Creating and saving Item Response score

[Sonnen Blume]

Hi,

I am using the following data to create disability score by the method highlighted on the picture. The authors used Stata 13 but didn't give any details of the procedure. And I couldn't find the option for creating scores from the IRT diaglog box. So I would like to know the commands for the two steps: generating the IRT scores and then transforing the scores to a scale of 0-100.

I've recoded the disability measures (seeing hearing communicating remembering walking dressing other) to 0 and 1 for ease of calculation.

Thanks in advance for your help!

* Example generated by -dataex-. To install: ssc install dataex
clear
input byte(seeing hearing communicating remembering walking dressing other)
1 1 1 1 1 1 1
0 1 1 1 1 1 0
1 1 1 1 1 1 1
1 0 1 1 1 1 0
1 1 1 1 1 1 1
1 1 1 1 1 1 1
1 1 1 1 1 1 1
1 1 1 1 1 1 1
1 1 1 1 1 1 1
1 1 1 1 1 1 1
1 1 1 1 1 1 1
0 0 0 0 0 1 0
1 1 1 1 1 1 1
1 1 1 1 1 1 1
1 1 1 1 1 1 1
0 0 0 0 0 0 0
1 1 1 1 1 1 1
1 1 1 1 1 1 1
1 1 1 1 1 1 1
1 1 1 1 1 1 1
1 1 1 1 1 1 1
1 1 1 1 1 1 1
0 1 1 1 1 1 0
0 0 0 1 1 1 0
1 1 1 1 1 1 1
1 1 1 1 1 1 1
1 1 1 1 1 1 1
0 1 1 1 1 1 0
1 0 0 0 0 0 0
1 1 1 1 1 1 1
0 1 1 1 0 1 0
1 1 1 1 1 1 1
0 0 1 1 0 1 0
0 1 1 1 1 1 0
1 0 0 0 0 0 0
1 0 1 1 1 1 0
1 0 1 1 0 1 0
1 1 1 1 0 1 0
1 1 1 1 1 1 1
0 0 0 0 0 1 0
1 1 1 1 1 1 1
0 1 1 1 1 1 0
1 1 1 1 1 1 1
1 1 1 0 0 0 0
0 0 0 0 0 0 0
0 0 1 1 1 1 0
1 1 1 1 1 1 1
1 1 1 1 1 1 1
1 1 1 1 1 1 1
1 1 1 1 1 1 1
0 0 0 0 0 0 0
1 1 1 1 1 1 1
1 1 1 1 1 1 1
1 1 1 1 1 1 1
0 1 1 0 1 1 0
0 0 1 1 0 1 0
0 1 1 1 0 1 0
1 1 1 1 1 1 1
1 0 1 1 1 1 0
1 1 1 1 1 1 1
0 1 1 1 1 1 0
1 1 1 1 1 1 1
1 1 1 1 1 1 1
0 1 1 1 1 1 0
0 1 1 0 0 1 0
0 1 0 1 1 1 0
1 1 1 1 1 1 1
0 0 1 1 1 1 0
1 1 1 1 1 1 1
0 1 1 1 0 1 0
0 0 0 1 1 1 0
0 1 1 1 1 1 0
0 1 1 1 1 1 0
1 1 1 1 1 1 1
1 1 1 1 1 1 1
1 1 1 1 1 1 1
1 1 1 1 1 1 1
1 1 1 1 1 1 1
1 1 1 1 1 1 1
1 1 1 1 1 1 1
1 1 1 1 1 1 1
1 1 1 1 1 1 1
1 1 1 1 1 1 1
0 1 1 0 0 1 0
1 1 1 1 1 1 1
1 1 1 1 1 1 1
1 1 1 1 1 1 1
0 1 0 0 0 0 0
1 1 1 1 1 1 1
0 1 1 1 1 1 0
1 1 1 1 1 1 1
1 1 1 1 1 1 1
1 1 1 1 1 1 1
1 1 1 1 1 1 1
1 0 0 0 0 0 0
1 1 1 1 1 1 1
1 1 1 1 1 1 1
1 1 1 1 1 1 1
1 1 1 1 1 1 1
1 1 1 1 1 1 1
end
label values seeing HDIS2_01
label def HDIS2_01 1 "no difficulty seeing", modify
label values hearing HDIS4_01
label def HDIS4_01 1 "no difficulty hearing", modify
label values communicating HDIS5_01
label def HDIS5_01 1 "no difficulty communicating", modify
label values remembering HDIS6_01
label def HDIS6_01 1 "no difficulty remembering/concentrating", modify
label values walking HDIS7_01
label def HDIS7_01 1 "no difficulty walking or climbing", modify
label values dressing HDIS8_01
label def HDIS8_01 1 "no difficulty washing or dressing", modify
label values other HDIS9_01
label def HDIS9_01 1 "no difficulty", modify

[Weiwen Ng]

Sonnen,

The forum FAQ asks not to post images for most things (barring graphical results). They don't always render well. In addition, I don't know the title of that study, hence I can't examine their methods.

