Re: st: reliability with -icc- and -estat icc-

[Nick Cox <njcoxstata@gmail.com>]

A scatter plot matrix is instructive.

Warning: destroys your data.

reshape wide Score rank , i(Application) j(Rator)
graph matrix Score?

#4 really is oddball.

Another interesting plot is

parplot Score?, tr(raw)

where -parplot- must be installed from SSC first.

Nick

On Tue, Feb 26, 2013 at 7:24 PM, Lenny Lesser <lenny3200@gmail.com> wrote:
> Hi Rebecca,
> Thank you for your help.  As a clarification:
> We used scores originally, but Rater 4's scores were all very low.
> Thus, when we ranked them, there were a lot of ties.  As seen below, 8
> of the 11 apps got a rank of "2" by rater.
> Lenny
>
> Application Rator Score rank
> 5 1 2 1
> 7 1 5 2
> 2 1 6 3
> 9 1 6 3
> 11 1 7 4
> 6 1 7 4
> 8 1 11 5
> 3 1 13 6
> 4 1 16 7
> 10 1 17 8
> 1 1 18 9
> 6 2 1 1
> 5 2 2 2
> 11 2 3 3
> 7 2 3 3
> 4 2 5 4
> 1 2 7 5
> 8 2 8 6
> 2 2 9 7
> 3 2 10 8
> 10 2 12 9
> 9 2 12 9
> 5 3 2 1
> 2 3 5 2
> 7 3 6 3
> 6 3 6 3
> 9 3 6 3
> 11 3 7 4
> 8 3 11 5
> 3 3 13 6
> 4 3 15 7
> 10 3 16 8
> 1 3 17 9
> 7 4 0 1
> 1 4 1 2
> 9 4 1 2
> 6 4 1 2
> 8 4 1 2
> 4 4 1 2
> 5 4 1 2
> 3 4 1 2
> 11 4 1 2
> 2 4 2 3
> 10 4 3 4
>
> On Tue, Feb 26, 2013 at 9:54 AM, Rebecca Pope <rebecca.a.pope@gmail.com> wrote:
>> Lenny,
>> I was just addressing your syntax error, not your underlying data
>> issues. Why would you expect a ratio to increase when you've made the
>> numerator 0? If you are getting an ICC close to 0, you should think
>> about what that is telling you about your data.
>>
>> If you look at e.g. judges.dta (example for -icc-), you'll see that
>> the results for the ICC is the same regardless of the method that you
>> use.
>>
>> webuse judges
>> icc rating target judge, mixed
>> xtmixed rating i.judge || _all: R.target, reml var
>> nlcom exp(_b[lns1_1_1:_cons])^2/(exp(_b[lnsig_e:_cons])^2+exp(_b[lns1_1_1:_cons])^2)
>>
>> The two ICCs are nearly equal (to 6 decimal places). Using -xtmixed-
>> will never give you a negative value though.
>>
>> An aside: "I'm using the ranks (within an individual) instead of the
>> actual scores."
>>
>> If you are using rankings (1-11 presumably) within individual rather
>> than actual scores it isn't clear to me how rater 4 could be "off the
>> charts" regardless of actual scores assigned. By converting scores to
>> rankings, you've wiped out the correlation of scores within rater. You
>> seem to be interested instead in how e.g. app 1 is rated by all 4
>> raters (correlation within app). If raters 1, 2, 3 all give it a score
>> of 1 (their preferred app) & rater 4 gives it a 6, you don't want to
>> drop that info. That is what you are analyzing.
>>
>> Regards,
>> Rebecca
>>
>>
>>
>> On Tue, Feb 26, 2013 at 10:16 AM, Lenny Lesser <lenny3200@gmail.com> wrote:
>>> Thanks Rebecca,
>>> With that code, I get the same problem when I eliminate one rater.
>>>
>>> the var(rater) goes to zero, which makes my ICC 0, rather go up to a
>>> higher number as I expected.
>>>
>>>
>>> ---------- Forwarded message ----------
>>> From: Rebecca Pope <rebecca.a.pope@gmail.com>
>>> Date: Tue, Feb 26, 2013 at 7:08 AM
>>> Subject: Re: st: reliability with -icc- and -estat icc-
>>> To: statalist@hsphsun2.harvard.edu
>>>
>>>
>>> Lenny,
>>> I don't think you've got the correct syntax for -xtmixed- if you are
>>> trying to duplicate ANOVA results, which is the type of analysis that
>>> -icc- appears to conduct (documentation is still limited, so I won't
>>> swear to anything).
>>>
>>> Use this syntax for -xtmixed-:
>>> xtmixed rank i.Application || _all: R.Rater, reml var
>>>
>>> -estat icc- is not a valid post-estimation command after this
>>> specification. However, you can just use the definition that ICC =
>>> Var(Rater)/(Var(Rater)+Var(Residual)).
>>>
>>> You might also want to take a look at
>>> http://www.ats.ucla.edu/stat/stata/faq/xtmixed.htm which will give you
>>> instructions for using -xtmixed- to conduct ANOVA-type analyses (using
>>> Stata 10, so you'll need to modify somewhat).
>>>
>>> Regards,
>>> Rebecca
>>>
>>>
>>>
>>> On Mon, Feb 25, 2013 at 10:56 PM, Lenny Lesser <lenny3200@gmail.com> wrote:
>>>> I have 4 raters that gave a score of 0-100 on 11 smartphone applications.
>>>> The data is skewed right, as they all got low scores.  I'm using the
>>>> ranks (within an individual) instead of the actual scores.  I want to
>>>> know the correlation in ranking between the different raters.
>>>>
>>>> I've tried the two commands:
>>>>
>>>> -xtmixed rank Application || Rater: , reml
>>>> -estat icc
>>>>
>>>> (icc=0.19)
>>>>
>>>> and
>>>>
>>>> -icc rank Rater Application, mixed consistency
>>>>
>>>> (icc=0.34)
>>>>
>>>> They give me two different answers. Which one is correct?
>>>>
>>>>
>>>> Next, we found out that rater 4 was off the charts, and we want to
>>>> eliminate her and rerun the analysis. When we do this we get wacky
>>>> ICCs.  In the first method we get an ICC of 2e-26.  In the 2nd method
>>>> (-icc), we get -.06.  Eliminating any of the other raters gives us
>>>> ICCs close to the original ICC.  Why are we getting such a crazy
>>>> number when we eliminate this 4th rater?
>>>>
>>>>
>>>> I'm guessing this might be instability in the model, but I'm not sure
>>>> how to get around it.
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