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Questions tagged [irt]

The Item Response Theory framework encompasses a wide range of psychometric methods and mathematical models (latent trait models) to study individual responses to items defining a measurement instrument (multi-item scales such as questionnaires or tests) that is used to assess a specific construct (e.g., examinee proficiency or liability to depression).

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How can I extract slope and location parameters, and χ^2 stats, from a Graded Response IRT model in R using grm (ltm package)? [on hold]

Using the ltm R package, and the grm function to fit a Graded Response IRT model, how can I extract the following: Slope ...
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first factor saturation vs. general factor saturation

a simple explanation between these two in the context of reliability analysis, specifically Cronbach's alpha.
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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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What's the requirement of dataframe length and sample size when detecting DIF? [closed]

When I try to detect DIF(Differential Item Functioning),my classmate told me DIF has no result if data has less then 10 items or sample size <1000. I am not sure is there any requirement of the ...
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42 views

Differential Item Functioning (DIF) Anchor Selection

I have a conceptual question regarding item anchor selection that seems to be so basic to the literature that authors of various online and print resources assume the reader understands. Namely, I am ...
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Is homogeneity same as unidimensionality in IRT?

Based on wiki, Unidimensionality should be interpreted as homogeneity, a quality that should be defined or empirically demonstrated in relation to a given purpose or use, but not a quantity ...
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Bifactor model and infit statistics?

Good afternoon, I am currently in the process of calibrating an item bank using a GPCM model. So, am I right to assume that the bifactor model allows me to work with my general factor by ...
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34 views

How should we select between various Item Response Theory Models? (E.g. RSM, GRM, LRSM, PCM)

If you ask me what's the application scenario difference between NRM and GRM, I will answer ...
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Comparing two IRT test information curves

I am fitting an IRT graded response model in R. I want to compare two measures in terms of at what levels each measure is most informative (e.g., is measure 1 informative at more extreme levels of the ...
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Get different IRT model result when use functions from different R package?

Reproducible example as below: ...
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54 views

Testing for IRT assumptions with large samples and short scales

I’m using R’s mirt package to fit some (unidimensional) GPC models to a set of Likert-style items with five levels in each. I’m looking for some advice on how to test for the standard IRT assumptions. ...
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Why item discriminations are missing in IRT GRM, estimated as a part of the Structural Equation Model? [closed]

I have run a Structural Equation Model that has four latent constructs (FI, SC, EM and RB) in R. All of the factors are continuous. Meanwhile, indicators are all ordered categorical variables measured ...
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30 views

Item Response Theory model to recover the item locations

I can't seem to find a model to solve the following problem. It seems to be closely related to IRT, but not exactly. I have a list of users and items, I know the preference between users and items, ...
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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 ...
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How to calculate overall reliability for an IRT test with subtests

I have an IRT, 2 parameter model ability test with three subtests - verbal, numerical and abstract reasoning. I have been able to calculate the reliability of each subtest using the methods outlined ...
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Combining multiple response models

Within a particular instrument, is it valid to combine multiple response models for subsets of items when estimating a latent trait? As an example, if I had some items that were conceptually suited ...
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35 views

IRT analysis on large sparse dataset

I have a dataset with 0/1 response data for a set of test questions. There are approx 7.5k items that have been randomly allocated to participants in an online quiz. Just over 10,000 participants (set ...
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1answer
34 views

Using IRT when most of the responses are null values

Greetings Cross Validated, I feel like I need to go into a little background before I bring up the specific issue I'm having. A few years ago Congress passed the FAST act, Part of this act mandated a ...
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How can I estimate student abilities with a Rasch Model?

I have a dataset of test results. There are 400 students, and 100 items. I ran ltm::rasch in R, and I computed ability scores for each student, and difficulty scores for each item. I would now like ...
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Couple questions regarding 3PL IRT model

It so happens we need to implement our own parameter estimation for 3PL IRT model in our small in-house tool we are developing. I'm using Stata which implements IRT to compare how our estimates fare ...
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How to convert IRT theta score to a percentage score

I am trying to implement an adaptive test using 3PL IRT model. We need to screen the candidates and label their expertise as ...
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IRT population dependent question

I'm currently reading "The Basics of Item Response Theory using R" and I can't wrap my head around something. IRT is sample independent so if you take 2 groups from 1 population of varying ability ...
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34 views

3PL IRT model. Could someone point to a nice explanation and/or tutorial?

I'm very new to IRT. Even so, have just been asked to try and learn to use 3PL model on the data that we have. I'm completely out of my depth, and what's worse is we'll have to run our own parameter ...
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Why won't a 3PL IRT run?

I'm running some IRT models on test data and encountered a new problem. There are 36 items (scored as "correct" and "incorrect") and 287 participants with no missing data. I'm using Stata (not by ...
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Poisson adaptation of IRT model: how to interpret parameters?

For my work I made an assessment in which users have to stack blocks in a certain configuration in as few steps as possible. If the user does this in the minimally required number of steps, they get ...
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In 1PL model, zero ability equals average ability, or change accuracy? [closed]

In a test evaluation scenario, latent variable analyses are used to represent the ability of the test-taker and the difficulty of the question. A 1PL model uses a latent, random log-odds threshold, $\...
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Ceiling effect of data-IRT Rasch EFA

Can you do IRT, CFA and/or Rasch if your data has items with large ceiling effects (i.e., no one was choosing the last two options of a 5-point likert scale)? Is it appropriate to do?
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How to proceed when collapsing ordinal items with levels that got no answer?

