R - Item Response Theory Example 

Thank you - I appreciate the feedback!

Thanks for the kind words!

Thank you and best of luck!

Thanks for the kind words!

Thanks for the kind words!

Glad it helped!

I haven't done much multi-IRT, but I highly recommend the mirt package and it's help guide!

@@StatisticsofDOOM I have heard that when I have a multidimensional construct, i can do IRT on each sub construct. However i am not sure how can i find an 'overall score'. I will have ability estimates for each constructs but how do i make a total score out of these ability estimates? My guess is to use these ability estimates as score for factor analysis and then find a factor score . Am i right in my thinking?

@@Dupamine AH, for that you might consider mirt ... I'm not sure how to estimate it from each one separately and have that be accurate, rather I think you'd probably have to combine them to get the higher order value.

No problem :). If your interested, there's also a Github wiki associated with the package with lots of exercises and examples (github.com/philchalmers/mirt/wiki). Feel free to cherry pick from them in your class if you see something you like. Cheers.

B is the difficulty parameter, while A is the discrimination parameter. So, B measures who is likely to get the question right (so B = 0 is that an average person will get it right or the in the case of poly where you might expect the person to answer that answer - low B values indicate a person is getting a low score and picking that response option). A is the slope or how well it discriminates between people below and above that B point. So A = 0 means the item is really bad and can't tell the difference between people who answer the question and higher A values means it's really good at telling you who got it right or wrong (or who is likely to pick that response option).

Haven't use that package, but I can check it out!

Yep! Just did it - I am slowly updating the website, links, and everything. Here's the current location: statisticsofdoom.com/page/structural-equation-modeling/ - the files are linked on that page on github and soon the viewing order will be available too.

I hadn't seen a lot with people using traditional SEM fit indices for IRT, but I don't know why you couldn't to look at fit. ICC is also great. I would assume that if I had a TIF showing me that the information was best measured at less than average thetas, then the data is probably also skewed that direction.

One way might be to use the loading weight times the person's score - I don't know that it helps much when items are scored zero and one though.

Wow, okaay. so, how can i calculate the loading using R?

You could create a vector of the loadings and multiply it by the dataframe with the answers - if you google matrix multiplication r, you can find a link for the practical r wordpress blog that covers this topic.

I would think you could multiply the weight of each item by the answer each person put to get that type of score? That's my best guess.

@@StatisticsofDOOM Thank you!

The lecture video covers the differences a bit better. I do think that the GRM can be harder to fit if your items are not ordered or at each point a highest threshold, so the GPCM tends to work better. They can be equal if the items behave well.

@@StatisticsofDOOM Thank you so much for getting back to me. Can I just ask what you mean 'at each point a highest threshold'? If the scale is a likert scale where all options are not being used but it is not theoretically sound to collapse the scale, then the GPCM would be the better model?

@@louisekatz4310 i.e., where each choice has a peak of being the most likely answer.

@@StatisticsofDOOM Thank you so much. I listened again to the lecture which gave the perfect explanation of the differences between GRM and GPCM. It was exactly what I was looking for. Your lectures and examples have been of so much help. Thank you again.

Using R? I'd tell you to check out fscores: rdrr.io/cran/mirt/man/fscores.html

@@StatisticsofDOOM , sorry, what I meant was raw score. After following the example in this video, I have managed to get the z1 value using factor.scores. Now, I need a raw score of the z1 value. So, how do you get a raw score? Thank you.

@@IfanIqbal Ah. Usually you are interested in theta, but I would think you could easily convert back to whatever scale you wanted using the traditional z score formula (Z = (X - mu)/sigma). You would have to know what you expected mu (population mean) and sigma (population standard deviation) to be.

@@StatisticsofDOOM Thank you, your response is very helpful to me. I have succeeded in generating theta from the fscores function, using a mirt package with item type 2PL, then converting that value to raw score (X = mu + (Z * sigma)), with mean and standard deviation calculated from the normal score population of each participant .

I'm not sure I understand your question? Are you looking for an estimation of the person scores?

@@StatisticsofDOOM Dear Dr. Buchanan Thanks for your feedback! I have some unknown things. Can you help me? 1. Is the value of column z1 in this video the ability of candidates? 2. When using factor.scores (..) command, the result shows 30 lines corresponding to the ability of 30 candidates. I want to use the abiltity of 1000 candidates, what will I do? Thank you so much!

@@nguyenvancanh2653 I am not sure I can really answer this question - factor.scores only shows 30 but you have 1000 lines or? z1 would be theta yes.

@@StatisticsofDOOM I mean I get 1000 responses but when using factor.scores () the result is only 30 lines. I want to display the theta value of all responses.

@@nguyenvancanh2653 Apologies - my brain was not connecting the dots - try using personfit instead: rdrr.io/cran/mirt/man/personfit.html

Excellent clarification - thanks! I need to update these videos, and will make this point clearer.

Like you want to plot the loadings and factors? I've recently discovered the FactoMineR package - don't know if it will do 4D space though: cran.r-project.org/web/packages/FactoMineR/index.html