dummy encoding in metafor

Dear Wolfgang and Michael,

thank you very much for your help!

Concerning the Variance: I took the variance I used for CMA (which 
is always 1), so I think it should be the right one.

Thank you for noticing and mentioning though :)

I really appreciate how helpful you both are.

best,
Alma



From: Viechtbauer Wolfgang (STAT) 
<wolfgang.viechtbauer at maastrichtuniversity.nl>
To: Michael Dewey <info at aghmed.fsnet.co.uk>; Alma Wilflinger 
<alma_anima at yahoo.com>; "r-help at r-project.org" <r-help at r-project.org>
Sent: Monday, January 21, 2013 11:10 AM
Subject: RE: [R] dummy encoding in metafor

As Michael already mentioned, the error:

Error in qr.solve(wX, diag(k)) : singular matrix 'a' in solve

indeed indicates that your design matrix is not of full rank (i.e., 
there are linear dependencies among your predictors). With this many 
factors in the same model, this is not surprising if k is "only" 94 
(which is actually quite large for a meta-analysis). One options is 
to leave out some of the predictors. You can also try collapsing 
some of the levels of the factors. Of course, you lose some 
"details" that way, but apparently you don't have enough data in the 
first place to carry out such a detailed analysis.

One other thing I noticed. You wrote:

rma(yi=Mean, vi=Variance, ni=N.1, ...)

I suspect that your variable "Variance" is actually the variance of 
the raw scores. However, the vi argument is used to pass the 
sampling variances of the yi values to the function -- not the 
variance of raw scores. The (estimated) sampling variance of a mean 
is s^2 / n, so if I am not mistaken, you really want to use:

rma(yi=Mean, vi=Variance/N.1, ...)

Best,
Wolfgang

--
Wolfgang Viechtbauer, Ph.D., Statistician
Department of Psychiatry and Psychology
School for Mental Health and Neuroscience
Faculty of Health, Medicine, and Life Sciences
Maastricht University, P.O. Box 616 (VIJV1)
6200 MD Maastricht, The Netherlands
+31 (43) 388-4170 | http://www.wvbauer.com

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From: 

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On Behalf Of Michael Dewey
Sent: Monday, January 21, 2013 10:40
To: Alma Wilflinger; Michael Dewey; 

<mailto:r-help at r-project.org>r-help at r-project.org

Subject: Re: [R] dummy encoding in metafor

At 14:48 20/01/2013, Alma Wilflinger wrote:

Hi,

thank you very much for your kind answer.

If you look a bit further down the manual page you will see
### using a model formula to specify the same model
rma(yi, vi, mods=~factor(alloc)+year+ablat, data=dat, method="REML",
btt=c(2,3))

which is much easier.

I have seen the possibility of using a model formula for dummy
encoding and you are right it is much easier than doing it by hand.
Thing is that if I include some moderator variables into the
parameters I get the error:

Error in qr.solve(wX, diag(k)) : singular matrix 'a' in solve

I suspect that you have a linear dependence between your moderator
variables. Depending on how many levels there are for country,
sample, and so on you do have a lot of predictors (you presumably
know that a factor counts as levels-1 for this purpose?)

For example this call works:
result = rma(yi=Mean, vi=Variance, ni=N.1, mods=~factor(Country) +
relevel(factor(Sample), ref="Students") + Gender + Age +
factor(Category) + relevel(factor(Block), ref="c")+
relevel(factor(order), ref="x"), data=csvDataCmaAll, method="REML")

If I add the trials which is of type INT:
result = rma(yi=Mean, vi=Variance, ni=N.1, mods=~factor(Country) +
relevel(factor(Sample), ref="Students") + Gender + Age +
factor(Category) + relevel(factor(Block), ref="c")+
relevel(factor(order), ref="x") + trials, data=csvDataCmaAll,

method="REML")

I get the error and I was not able to find a definite reason for
this error or how to solve it I wanted to try it by doing it manually.
I think I have found out that it somehow relates to the

If you code them yourself R does not know. You know.

Regarding this I think my question was not clear enough. If R does
the dummy encoding automatically via a model formula it leaves out
one of the factors and uses it as a baseline automatically. If I do
it by hand R is still able to execute the function but the baseline
is missing because I do not define it via a parameter.

You perhaps would benefit from rereading some of the introductory
material about formulas. Also look for anything about the model
matrix (also called the design matrix)

I simply want to know how R is handling this and what I have to do
by hand to get the correct results. Sorry, this may be a beginners
question, but as stated I am new to this field.

You say you have seven moderator variables. Unless you have a shed
load of studies you will not be able to look at them simultaneously.
Apologies if you already knew that.

No I have not known that. In total I have about 94 studies and want
to test different sets of moderators. Do you think this is
sufficient or do you suggest another approach?

The truthful but perhaps unhelpful answer is that you need to collect
more data or use fewer moderators.

I started in CMA (comprehensive meta analysis) but one of the
benefits of R is that I am able to test multiple moderators at once
- at least as I was told.

kind regards,
Alma


From: Michael Dewey 

<<mailto:info at aghmed.fsnet.co.uk>info at aghmed.fsnet.co.uk>

To: Alma Wilflinger 

<<mailto:alma_anima at yahoo.com>alma_anima at yahoo.com>; 
"<mailto:r-help at r-project.org>r-help at r-project.org"

<<mailto:r-help at r-project.org>r-help at r-project.org>
Sent: Sunday, January 20, 2013 12:52 PM
Subject: Re: [R] dummy encoding in metafor

At 17:14 19/01/2013, Alma Wilflinger wrote:

Hi,

I am quite new to R and in need of some advice. I am trying to
conduct a meta regression over a some studies with about 7 mod
variables which I have to dummy encode.

Alma, although you can generate your own dummy variables by hand you
do not have to as R will do it for you. See below for more comments.

I have found the following piece of code in the manual for the
metafor library:

### manual dummy coding of the allocation factor
alloc.random <- ifelse(dat$alloc == "random", 1, 0)
alloc.alternate <- ifelse(dat$alloc == "alternate", 1, 0)
alloc.systematic <- ifelse(dat$alloc == "systematic", 1, 0)

If you look a bit further down the manual page you will see
### using a model formula to specify the same model
rma(yi, vi, mods=~factor(alloc)+year+ablat, data=dat, method="REML",
btt=c(2,3))

which is much easier.

### test the allocation factor (in the presence of the other

moderators)

### note: "alternate" is the reference level of the allocation factor
### note: the intercept is the first coefficient, so btt=c(2,3)
rma(yi, vi, mods=cbind(alloc.random, alloc.systematic, year, ablat),
data=dat, method="REML", btt=c(2,3))

What I do not understand is the following:
How does R know which columns in my data.frame are related to the
dummy encoded variables?

If you code them yourself R does not know. You know.

It is clear that in the call of cbind I just do not use the
reference variable as a parameter but I do not get it how R knows
that alloc.random and alloc.systematic refer to the column alloc in
the data frame.

Thank you very much in advance for your help,

You say you have seven moderator variables. Unless you have a shed
load of studies you will not be able to look at them simultaneously.
Apologies if you already knew that.

kind regards,
Alma
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