How many items are needed to calculate M2 Statistic?

[Seongho Bae]

Dear all.

I have to calculate M2 statistic in my EFA model.

So, I tried to estimate M2 statistic with 12 items 6 categories measured. But I can not estimate M2 statistic. Because "degree of freedom was low" since estimate 2 factors.

How many items are needed to calculate M2 statsitc? May I can not estimate M2 statistic with 12 items? 12 items were not enough to estimate M2 statistic?

※ p.s. : I added my 12 items. And I was used default options in version 1.3.11 installed via github.

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Sincerely,

Seongho Bae.

[Phil Chalmers]

There are 78 unique first and second moments which are used in computing the M2* statistic, 12 * (12 + 1)/2. However, if you fit these data with the graded model, each item has 7 parameters estimated (1 slope and 6 intercepts). That makes 7 * 12 = 84 parameters, so you're just shy of having a meaningful statistic, and is why there is not enough df. This is one of the issues with the M2* statistic. 

You could try collapsing one or more categories in your data to try and compute the M2. If you collapse say the last category into the second last, and the first category into the second, then that will save you 24 df and you'll be able to calculate the M2 statistic properly with good room for variation (though of course that is a slightly different model, but in your case since the sample size is so small estimating 6 intercepts per item is probably way too much anyway). Hope that helps.

Phil

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[Seongho Bae]

Thanks for your advice, Dr Phil. ;)

Your main advices were collapsing the first category into second, and the last category into second last. So, I have a one more question. Can I convert this item responses to dichotomous type to save degree of freedom?

Seongho Bae.

2014년 6월 19일 목요일 오전 12시 48분 39초 UTC+9, Phil Chalmers 님의 말:

[Phil Chalmers]

You can do this of course, but you'll lose the property of you test being polytomous and ordered (and as a consequence lose precision when trying to estimate θ, if that's your end goal). How you try and dichotomize the data will also affect the fit statistics as well as the estimated parameters, so it's not entirely clear what the best way to dichotomize is. I would recommend trying to preserve the nature of your test to the best of your ability, since in the end that's likely what you are trying to understand. Collapsing from 7 to 5 categories isn't unheard of in the literature, but reviewers may have a bigger issue when going from 7 to only 2. Cheers.

Phil

[Seongho Bae]

I collapsing six categories to four categories. That's so helpful advice in my case. When I had six categories, I can't get a clear item trace lines. But after collapsing four categories, I can get, the more clear item trace lines.

Anyway, How many samples are needed for estimating 6 intercepts per item? I want to know it's practical issues.

2014년 6월 19일 목요일 오전 12시 58분 22초 UTC+9, Phil Chalmers 님의 말:

[Phil Chalmers]

It's pretty difficult to give a rule of thumb for IRT models since it depends on many things, including, but not limited to: item skewness, dimensionality, item type, parameter type (slopes are generally harder to estimate than intercepts), etc. Also whether your end goal is to ultimately create reasonable predictions of θ will matter, since estimating too many imprecise item level parameters will cause imprecision in these predictions (the so-called parameter drift issue) but including too few item parameters may give larger SE's than you'd like to tolerate.

Might be better to refer to simulation studies like the following to get a better idea of these models:

Forero, C. G. & Maydeu-Olivares, A. Estimation of IRT Graded Response Models: Limited Versus Full Information Methods. Psychological Methods, 2009, 14, 275-299.     

[Seongho Bae]

Okay, I will check out your advice soon. :)

Anyway, If I can't know to get a rule of thumb for IRT models from many complex reasons, May I get CFI, TLI, and RMSEA using alternative methods without calculation of M2 statistic in the graded response model?

2014년 6월 19일 목요일 오전 3시 58분 42초 UTC+9, Phil Chalmers 님의 말:

[Phil Chalmers]

On Wed, Jun 18, 2014 at 3:30 PM, Seongho Bae <seongh...@gmail.com> wrote:

Okay, I will check out your advice soon. :)

Anyway, If I can't know to get a rule of thumb for IRT models from many complex reasons, May I get CFI, TLI, and RMSEA using alternative methods without calculation of M2 statistic in the graded response model?

Not that I'm aware of. Your only other bet for these types of models is to compare them with structural equation modeling methods using special optimizers (like the WLSMV). But even then, I'm not sure how well those are standardized compared to using continuous data, were they were initially studied in depth.

Phil

[Seongho Bae]

Okay, I understand. So, I can guess to try perform IRT analysis or ESEM analysis using special optimizers in Mplus.

2014년 6월 19일 목요일 오전 4시 34분 34초 UTC+9, Phil Chalmers 님의 말:

[Seongho Bae]

Dear Phil,

I want to know a one more thing.

What kind can I try special optimizers?

2014년 6월 19일 목요일 오전 4시 34분 34초 UTC+9, Phil Chalmers 님의 말:

[Phil Chalmers]

I'm not sure what you are asking about. Could you clarify?

Phil

[Seongho Bae]

Some weeks ago, I was asked how can I estimate fit indices without M2 Function.

You were saying to me, special estimators in SEM like WLSMV can try to estimate CFI without M2 calculation.

So, I tried to use WLSMV, but I failed; sample size was too small. Can I know other estimators in my case use alternatives?

Seongho

2014년 7월 6일 일요일 오전 3시 30분 29초 UTC+9, Phil Chalmers 님의 말:

[Phil Chalmers]

I'm afraid I do not know of others. The WLSMV is based on the diagonally weighted WLS estimator, so if that doesn't converge then I'm unsure what other route to take in SEM. 

Phil