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Re: st: Mata: Calculating conditional expectation


From   Nick Cox <njcoxstata@gmail.com>
To   "statalist@hsphsun2.harvard.edu" <statalist@hsphsun2.harvard.edu>
Subject   Re: st: Mata: Calculating conditional expectation
Date   Thu, 25 Apr 2013 12:09:02 +0100

In this there is a lot of putting constants into variables, only to
drop them later.

In addition, whenever you want only one mean, -egen-'s -mean()-
function is overkill.

If you want to handle constants, that usually calls for scalars, not variables.

-summarize, meanonly- leaves r(mean) behind in memory, which you can
exploit more than you do.

Your first block I would rewrite as

count if Y == 1 & Y_T == 0
scalar fp = r(N)/_N
count if Y == 0 & Y_T == 1
scalar fn = r(N)/_N

Indeed

su Y_T if inlist(Y_T, 0, 1), meanonly
scalar fp = r(mean)
scalar fn = 1 - fppct

is better technique, I suggest. It does not presume there are no
missing values on -Y_T-. (In addition, you calculated fractions, not
percents.)

The block

local dummies
forvalues i = 1/1000 {
     egen fpmean`i' = mean(id`i') if Y == 1 & Y_T == 0
     gen  idfp`i' = fppct * fpmean`i'
     local dummies "`dummies' idfp`i'"
     drop fpmean`i'
}

could be simplified to

local dummies
forvalues i = 1/1000 {
     su id`i' if Y == 1 & Y_T == 0, meanonly
     gen  idfp`i' = fppct * r(mean)
     local dummies "`dummies' idfp`i'"
}

These are small changes. I've not tried to understand the whole of
what you are doing.

Nick
njcoxstata@gmail.com


On 25 April 2013 11:22, Ivan Png <iplpng@gmail.com> wrote:
> Let me try to explain how I did it.  I did not use Mata to  direct
> computing the vector of conditional expectation of the explanatory
> variables.  Rather, I constructed the conditional expectation of each
> explanatory variable separately, and then collected them into the
> vector.  Not very elegant, but seems to work.
>
> == code fragment ==
>
> . count if Y == 1 & Y_T == 0  /* Y = observed Y; Y_T = true Y */
> . gen fppct = r(N)/total      /* total = no. of observations */
>                                         /* fppct = percent false positives */
> . count if Y == 0 & Y_T == 1
> . gen fnpct = r(N)/total      /* fppct = percent false negatives */
>
> . gen const = 1
>
>
> *** create X including dummy variables (fixed effects) ***
>
> . local dummies
> . forvalues i=1/1000 {
>     local dummies "`dummies' id`i'"
>     }
>
> . mata : st_view(X = .,., ("hhr", "const", "`dummies'"))  /* hhr =
> higher degree */
> . mata : rows(X), cols(X)  /* check matrix */
> . mata : X[|1,1 \ 7,7|]    /* check matrix for empty rows */
>
>
> ** construct conditional mean(X) **
> . sort lower year
>
> . foreach var in const hhr {
>    egen `var'_fpmean = mean(`var') if Y == 1 & Y_T == 0
>    gen  `var'_fp = fppct * `var'_fpmean
>    egen `var'_fnmean = mean(`var') if Y == 0 & Y_T == 1
>    gen  `var'_fn = fnpct * `var'_fnmean
>    drop `var'_fnmean
>    }
>
> ** construct P = mean(X) conditional on false positive **
> . local dummies
> . forvalues i = 1/1000 {
>     egen fpmean`i' = mean(id`i') if Y == 1 & Y_T == 0
>     gen  idfp`i' = fppct * fpmean`i'
>     local dummies "`dummies' idfp`i'"
>     drop fpmean`i'
>     }
>
>
> . mata : st_view(F = .,., ("hhr_fp", "const_fp", "`dummies'"))
> . mata : rows(F), cols(F)  /* check matrix */
> . mata : F[|1,1 \ 15,15|]    /* check matrix for empty rows */
>
> . mata : st_subview(P = . , F, 1 , .)  /* choose first non-empty row */
> . mata : rows(P), cols(P)
> . mata : P[|1,1 \ 1,20|]    /* check vector */
>
>
> ** construct N = mean(X) conditional on false negative **
> . sort lower year
>
> . local dummies
> . forvalues i = 1/1000 {
>     egen fnmean`i' = mean(id`i') if Y == 0 & Y_T == 1
>     gen  idfn`i' = fnpct * fnmean`i'
>     local dummies "`dummies' idfn`i'"
>     drop fnmean`i'
>     }
>
> . mata : st_view(G = .,., ("hhr_fn", "const_fn", "`dummies'"))
> . mata : rows(G), cols(G)  /* check matrix */
> . mata : G[|1,1 \ 20,20|]    /* check matrix for empty rows */
>
> . mata : st_subview(N = . , G, 3 , .)  /* choose first non-empty row */
> . mata : rows(N), cols(N)
> . mata : N[|1,1 \ 1,20|]    /* check vector */
>
>
> ** estimate bias **
> . mata : D = invsym(cross(X,X))*(P' - N')
> . mata : rows(D), cols(D)
> . mata : D[|1,1 \ 9,1|]    /* check vector */
>
> . mata : st_subview(E = . , D, (1::5) , .)  /* coefficients of focal
> variables */
> . mata : E
>
> . mata : H = 9898 * E      /* total = 9898 */
> . mata : H
>
> === end fragment ===
>
>
> On 23 April 2013 11:45, Ivan Png <iplpng@gmail.com> wrote:
>>
>> Many thanks to Statalist members for their previous help on
>> constructing the matrix.
>>
>> To recall, my dependent variable is categorical: Mobility = 1 if
>> inventor changed employer, else = 0.  I'm investigating the effect of
>> classification error.  Obviously, this cannot be classical.  Let Y =
>> true mobility and Z = recorded mobility. If Y = 0 and Z = 1, then
>> error = -1, while if Y = 1 and Z = 0, error = +1.
>>
>> Meyer and Mittag, U of Chicago (2012) characterize the bias as
>> N(X'X)^{-1} [ Pr( Y = 0 & Z = 1) E(X :  Y = 0 & Z = 1) - Pr(Y = 1 & Z
>> = 0) E(X :  Y = 1 & Z = 0) ].  I have a benchmark data set with both
>> the true and inaccurate mobility data, and would like to compute the
>> bias.
>>
>> So, I need to compute the conditional expectations, E(X :  Y = 0 & Z =
>> 1) and E(X :  Y = 1 & Z = 0), and then weight by the probabilities,
>> take the difference, and pre-multiply by N(X'X)^{-1}.  My idea:
>>
>> . keep if Y = 0 & Z = 1
>> . mata : F = mean(X)
>> . mata : mata matsave filename
>>
>> and repeat for Y = 1 & Z = 0.
>>
>> But, sadly, I don't how to proceed.  How to combine the original data
>> with the two new files containing the conditional expectations, and
>> then going back to MATA to calculate the bias.  Grateful to
>> Statalisters for help.
>>
>
>
>
> --
> Best wishes
> Ivan Png
> Skype: ipng00
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