I have a set of 8 Likert-type items with 9 levels each. In no case do we have an item for which responses fill all possibilities and this has shown to be an issue for the SEM I'm trying to run (as ...
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Performance metric for math tasks

I have several math items which are varying in terms of difficulty. The difficulty ranges from zero to one, where zero is the most difficult one. Let's say users are solving such math tasks. I would ...
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1answer
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IRT: Standard errors for intercepts vs. locations

In item response theory (IRT), the argument of the logit function can be expressed using a discrimination (a) and an intercept (b) as $a \theta + b$ or using a discrimination and location (c) as $a ( \...
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1answer
73 views

Convert ordinal to interval data with mirt package in R [closed]

I have ordinal data from 2 questionnaires. One questionnaire has a scale of 1:7 and the other of 1:5. I would like to convert these data to interval using polytomous item response theory. I can ...
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Extended Rasch analysis in R (PCM)

I am trying to replicate a previous piece of work using Rasch analysis to categorise respondents to a 8-item questionnaire in 3 groups. In the work I'm replicating, the Rasch analysis is used to get a ...
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1answer
76 views

Measure of fit to simulated data for item response theory model

Starting with randomly generated person ability parameters $\textbf{z}$ and item parameters $(\boldsymbol \alpha,\boldsymbol{\beta})$, I simulated data representing correct/incorrect responses of $N$ ...
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What is the probability that a student gets a better score than another on a test with randomly selected questions?

Suppose there is a set $S$ of $100$ questions and there are $2$ students $a$ and $b$. Let $P_{ai}$ be the probability that $a$ answers the question $i$ correctly, and $P_{bi}$ the same for $b$. All $...
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1answer
444 views

Guessing Factor in Item Response Theory

I'm currently trying to learn basics (nah who am i joking I'm only trying to learn the concept) of IRT since i have a high stake test (college entrance exam) coming in a few months that used IRT but i ...
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168 views

What do I do with local dependence in a polytomous IRT model?

I have built an GPCM IRT model using survey data, but have found significant local dependence (in violation of the LID assumption) using residuals() in R. I've found information online for dealing ...
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Handful of IRT scores all exactly the same value

I am using the mirt package in R to model some latent variables. They seem to be working fine, except that a bunch of the scores generated are exactly the same. Most of the scores are within two or ...
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Is Item Response Theory (IRT) a form of reinforcement learning?

I was doing studies in reinforcement learning and trying to apply it in Computerised Adaptive Testing (CAT). While learning IRT, I felt it is similar to behaviour of RL setting - receiving feedback ...
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227 views

constraining item difficulty in 2PL estimation using “ltm”

I was planning to bridge IRT estimations of different tests using one particular item as an anchor. Currently, I am using the ltm package in R and am planning to do it using the option ...
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IRT diferences in using callibrated itens and doing the callibration

Recently I applied a mathematics test for ensino fundamental (the Brazilian elementary school) composed by 24 items previously calibrated under a 3 parameters logistic model. The calibration of these ...
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Bayesian Model Fit for Binary Data

I am looking for methods (and preferably references) for assessing model fit for Bayesian analyses of binary data. Specifically, I am fitting Bayesian parametric and nonparametric item response models ...
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IRT vs proportion/frequency

Lets say I have response data from a multiple choice exam question and I want to understand whether the item was too difficult, or if I should change it somehow to improve it What benefits do I get ...
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When to use which ability estimates method?

There are several methods in IRT ability estimation,such as : expected a-posteriori ("EAP"), Bayes modal ("MAP"), weighted likelihood estimation ("WLE"), maximum likelihood ("ML"), expected a-...
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How to do unidimension test for graded response model?

Is there any method or R function can be used to check whether data is unidimensional with graded response model (grm)?
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Can IRT supersede CTT nowadays?

CTT is Classical Test Theory, IRT is Item Response Theory. IRT can handle anything CTT can. But I am curious why IRT is seldom mentioned on this site. Can IRT supersede CTT nowadays?
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Should I use both CTT and IRT to analysis data?

Theses questions are about competence of 2 analysis systems. 1.Is there any analysis can be done within CTT but not IRT? 2.If I done analysis within IRT, should I use CTT to check again? According to ...
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81 views

What's the criteria of deleting item? [closed]

What's the recognized criteria in statistics world?
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267 views

Reporting LRT(log likelihood ratios) from anova()

I' ve got two logistic models/ based on IRT that I wanted to compare them using the log likelihoodratio test, so I used anova(model1, model2) in R. My output looks like following: ...
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IRT Model for number of attempts before correct response

I have a test where respondents are able to attempt each item as many times as required until they get it correct. I am looking to fit an IRT model to data from this test in order to look at the ...
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Is location and scale of IRT parameter estimates arbitrary?

There is a thing I’ve never understood in IRT completely. Packages in R such as mirt or ltm are usually consistent in their ...