Random assignment of a categorical variable - with know frequency distribution - taking weights into account

[Andreas Thiemann]

(Stata: Version 14.2)


Dear all,

I would like to kindly ask for suggestions on the following imputation/random assignment problem:

Let’s assume that a categorical variable X (values are 1,2,3,4) has the following distribution (based on ‘reference data’):

X		%	Cum. %
1		20%	20%
2		20%	40%
3		30%	70%
4		30%	100%
Total		100%

Now, lets have a look at my example data:

sysuse nlsw88, clear

// Further, let's assume that the frequency weights are distributed in the following (very unequal) way:

gen weight = (2.25/(_n^(2.5)))*20000

//Now, I generate the new variable X and randomly assign its values to the observations, replicating the initial distribution:

set seed 123
gen random = runiform()

gen x=0
replace x=1 if random < .2
replace x=2 if inrange(random,.2,.4)
replace x=3 if inrange(random,.4,.7)
replace x=4 if random>.7

//Replicating the initial sample distribution has worked relatively well in the unweighted case:

tabulate x

X	Freq	%	Cum. %
1	439	19.55%	19.55%
2	440	19.59%	39.14%
3	695	30.94%	70.08%
4	672	29.92%	100%
Total	2246	100%

However, when tabulating the weighted frequency distribution, the random assignment has not worked well:

tabulate x [aw=weight]

X	Freq	%	Cum. %
1	55.4565667	2.47%	2.47%
2	1,690.2808	75.26%	77.73%
3	312.920003	13.93%	91.66%
4	187.342635	8.34%	100%
Total	2,246	100%

Does anyone have a suggestion randomly assigning a categorical variable, taking frequency weights into account when weights are unequally distributed?

Any suggestion is greatly appreciated!




-----------------------------------------------------------
Plain Stata code:

sysuse nlsw88, clear

gen weight = (2.25/(_n^(2.5)))*20000
sum weight

set seed 123
gen random = runiform()

gen x=0
replace x=1 if random < .2
replace x=2 if inrange(random,.2,.4)
replace x=3 if inrange(random,.4,.7)
replace x=4 if random>.7

tab x
tab x [aw=weight]

[Andreas Thiemann]

(Stata: Version 14.2)


Dear all,

I would like to kindly ask for suggestions on the following imputation/random assignment problem:

Let’s assume that a categorical variable X (values are 1,2,3,4) has the following distribution (based on ‘reference data’):

X		%	Cum. %
1		20%	20%
2		20%	40%
3		30%	70%
4		30%	100%
Total		100%

Now, lets have a look at my example data:

sysuse nlsw88, clear

// Further, let's assume that the frequency weights are distributed in the following (very unequal) way:

gen weight = (2.25/(_n^(2.5)))*20000

//Now, I generate the new variable X and randomly assign its values to the observations, replicating the initial distribution:

set seed 123
gen random = runiform()

gen x=0
replace x=1 if random < .2
replace x=2 if inrange(random,.2,.4)
replace x=3 if inrange(random,.4,.7)
replace x=4 if random>.7

//Replicating the initial sample distribution has worked relatively well in the unweighted case:

tabulate x

However, when tabulating the weighted frequency distribution, the random assignment has not worked well:

tabulate x [aw=weight]

Does anyone have a suggestion randomly assigning a categorical variable, taking frequency weights into account when weights are unequally distributed?

Any suggestion is greatly appreciated!




-----------------------------------------------------------
Plain Stata code:

sysuse nlsw88, clear

gen weight = (2.25/(_n^(2.5)))*20000
sum weight

set seed 123
gen random = runiform()

gen x=0
replace x=1 if random < .2
replace x=2 if inrange(random,.2,.4)
replace x=3 if inrange(random,.4,.7)
replace x=4 if random>.7

tab x
tab x [aw=weight]