I imagine the following scenario: You have 12 items that measure 2 sub dimensions of a construct, 6 items each construct.
Say the construct is happiness, the sub dimensions were eudaimonic and hedonic happiness. You find the 2 sub dimensions in an exploratory factor analysis, just as theory says.
But the Rasch model does not fit each sub dimension. It fits when you analyze ALL items at once. Can we now combine these insights? E.g. we measured each sub dimension reliably and therefore we can assume that items 1e-6e assess eudaimonia, 1h-6h measure hedonia. These items are then labeled with the respective dimension. In Rasch analysis with all items we would then find that 8.3% (=100%/12) participants were measured well per item. Hedonic item 1h has the largest logit, eudaimonic item 1e the second largest, hedonic 2h the third largest, eudaimonic 2e the fourth etc.
Could we now argue that in the case of happiness the item 1h assesses the most happy persons and this happiness is of hedonic nature?
In case I messed it up or anything is not clear, please ask.
All 12 items fit the Rasch model's measurement requirements? But each half does not? Very strange. What are your indicators of / criteria for (mis)fit? Item format? Which analysis? Which software?
Try using multidimensional item response theory (mIRT, using Rasch if you wish) with "mirt" R package. You should apply a bifactor or a second factor to your data. Also, it is possible to calculate exploratory and confirmatory models. So, goodness-of-fit indices can be analysed to the models.
Hi friends, I'm happy to read your answers!
First, thanks for your replies!
Yes, some other analysis would be more appropriate, e.g. a nested model as we deal with with students in classes. mirt would do that as well? I'm not very informed about R and its packages. We use RUMM 2030. As to my knowledge there we can only operate on "simple" scales, do we?
@Trevor: We have dichotomous indicators (agree - don't agree) on school satisfaction in grammar school students. So they agree to most of the items. If I analyze each scale separately, RUMM treats each scale separately. I.e. if a student agrees to all items RUMM would take it as an extreme case, I guess. So RUMM extrapolates these cases.
If I then use all items of all scales, chances are higher that there is a "don't agree". So, from my point of view, this leads to a "better" analysis in RUMM.
I hope this helps!
Yes, "mirt" package compares nested models with anothers using ANOVA statistics (in the case, BIC and AIC indices)... it is a very powerful R package (I use also IRTPro 2.1 for some of the mIRT analysis). At first, I recommend check dimensionality using EFA in Mplus 7.2 (statmodel.com), which it is possible to calculate dichotomous and continuous items simultaneously. Some structural equation modeling (SEM) can be applied (which uses mixed CFA in the model). Bayesian SEM or skew SEM are possible. I can help you and your team in a web conference...
Hello Alexander,
have you conducted in RUMM2030 an analysis at the subscale level invoking the subtest strategy?
This analysis would give you an estimate of the latent correlation between the two latents subdimensions
You could also consider using R's psych package or tam package.
The psych package is designed to facilitate factor analysis but will allow you to estimate IRT parameters from factor analysis based on polychoric correlations. William Revelle, the package author, also has a website with very helpful examples and vignettes. It is not as full-featured for IRT as IRT packages, but it might provide results that you can interpret.
The tam package is based on Mark Wilson's Mixed Coefficients Multinomial Logit Model. This is a very flexible and unified framework for logistic IRT models that can accommodate multidimensional IRT.
But MIRT is more useful at the estimation of groups, not individual persons
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