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Mplus Discussion > Confirmatory Factor Analysis >
 Katherine Keyes posted on Tuesday, August 04, 2009 - 7:10 am
Is there an MPLUS option to calculate the total area under the aggregate information curve in an IRT analysis?

Thanks in advance.
 Linda K. Muthen posted on Tuesday, August 04, 2009 - 9:19 am
No, there is not such option.
 Miyako Tsuchiya posted on Tuesday, July 10, 2018 - 11:51 pm
Dear Linda,

I have two questinos about Mplus 8 options.

1. Is there an option to calculate total information automatically?

2. How can I draw standard error of test infomarion and calculate it?

Sincerely yours,

 Bengt O. Muthen posted on Wednesday, July 11, 2018 - 5:44 pm
1. Yes, there is a plot option for graphing the information curve for all items.

2. The SE is the square root of the inverted information, right, and the plot information values can be saved.
 Miyako Tsuchiya posted on Thursday, July 12, 2018 - 7:02 pm
Dear Bengt,

Thank you for your quick response.

I could graph information curve in an IRT analysis
1. Could you please clarify how to calculate percentage of total information (range: -3 s.d. to +3 s.d.)?

2. IRT analysis shows plot information as below.
@ Could you please explain how to calculate and graph standard error of test information?


The following plots are available:

Histograms (sample values, estimated factor scores, estimated values, residuals)
Scatterplots (sample values, estimated factor scores, estimated values, residuals)
Sample proportions and estimated probabilities
Item characteristic curves
Information curves
Latent variable distribution plots

 Bengt O. Muthen posted on Friday, July 13, 2018 - 2:09 pm
Q1: I am not familiar with "percentage of total information" - do you have a reference?

Q2: When you are looking at the information plot, you can pull down the plot menu and at the bottom you find the option "Save plot data". There you will the information value for each x-axis value, from which you can calculate the SE.
 Miyako Tsuchiya posted on Monday, July 16, 2018 - 6:33 pm
Thank you for your reply,

Q1. I apologize for "percentage of total information." My question is about "amount of total information"

The reference is "Item response theory and the measurement of clinical change".
Reise SP, Havil MG.2005. Journal of Personality Assessment.Jun;84(3):228-38.

They report the test reliability in IRT as below.
The lower line corresponsd(approximately) to a reliability coefficient of 0.90(SE=.316), and the upper line corresponds to a reliability coefficient of 0.95(SE=.223).

1. How to calcurate a reliability in IRT?

2. Is there way to calcurate amount of test information in the range -3< Theta <3 ?
 Bengt O. Muthen posted on Wednesday, July 18, 2018 - 8:03 am
Which page in the article are you looking at?
 Miyako Tsuchiya posted on Thursday, July 19, 2018 - 9:28 pm
It's on the right side of page 233 in the article.
Could you please check it out?

 Bengt O. Muthen posted on Sunday, July 22, 2018 - 11:51 am
I checked with the authors - they use

Reliability = 1 - [SE(theta-hat)]^2

where SE(theta-hat) is the standard error of an estimated theta score (on the mean=0, sd=1 metric).
 Miyako Tsuchiya posted on Monday, July 23, 2018 - 5:55 pm
Hello Bengt!
Thank you so much for checking with the authors and your kind instruction.

I could obtain the information value in IRT by following your instructions.
1.Is there a way to calculate reliability automatically in IRT with Mplus8?
Reliability = 1 - [SE(theta-hat)]^2

I still donft understand how to obtain total information in IRT with Mplus8.
In R, calculating total amount of information can be done with code and shown as below.

Total Information = 108.38
Information in (-3, 3) = 97.81 (88.5%)
Based on all the items

2.Is there a way to calculate them automatically in IRT? If so, could you please tell me how to do it?

 Bengt O. Muthen posted on Monday, July 23, 2018 - 6:17 pm
1. No - because the formula does not involve model parameters (otherwise Model Constraint could be used).

2. Here is how you do it in Mplus.

Use the plot menu's "View plots" and choose "Total information curve (TIC) for all items". Then go back to the plot menu and click on "Save plot data". That saved data then contains the information value for every x-axis (theta) value. You can then find SE(theta-hat) as the inverse square root of the information value and any x-axis point (like in that IRT article). And then you can get reliability from that - using the formula and e.g. Excel or R.
 Miyako Tsuchiya posted on Monday, July 23, 2018 - 8:48 pm
Hello Bengt,
Thank you so much for the clarification.
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