You asked about this topic before. There, we discussed that the underlying items (i.e. the questions on activities of daily living and sensory function) are actually ordinal (e.g. no difficulty = 0, some difficulty = 1, moderate difficulty = 2, etc). In addition, the IRT model in the study you're trying to replicate (the partial credit model) is inherently for ordinal outcomes. However, above, you're presenting binary indicators. You will most likely want to use the original ordinal ones, otherwise you will be unable to replicate the author's scores. You are discarding information by recoding as binary.

Second, IRT will scale individual scores such that everyone is on a standard normal distribution (i.e. 0 means average disability, 1 means 1 SD above the mean; sort of like if you were using a standard normal prior distribution in some Bayesian estimation). I'm not sure how the author transformed things.

If you're set on treating the indicators as dichotomous, then I believe the 1 parameter logistic model is the binary equivalent to the PCM. You'd type:

irt 1pl seeing hearing communicating remembering walking dressing other
predict disability, latent

If you get the ordinal indicators, you'd run the partial credit model by doing:

irt pcm seeing hearing communicating remembering walking dressing other
predict disability, latent

The second line in each code block gives you the predicted IRT scores on a standard normal scale. Presumably the minimum score gets scaled to 0 (no disability) and the maximum score gets scaled to 100 (maximum measurable disability). You can find min and max by typing:

summarize disability, detail
*equivalent: sum disability, det
scalar max = r(max)
scalar min = r(min)

I think you could scale things by typing the block below. I tested it with your data, and I believe it outputs correctly.

generate disability_100 = (disability - min) / (max - min)
replace disability_100 = disability_100 * 100

Now, if you're going to get into IRT, then I think it's your responsibility to at least understand what the model is doing. Do read through the IRT manual. In particular, I would question the use of a Rasch model, where the discrimination parameters for all the items are equal. Not all the items above may be equally informative about the latent trait being measured. I am under the impression that many people in education might prefer Rasch models. In education, you can toss out questions that violate the Rasch assumptions (e.g. equal discrimination to the rest of the questions), and simply write new ones. In health services research, we may not get to do that. Here, you are clearly stuck with the items that WHODAS developed. I wouldn't use a Rasch model unless I could show that the items had roughly equal discrimination. One way to do that might be to fit the generalized partial credit model and do a likelihood ratio test:

irt pcm seeing hearing communicating remembering walking dressing other
estimates store pcm
irt gpcm seeing hearing communicating remembering walking dressing other
estimates store gpcm
lrtest pcm gpcm

[Sonnen Blume]

Hi Weiwen,
Thanks indeed for your help! I remember you helped with a similar issue before. This time I am using IRT, and was not sure if the two scenarios are similar. I'll use the ordinal categories for my analysis. So, if I understand the last part right, I should use -1pl- for binary and -pcm/gpcm- for ordinal variables, right?

[Weiwen Ng]

Hi Weiwen,
Thanks indeed for your help! I remember you helped with a similar issue before. This time I am using IRT, and was not sure if the two scenarios are similar. I'll use the ordinal categories for my analysis. So, if I understand the last part right, I should use -1pl- for binary and -pcm/gpcm- for ordinal variables, right?

1PL is the Rasch model for binary items, i.e. one model-wide discrimination parameter.

2PL is a non-Rasch model for binary items, i.e. each item has its own discrimination parameter. I know I suggested you not use binary items, so this may be moot.

The PCM is the Rasch model for ordinal items. The GPCM is the non-Rasch version of that model. The graded response model is an alternative to the GPCM, but I'm not clear that either of the two is superior.

I'd suggest that non-Rasch models will probably fit your data better than Rasch models (but I could be wrong, and you can test that statement). Then again, if all you need to do right now is to replicate the original paper, you can use the PCM.

[Sonnen Blume]

Thanks Weiwen for the nice interpretation!