# Questions tagged [item-response-theory]

Item Response Theory (IRT) is a set of statistical methods for modeling responses to test items. Use this tag for on-topic questions about (a) the theory itself (b) models appropriate for a specific case (c) implementing IRT in a specific tool such as an R package.

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### Reliability in IRT Style

Reporting 'reliability' in IRT is more to 'informations' obtained and a bit different from a classical way using such as Cronbach alpha and KR20. Therefore, how to report the test reliability in ...
• 111
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### Item Response Theory vs Confirmatory Factor Analysis

I was wondering what the core, meaningful differences are between Item Response Theory and Confirmatory Factor Analysis. I understand that there are differences in the calculations (focusing more on ...
• 779
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### What is Item Response Theory (IRT) called for continuous response?

I would like to model my problem using something similar to Item Response Theory, but my responses are not binary. They are continuous in $[0, 1]$. What are these models/the research field called?
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### How to get started with applying item response theory and what software to use?

Context I have been reading about item response theory, and I find it fascinating. I believe I understand the basics, but I am left wondering how to apply statistical techniques related to the area. ...
• 5,064
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### Estimating ability using IRT when the model parameters are known

I have 3PL model parameters (guessing, difficulty and discrimination item parameters). Is there any function with which I can estimate individual ability from item response data? I tried the function <...
• 1,231
610 views

### Item information in IRT

According to item information curves, item information for a 2PL IRT model is $I(\theta)=a^2_i p_i(\theta) q_i(\theta)$ To determine $p_i(\theta)$ and $q_i(\theta)$, do you just use the observed ...
• 4,842
255 views

### 2PLM IRT modeling of rare event behavioral data: Why changing discrimination and difficulty values?

I am using the 2PLM (2-parameter logistic model) IRT model to examine how sets of very rare (negative/aversive) maternal behaviors (towards their children) are associated with a priori ...
• 308
1 vote
69 views

### Interdependence of hyperparameters of bernouilli laws [closed]

Suppose that you have $N$ people passing an exam having 2 type of questions (type A and type B) which all have correct/uncorrect outcomes. After seeing the results, I want to modelize the probability ...
1 vote
271 views

### How do I appropriately examine the dimensionality of binary data?

I have 72 binary variables and, at a theoretical level, I am trying to identify groups of variables that seem to vary together. In practice, I am struggling with how to analyze this data properly. I ...
3k views

### Simulating responses to a test for item-response theory

I am developing an online assessment system and I need to calibrate the bank of questions but I do not have enough people to implement a pilot test. That is why I decided to simulate the responses of ...
975 views

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### IRT/Rasch modeling with very large N

I want to fit a 1-parameter IRT model on a questionaire with 15 questions and about six million people. Considering the large N, standard errors aren't essential. It looks like the IRT world is sort ...
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### Longitudinal item response theory models in R

I'm trying to fit longitudinal item response theory (IRT) models in R. I have a test that was administered at multiple measurement occasions. I'd like to examine individuals' growth curves of factor ...
• 455
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### Predict person parameters in explanatory IRT with lme4

I am using glmer from lm4 in R to run an explanatory IRT analysis. The aim is to model person parameters with items nested in persons and to control for age (the test scale has 10 items; all persons ...
3k views

### Internal consistency reliability in item response theory models

How can internal consistency reliability of a test and of individual test items be quantified in Item Response Theory models? I know I can resort to Classical Test Theory, Cronbach's alpha, and other ...
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### How to check goodness of fit for a graded response model in R

I am using the grm function in the ltm package in R. There is no function to check the goodness of fit of the output. How can I ...
2k views

### How to extract factor scores for each observation in IRT? [closed]

library(ltm) fit <- rasch(LSAT) factor.scores(fit) This code can generate latent trait scores for response patterns. How can I extract latent trait scores for ...
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### Difference between IRT and EFA to find factors

I am learning about Item Response Theory in which items are used to assess ability. In principle, multiple latent abilities may exist and some items test the one, while other items test another. This ...
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### Meaning of large values of parameter b (|b| >>) 4 in IRT theory

I'm working with a data set of 100 itens, 5 alternatives, medicine test and analyzing them by means of IRT (. The IRT - 3 parameter model yielded some values of b that are very large (...
• 143
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### Acceptable values for discrimination parameter - 2PL IRT Model

What is the acceptable range for discrimination parameters with the two-parameter IRT model? I have information from Baker (2001) but would love additional information. I have heard discrimination ...
• 53
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### Do 1PL IRT models measure both ability and difficulty, or just difficulty?

I'm trying to better understand Item response Theory (IRT) from a Bayesian perspective. Hypothetically, suppose I want to use a 1PL model and my data is a binary matrix ...
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### Item response theory for continuous variables, and estimating standard error of measurement

I really like how traditional item response theory (IRT) packages tell you the standard error of measurement conditional on one's ability level, and from that, you can calculate the test information ...
• 525
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### How is a bifactor IRT model different from a factor analysis?

How is a bifactor IRT model different from a factor analysis? How would you describe their key differences? Any references you could direct me to would be very helpful. Thank you for sharing your ...
• 416
175 views

### Pros/cons of estimating parameters for missing observations?

Some people are playing a game online. Every time a person plays, a new game board is generated randomly. On generation of a new board, the player can also choose a special weapon. (The choice of ...
• 4,842
656 views

### Is it acceptable/common practice to report IRT theta scores as a percentile?

I have been teaching myself IRT. I think I get it, however, I've not yet reached a point where I would say that I'm totally confident. In assuming that the latent trait is normally distributed with ...
• 265
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### Is it possible to do IRT distractor analysis using R?

I've been using the mirt package to analyse a few response matrixes I have through IRT. However, every time I need to perform distractor analysis, I end up having ...
1k views

### Is empirical reliability in IRT the counterpart of internal consistency in CTT?

In IRT it is not meaningful to compute internal consistency coefficients such as Cronbachs alpha, because standard error of measurement (and thus measurement precision) is not assumed uniform across ...
• 133
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### Error using ltm R package [closed]

I'm using the R package ltm to create a 2-parameter logistic regression. The input matrix is sparse - many users have taken a small subset of the items in the item bank. For some of my data sets i'm ...
• 71
531 views

### Unidimensionality in IRT

I recently came across the definition of unidimensionality (in the context of IRT and internal consistency reliability, specifically Cronbach's alpha). Johnsosn (2007) states that There is a one-...
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59 views

### Item Information Distorting Scale

I'm refining a psychometric questionnaire and working to estimate (2PL) IRT parameters for the items in order to score the items. It's a small scale consisting of 5 questions. The MAP and VSS-1 ...
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