IRT 2PL parameters

[Ye Seul Kim]

Hi,

I am pretty new to Stata and IRT. Using IRT 2PL model, I tried to estimate item difficulty and item discrimination parameters. There are 17 items (binary: 1-yes, 0-no) and the sample size is only 31.. I admit the sample size is too small, but anyway I analyzed it and most of item discrimination parameters were negative values. Can anyone explain the negative discrimination? Does it simply mean that I cannot trust the results from a small sample size or that item coding is wrong, etc? Plus, how can I check df for each item?
Thank you in advance!

[wbuchanan]

Ye Seul Kim
Can you provide an example of your output and also maybe show some of your item characteristic curves? The sample size is definitely too small to obtain any type of stable estimates, but congrats on getting the model to converge on a solution in either case. The discrimination parameter affects the slope in the item characteristic curve. Items with high discrimination with have an ICC that looks like a step function, while items with lower discrimination will have a flatter slope between the upper and lower asymptotes. In short it would be telling you that the items are not good at discriminating between individuals with high and low ability. If you fit a 1PL model the discrimination parameter will be estimated and constrained to be equal across all items. If instead you wanted to use a Rasch model you would effectively be forcing the discrimination pattern to have a value of 1 for each item and would only be estimating the difficulty parameter for the items.

[Ye Seul Kim]

wbuchanan
Hi, here is the example of the output and corresponding ICCs (5 items). As you can see, item 4 and 7 have negative values of discrimination parameter. And one item not shown here has discrimination parameter like 86.. I am not sure whether I can rely on these estimates.
Thank you for your help!

	Coef.	Std.Err.	z	P>|z|	[95% Conf. Interval]
Item1
Discrim	1.766657	3.798171	0.47	0.642	-5.677621	9.210935
Diff	-2.667019	3.004482	-0.89	0.375	-8.555696	3.221658
Item4
Discrim	-2.560687	3.784836	-0.68	0.499	-9.978829	4.857455
Diff	1.570736	.8872806	1.77	0.077	-.1683017	3.309774
Item5
Discrim	1.766657	.9357621	1.89	0.059	-.0674028	3.600717
Diff	-2.667019	1.412665	-1.89	0.059	-5.435792	.1017541
Item6
Discrim	.69922	.7468212	0.94	0.349	-.7645227	2.162963
Diff	-.5220724	.7351172	-0.71	0.478	-1.962876	.9187309
Item7
Discrim	-2.220843	2.895629	-0.77	0.443	-7.896171	3.454486
Diff	1.934546	1.108182	1.75	0.081	-.2374511	4.106543

[wbuchanan]

Ye Seul Kim
You have items that have a reverse function. The probability of a correctly scored response should always increase as the value of theta increases. Basically, you'd need to have some extremely strong theory to support keeping those items in the scale since they function inconsistently with the expected behavior and other items.