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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 (...

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127 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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1answer
20 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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1answer
28 views

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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43 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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1answer
24 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
42 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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23 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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1answer
43 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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2answers
136 views

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
377 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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11 views

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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0answers
30 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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173 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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1answer
82 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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0answers
29 views

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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0answers
119 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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0answers
29 views

Factor Scores from Generalised Partial Credit Model in IRT versus Confirmatory Factor Analysis

I have run a CFA on a questionair with 25 item and calculated the corresponding Factor Scores (5 dimensions) for each case (in R with the package 'lavaan'). I also have run 5 generalised partial ...
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17 views

Mixed Model IRT (MMIRT) versus Factor Mixture Modeling (FMM)

I wonder if my following description about MMIRT and FMM is correct. This will help me check my understanding of the two statistical techniques: MMIRT is a hybrid between latent class analysis (LCA) ...
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22 views

Item response theory

I have a question please regarding the adjustment in Item Response Theory. There are two proposals about the infit and outfit where I am a bit confused of choosing one of them as a reference to work ...
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1answer
105 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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0answers
30 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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0answers
38 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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21 views

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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34 views

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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91 views

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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66 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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47 views

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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1answer
70 views

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

What's the recognized criteria in statistics world?
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182 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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1answer
38 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
36 views

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
84 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"?
2
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1answer
179 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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39 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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1answer
38 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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1answer
55 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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1answer
70 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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1answer
291 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?...
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1answer
548 views

theta parameter in R's LTM package

I am curious whether there is an intuitive way in ltm package in R to display person's estimated latent trait after fitting the ...
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1answer
133 views

Estimating of item difficulty in IRT

Which approaches are exist for the estimation of a item difficulty from the statistical data? Are they measure objective item's complexity?
2
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1answer
136 views

How can I rate the question according to the difficulty?

I have a set of problems to analyze from a programming contest. My work is to rate the question according to its difficulty (easy,medium,hard) by analyzing the ...
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1answer
95 views

Meaning of several peaks of information curves in GRM

I fitted my data to GRM, got the information curves and try to interprete the pictures. I'm new to IRT and still don't get a lot of things. Here I can observe that the items are pretty good and ...
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61 views

Quantifying rater consistency

I have a test in which students must give scores to 3+ items, for which we can compute distances from "true" (instructor) scores. ...
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1answer
789 views

Similarities and differences between IRT model and Logistic regression model

Despite the basic similarities like both of these model the probability of success rather than modelling the response variable directly; I believe that there are more reliable answers which point out ...
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0answers
112 views

Quantifying internal consistency with multiple raters and continuous rating scales

I have data from an assessment where people are rated by multiple raters on a set of criteria using a rating scale that is (essentially) interval. All people are rated by all raters. I believe that ...
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0answers
31 views

Evaluation of experiment based on Multidimensional Item Response Theory?

For my master thesis within Educational Science and Technology, I have an experimental design with students divided over a control and an experimental group based on an educational intervention, and ...
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92 views

If I know difficulty and thresholds of all items can I build a Rasch model and calculate the ability of new patients

I'm trying to "reverse engineer" a statistal model used in this article: ACTIVLIM : A Rasch-built measure of activity limitations in children and adults with neuromuscular disorders In this article a ...
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69 views

Longitudinal IRT estimation - wrong approaches?

I have been fitting longitudinal IRT models, checking for measurement invariance over time, constraining item parameters not to change over time, as recommended in the literature, and had good ...
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0answers
216 views

What does sample independence mean in Item Response Theory (IRT)

I keep reading that (at least the difficulty parameters of) an IRT model is sample independent. I find it difficult to get my head around this concept. Surely there must be limits to this statement. ...