To:  <eb875ad3-318d-40e9-b293-c257be1e5b7d@b18g2000vbl.googlegroups.com>
Content-Type: text/plain; charset=iso-8859-1

--- On Tue, 10/6/09, cat.. <cat.b41@GMAIL.COM> wrote:

> From: cat.. <cat.b41@GMAIL.COM> > Subject: Re: Appropriate model for intra-class correlation coefficient > To: SAS-L@LISTSERV.UGA.EDU > Date: Tuesday, October 6, 2009, 10:55 PM > On Oct 5, 7:27 pm, stringplaye...@YAHOO.COM > (Dale McLerran) wrote: > > Cat, > > > > With only a single assessment from any one rater (one > child, > > one parent of that child), I don't see how you can > estimate > > a random rater effect. Assuming there might be > some sort > > of generation effect (parents tend to respond > differently > > than the child), the model which I would use for > anICCin > > this setting is: > > > > 4 - random family effect and fixed generation effect > > > > and estimate theICCfrom code something like the > following: > > > > proc mixed data=mydata; > > class family generation; > > model y = generation / s; > > random intercept / subject=family; > > run; > > > > This code will give you two variance components, the > family > > variance component (Vf) and the residual variance > (Vresid). > > TheICCwould be obtained as: > > > > ICC= Vf / (Vf + Vresid) > > > > I would note that this model is a variant of your > model 3a. > > But if you have a fixed rater effect and every parent > and > > every child is a rater, then the fixed rater effects > in > > model 3a would fully parameterize the model even > before you > > include random patient (or, in my presentation, > random > > family) effects. Note, too, that there would be > no error > > df for the residual term when every response is from > a > > different rater. This is a problem for a > normally > > distributed response (which is what I presume you wish > to > > assume). > > > > Dale > > --------------------------------------- > > Dale McLerran > > Fred Hutchinson Cancer Research Center > > mailto: dmclerra@NO_SPAMfhcrc.org > > Ph: (206) 667-2926 > > Fax:(206) 667-5977 > > --------------------------------------- > > > > - Show quoted text - > > Thanks Dale for this quick answer ! > > I agree with the fixed effect for the generation. In fact, > the model > you mention is exactly y = patient (random) + rater (fixed) > + error. > Family effect = patient effect as we have no sibling in the > sample. > rater effect = generation effect. > > What I'm less clear about is the code. I'm not very > familiar with proc > mixed and I wonder how you can fit a model y = family + > generation and > get a Vf variance with a statement like "model y = > generation" instead > of "model y = family generation". > > Would the code > > proc mixed data=mydata; > class family generation; > model y = family generation / s; > random family; > run; > > yield the same results ? > > Also, what about the - required - independance between > family and > generation when they are in fact patient and rater and the > rater is > either the patient him/herself or one of his/her parents ? > > Catherine. >

Catherine,

The MIXED procedure employs code which is similar to, but not identical to, GLM procedure code.

When using the GLM procedure, you name every effect of interest on the MODEL statement. You then declare which of those effects are random on the RANDOM statement. Thus, the MODEL statement for the GLM procedure names both fixed and random effects.

When using the MIXED procedure, the MODEL and RANDOM statements both identify effects that enter the model. The MODEL statement identifies only those effects which enter into the model as fixed effects while the RANDOM statement identifies those effects which enter the model as random effects. Thus, in the MIXED procedure, fixed and random effects do not appear together on the MODEL statement.

If you were to name family as an effect on both the MODEL and RANDOM statements of the MIXED procedure, you would be declaring that FAMILY has a fixed effect and a random effect. This is not at all what you want. In fact, this would be an overparameterized model.

As far as your question about independence between family and rater, I don't believe there is any such requirement. You need to be able to assume that the random family effects are independent of the person-specific residuals. That is a trivial assumption. After conditioning on the family effects, the person-specific residuals must be independent of the family effects. I would note, though, that since you have a balanced design with one child and one parent completing the assessment (I am correct about that, aren't I?), then the generation effect is totally independent of family effects.

By the way, I don't understand your equivalence statement, that

patient(random) + rater(fixed) + error

and

family(random) + generation(fixed) + error

represent the same model. To my way of thinking, every individual is a different rater. There would be as many raters as there are assessments. Put another way, in each family, there would be two raters - parent and child. The raters in family i would be different from the raters in family j. Thus, the rater effect would exactly produce the assessment.

The generation effect represents a systematic difference between parent and child ratings. This difference is a 1 df effect, regardless of the number of families in the data set.

Perhaps it is just terminology, that by rater you mean parent or child. That just isn't terminology which I would use. I think of rater as the person who completed the assessment.

Dale

--------------------------------------- Dale McLerran Fred Hutchinson Cancer Research Center mailto: dmclerra@NO_SPAMfhcrc.org Ph: (206) 667-2926 Fax: (206) 667-5977 ---------------------------------------


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