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 david john allsop posted on Tuesday, September 14, 2010 - 2:21 pm
Hi, I need to do a multilevel EFA because my dataset has repeated measures on a prototype scale I am developing (participants in the study fill out my scale every day for 14 days to track a withdrawal syndrome). It seems as though MPlus is the best thing on the market for this type of analysis.

Unfortunately my sample size is small (only 45 people). I understand that this doesn't necessarily preclude an EFA - as sample size considerations depend on many factors, and if the data behave well, its still possible to do an EFA. Is this correct and can you point me to any refs on this? My main question is - is the same thing true for Multilevel EFA? i.e. do I automatically need a larger sample size for a multilevel EFA than I would for a straight EFA? If so it would seem inappropriate to even begin to attempt such an analysis with my small sample size?

Many thanks for any input you can offer.

Best wishes

 david john allsop posted on Tuesday, September 14, 2010 - 2:27 pm
Also, do I need to purchase the combination add on version of MPlus to do such an analysis? (My data are ordinal - likert responses - 7 days during a baseline drug use period, 14 days during a drug abstinence period). I want to do EFA on the abstinence period alone. I currently have 26 items in my scale - but the whole idea of the mEFA is to identify items that don't load so that I can justify removing them..Given my very small sample size I am currently using other analysis methods to try and prune my items before I attempt the EFA.
 Bengt O. Muthen posted on Tuesday, September 14, 2010 - 2:54 pm
It sounds like you have a 26-item instrument given 14 times to 45 subjects and perhaps you want to assume measurement invariance across times so that you end up with a twolevel situation with 26 variables, 45 level 2 units, and cluster size 14.

This is a very small sample of subjects (45) relative to the number of variables (26). Even a single-level 1-factor model would have more parameters than subjects. A twolevel model would have more parameters.

Using EFA sounds like you want to explore how the 26-item instrument works. If so, it sounds like it would be better to try to get a larger sample even if using only one time point.
 david john allsop posted on Tuesday, September 14, 2010 - 5:18 pm
Hmmm - I thought it was problematic...Increasing the sample size isn't really feasible for my current analysis - in the future yes - but thats at least a year away and I would like to publish a preliminary exploratory paper on what I have done so far. My plan is to reduce the 26 items down to 10 or 15 items by doing a validity analysis (by comparing withdrawal scores to scores given during the baseline period). Any items that don't show a significant change above baseline levels will be discarded.

If I have my items reduced to 10 items, is an EFA now feasible? (I thought that such a ratio of items to datapoints can be ok if the data behave well?). I'm assuming that even with only 10 items, a multilevel EFA (as per the one you describe above)is still not really feasible? What if I select only a subset of my 14 days of data? i.e. multilevel EFA using a cluster size of the first 4 days or something? Or would you say that with my sample size I can only really justify a single time point, single level, 1 factor model (even with only 10 items?)?

By the way, does the item response approach have the same problems with sample size restriction? Might I be able to generate some information curves from this data using your IRT approaches?
 Bengt O. Muthen posted on Tuesday, September 14, 2010 - 5:26 pm
It depends on how many factors you think there are. Really, the only way to tell if it will work ok is via a Monte Carlo simulation - see Chapter 12 in the Mplus UG.

With categorical outcomes (IRT) you have less power, more sampling variability, so harder.
 david john allsop posted on Tuesday, September 14, 2010 - 5:36 pm
OK Thanks - I didn't realise that IRT is only for categorical (although does categorical include more than 2 categories? i.e. ordinal like my data?)

Thanks for your input - I will have a look at the monte carlo simulation - that could make a nice addition to a paper in its own right.


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