Bootstrapping test statistic for two paired ratios

[Kate Rosener]

Hi,

I am trying to bootstrap a paired t test statistic for two paired ratio estimates (ifr0 and ifr1). I am getting the error 'variable ifr0 not found' when I run the below syntax. Can anyone advise on what I am doing wrong?

Thanks,
Kate

capture program drop meandiff
program meandiff, rclass

ratio (ifr0: q309/Q214) if r1==1, vce(bootstrap, cluster(id))
scalar define ifr0 = _b[ifr0]
summarize ifr0 if r1==1
scalar define mean_ifr0=r(mean)

ratio (ifr1: r309/Q214) if r1==1, vce(bootstrap, cluster(id))
scalar define ifr1 = _b[ifr1]
summarize ifr1 if r1==1
scalar define mean_ifr1=r(mean)

return scalar meandiff = mean_ifr0-mean_ifr1
end

bootstrap t=r(t), reps(100): meandiff ttest mean_ifr0 mean_ifr1

[Carlo Lazzaro]

Kate.
welcome to the list.
A temptative answer would consider that the -if- condition is the same (-if r==1-) for both ratios.
Was it intentional or not?

[Kate Rosener]

Hi Carlo,

Thanks for your response. Yes, the (if r1==1) condition is intentional for both ratios to select a sub-sample of the data included in round 1. The idea is to compare the ratio of participant reporting at time 1 (q309) and time two (r309) to an observer report (Q214 at baseline).

To test if the two paired ratio estimates are significantly different from each other, I first tried the below syntax. However, I was unsure if using the 'test' command after the ratio estimations was appropriate for paired data, which is why I tried the approach listed in my first post. Also I wanted to use bootstrapping given these are ratios and the distribution is not normal. Any help would be greatly appreciated!

Syntax:

ratio (ifr0: q309/Q214) (ifr1: r309/Q214) if r1==1, vce(bootstrap)
test _b[ifr0] = _b[ifr1]

Output:
Ratio estimation Number of obs = 506
Replications = 50

ifr0: q309/Q214
ifr1: r309/Q214

--------------------------------------------------------------
| Observed Bootstrap Normal-based
| Ratio Std. Err. [95% Conf. Interval]
-------------+------------------------------------------------
ifr0 | .9356223 .0095552 .9168944 .9543502
ifr1 | .8681904 .0099048 .8487773 .8876034
--------------------------------------------------------------


( 1) ifr0 - ifr1 = 0

chi2( 1) =37207.41
Prob > chi2 = 0.0000

[Kate Rosener]

Hi everyone,

Does anyone know if it is possible to perform a paired t test (using bootstrapping) of ratio estimation results? I've tried various approaches to saving ratio estimates in a scalar or matrix and then to bootstrap the test statistic, but to no avail after a great deal of time. Any guidance on the syntax posted in my Post 1 would be hugely helpful.

Thanks!
Kate

[Carlo Lazzaro]

Kate:
what if you change:

summarize ifr0 if r1==1

in:

summarize ifr0 if r1==1, meanonly

and do the same variation for -ifr1-?

[Joseph Coveney]

You cannot use summarize ifr0 when ifr0 is a scalar and not a dataset variable, and that's what your error message ('variable ifr0 not found') is all about.

I'm not sure what you're dataset is like. You keep talking about paired t-test of ratios, but the Stata command ratio is for unpaired data. Are the observations paired? If so then something like that below would give you a bootstrapped paired t-statistic of the ratios.

generate double q_Q = q309 / Q214
generate double r_Q = r309 / Q214

bootstrap t=r(t), rep(1000) nodots nowarn: ttest q_Q = r_Q
estat bootstrap, all

But if the observations are paired, why not just to a paired t-test of q309 to r309?

I suppose there's an easy explanation, but I'm not seeing it at the moment, how the observations are not paired (hence the use of ratio), but the ratios formed are paired.