Re: st: SE and CI by mrtab

[Nick Cox <njcoxstata@gmail.com>]

My constructive suggestion for getting standard errors and confidence
intervals for percentage of mentions is to base them on bootstrap
samples of persons.

Nick

On Tue, May 15, 2012 at 10:17 AM, Nick Cox <njcoxstata@gmail.com> wrote:
> That sounds a plausible first approximation, but the data generation
> process varies. To make matters concrete, let's imagine a question
> asked of n persons:
>
> Which statistical software do you use routinely?
>
> However, the protocol can vary:
>
> 1. People can name as many distinct programs as they like.
>
> 2. People should name precisely k distinct programs. (Perhaps a bit
> unlikely with this particular question, but bear with me.)
>
> 3. People may name up to k distinct programs.
>
> 1', 2', 3'. As above, but the order of mention is important.
>
> In practice these protocols all lead to datasets in which responses
> are stored as several variables for analysis. (The exception in which
> (e.g.) "Stata R SAS" is packed into a single string variable is not
> much of an exception, as the contents need to be unpacked to do much
> with them.)
>
> Now, it seems key to me that the number of persons is an upper limit
> on the number of mentions of a particular program, so the percent of
> mentions of a particular answer is not bounded by 100, but by a lower
> limit. (What to do about the enthusiast who says "Stata Stata Stata"
> is a practical point, just as what to do about the enthusiast who says
> "Manchester City".)
>
> Also, although this may well be a much smaller point, the
> interpretation of missing values differs between these protocols.
>
> Nick
>
> On Mon, May 14, 2012 at 10:43 PM, Steve Samuels <sjsamuels@gmail.com> wrote:
>> Each "percentage" has the form P = (mentions of category X)/(number of mentions).  Numerator and denominator are random for each person, so the percentages are actually
>> ratios:
>>
>> ******************************
>>  use http://fmwww.bc.edu/RePEc/bocode/d/drugs.dta, clear
>>  mrtab inco1-inco7, include title(Sources of income) width(24)
>>  egen sumi = rowtotal(inco*)
>>  ratio inco1/sumi
>> *****************************
>>
>> Since Abu is knowledgeable about SPSS, I'd appreciate a reference to the confidence interval formulas that SPSS uses when percentages add to more than 100%.  (I couldn't find one in the SPSS 16 algorithms manual.)  I'd appreciate it also if he would compare the calculation above to the one that SPSS reports.
>>
>> Steve
>> sjsamuels@gmail.com
>>
>>
>> On May 14, 2012, at 8:40 AM, Nick Cox wrote:
>>
>> If a program is counting mentions, they are not people. Either way, I stand by what I said. I don't think even "sample size" is well defined for such data, so I don't see how inference is well defined.
>>
>> I can't comment on what SPSS does, but I repeat my request. I would be grateful for literature references showing that SPSS, or anybody else, really has a solution for this problem. Just counting mentions regardless of where they come from sounds somewhere between dubious and fallacious to me.
>>
>> The author of -mrtab- is Ben Jann, who is not a member of Statalist. If you want his answers, you need to write to him directly.
>>
>> Nick
>> n.j.cox@durham.ac.uk
>>
>> Abu Camara
>>
>> Thanks Nick. Consider the table below and you want to get the "se"
>> & "ci"for the responses variable which are in percentages. I was able
>> to do this for
>> other survey questions which are not multiple responses. Perhaps the
>> author might consider
>> including standard errors & confidence interval generation in his
>> program. I will have to turn to
>> SPSS which has the facility.
>>
>> --------------------------------------------------------------------------------------------------------.
>>
>> mrtab inco1-inco7, include title(Sources of income) width(24)
>>
>> Pct. of     Pct. of
>> Sources of income       Freq.   responses       cases
>> -------------------------------+-----------------------------------
>> inco1          private support         226       12.83       23.25
>> (partner, family,
>> friends)
>> inco2           public support         607       34.47       62.45
>> (unemployment insurance,
>> social benefits)
>> inco3             drug dealing         293       16.64       30.14
>> inco4    housebreaking, theft,          50        2.84        5.14
>> robbery
>> inco5             prostitution          82        4.66        8.44
>> inco6       "mischeln"/begging         151        8.57       15.53
>> inco7         legal occupation         352       19.99       36.21
>> -------------------------------+-----------------------------------
>> Total        1761      100.00      181.17
>>
>>
>> On 14 May 2012 14:35, Nick Cox <n.j.cox@durham.ac.uk> wrote:
>>> I don't really have further comments. I was half-assuming that you know exactly what you seek, but if so you are not spelling it out.
>>>
>>> As I see it, you would need to specify what data generation process you expect to apply and e.g. how confidence intervals are to be defined and calculated.
>>>
>>> For example, if the question is mode of transport to work and the answers look like
>>>
>>> Car
>>> Car, train, walk
>>> Walk
>>> Yak
>>> Horse
>>> Camel
>>> Personal helicopter
>>> ...
>>>
>>> it is not clear to me what meaning there could be to a standard error around the percent of people who say "walk". If the principle is that people can specify a variety of answers, the associated data generation process seems elusive to me. You can always count "mentions" rather than "people" but the inference for that I don't think is obvious.
>>>
>>> So, I don't think you can blame Stata for neglecting this area unless you can point to literature in which the logic is explained.
>>>
>>> Nick
>>> n.j.cox@durham.ac.uk
>>>
>>> Abu Camara
>>>
>>> Hi Nick,
>>>
>>> Thanks for the reply.
>>> I have no idea of writing my own program for "mrtab" to compute "se" &
>>> "ci". Further help/suggestion would be appreciated.
>>> Official Stata appears to be weak in complex tabulation.
>>> Abu.
>>>
>>> On 14 May 2012 12:18, Nick Cox <njcoxstata@gmail.com> wrote:
>>>> SJ-5-1  st0082  . . . . . . . . . . . . . . . Tabulation of multiple responses
>>>>        (help _mrsvmat, mrgraph, mrtab if installed)  . . . . . . . .  B. Jann
>>>>        Q1/05   SJ 5(1):92--122
>>>>        introduces new commands for the computation of one- and
>>>>        two-way tables of multiple responses
>>>>
>>>> You are correct, I think. -mrtab- doesn't provide these, so you may
>>>> need to write your own program.
>>>>
>>>> Nick
>>>>
>>>> On Mon, May 14, 2012 at 10:09 AM, Abu Camara <abucamara@gmail.com> wrote:
>>>>
>>>>> I am running one and two way tables of multiple response using the
>>>>> user-written command "mrtab" (Stata 11.2). I tried to generate both
>>>>> standard errors and
>>>>> confidence intervals for tables of percentages but I could not find
>>>>> this as an option.

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