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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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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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32 views

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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Bayes hw question; estimating parameters of an IRT model [closed]

Differences and similarities between a marginalized Bayesian estimation method and a fully Bayesian method in estimating item parameters of a 2-parameter logistic item response model.
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39 views

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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33 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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30 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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22 views

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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13 views

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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51 views

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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21 views

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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1answer
24 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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52 views

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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140 views

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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25 views

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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45 views

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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33 views

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
62 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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42 views

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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66 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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419 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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Similar questions across similar samples at different times - reliability?

I'm working with pilot data where there exist several versions of the same questionnaires that were administered to different participants across various time points. I'd like to get a better sense of ...
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46 views

what does a negative slope mean in a 2-PL model?

i'm an IRT novice. in classical test theory, negative discrimination occurs when high test performers score lower on an item than low test performers. is this synonymous to a negative slope in the 2-...
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222 views

Comparing AIC and BIC of CFA and IRT

I was wondering does it make sense to compare AIC and BIC values of confirmatory factor analysis models and item response theory models? In many cases, goodness of fit indices for item response theory ...
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133 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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179 views

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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194 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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33 views

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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40 views

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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68 views

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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80 views

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

What's the recognized criteria in statistics world?
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232 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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39 views

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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1answer
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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 ...
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1answer
97 views

Item information for 4PL under IRT

What is the item information curve for 4PL model under item response theory (IRT)? the information of 3PL has quite a neat form: But what it is like if I add parameter of carelessness "d"?
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217 views

Item Response Theory vs Rasch Model

1) What's the difference between Item Response Theory and Rasch model? 2) What's the pros and cons between them? To me, they seem to be very similar as in they both analyze the performance of ...
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1answer
42 views

Estimating user ability (success or fail) using maximum likelihood and Item response theory

I am trying to estimate the user ability (success or fail) using item response theory. So, I am re-implementing an algorithm from this paper but I can not understand the following line: In the ...
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41 views

Item Response Models with Few Measures

Are there any problems with using Item Response Theory models such as the Graded Response Model when the number of measures is small? I don't know if there are any asymptotic results that would make a ...
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39 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 ...
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61 views

Dependency in IRT with pseudoitems as a testlet

I'm curious whether a testlet IRT model would be appropriate for a situation where polytomous responses on a 1-5 scale are decomposed into pseudoitems indicating whether the response is $\ge X$ ...
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77 views

Joint estimation of item and ability parameters

Most Common Approach of estimation is Marginal Maximum Likelihood. Other procedures: 1) Joint Maximum Likelihood (Rasch only); 2) Markov Chain Monte Carlo(MCMC): Typically only used for highly ...
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325 views

IRT monotonicity

I am trying to analyse data from a questionnaire containing 24 items using a 2pl IRT. Responses are provided on yes-no format. How can I examine the assumption of monotonicity in IRT for binary data?...