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.

Filter by
Sorted by
Tagged with
1 vote
1 answer
50 views

How to interpret Location parameters in Generalised Partial Credit Model?

I am struggling to interpret the location parameters in generalised partial credit models. Say you have location parameters $a_1$,$a_2$ and $a_3$. My professor said that for the item to be accepted ...
2 votes
3 answers
307 views

Understanding and applying Item Response Theory

In the process of designing a quiz application that can assess the student for understanding of a particular concept, I came across Item Response Theory. I have absolutely no clue whether applying ...
0 votes
1 answer
89 views

$M_2$ Function in MIRT R Package

I am facing an error. The $M_2$ function is throwing an error when I have three items in a test. How can I resolve this?
1 vote
1 answer
252 views

There is a easy way in R to check dimensionality in IRT with principal component analysis on standardized residuals?

I suspect that a test done by thousands of students has a dimensional problem (there are two or more dimensions influencing the students' chance of getting the items right). I have a dichotomous ...
0 votes
1 answer
35 views

Item Response Theory (IRT) -- Problem (?) or unxepected result using the mirt package with a 2PL model for binary variables?

I'm working with 5 variables related to "child and family health" using Item Response Theory to check the model and identify its parameters. My model is composed of items such as "Do ...
0 votes
0 answers
21 views

Item Response Theory - Calculations with and between Latent Trait Scores

After conducting an exploratory IRT analysis, the most suitable theoretical and numerical solution suggests the utilization of five latent traits. These latent traits stem from 18 items, all measured ...
2 votes
2 answers
73 views

Weighing Questions within a Survey

I work for a public child welfare agency. We have something called a level of care tool that categorizes children based on the amount of care they need. This helps us identify appropriate care options ...
2 votes
0 answers
48 views

IRT vs proportion/frequency

Let's 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 ...
0 votes
1 answer
53 views

IRT models for repetitive items

I'm looking for literature about IRT models that fit for tests in which items are presented for each examinee more than once and/or different questions are asked for the same item. For example, in the ...
3 votes
2 answers
670 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 ...
0 votes
1 answer
68 views

What does extremely high "item information value" mean in IRT?

As far as I understand, item information tells us how well an item contributes to score estimation precision and it ranges between 0 and 1. However, in my analysis (see the image), item 15 and item 6 ...
4 votes
0 answers
223 views

IRT analysis on large sparse dataset

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

IRT analysis: duplicate columns?

I am trying to create a 2-parameter logistic regression model. My data has no NA's, 233 rows (plus 1 header row), and 458 columns of 0's and 1's only (but many ...
2 votes
2 answers
101 views

IRT Nominal Response Model theta

I'm quite familiar with multiple IRT models; however, I can't seem to understand the Nominal Response Model. How is theta estimated? For example, if we have a science test with multiple-choice items (&...
2 votes
1 answer
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 ...
2 votes
1 answer
159 views

how do i transform irt discrimination parameters of a 2PL model into factor loadings

I estimated a 2PL model for ordinal data and got discrimination as well as difficulty parameters for each item. To be able to estimate a cut-off value for the discrimination parameter, I wanted to ...
2 votes
1 answer
58 views

How to aggregate standard errors of multiple test scores?

I have three test scores of a student. The three single scores are generated by an IRT-based test using computer adaptive testing and are reportet with standard error bars. For the report I want to ...
2 votes
1 answer
348 views

Chi square statistics (chen & thissen, 1997) for local dependence testing in IRT models

I have recently computed the test for local dependence based on X2 statistics (Chen & Thissen, 1997) in RStudio with the mirt package like this: residuals(fit.SKIDDETdisc, type = "LD", ...
5 votes
1 answer
374 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 ...
2 votes
1 answer
445 views

IRT: What is enough information? And can a test provide too much?

I was wondering what makes for a good test information value in IRT, and came across this: Reliability: Item and test information functions graphically reflect how reliably the individual items and ...
0 votes
2 answers
55 views

What is the name for an explanatory item response model where the predictors include latent variables?

Explanatory item response models add predictors of the $\theta$ "ability" parameter. However, these predictors are always observed covariates. Sometimes, one may want to include latent ...
4 votes
1 answer
341 views

How many parameters are estimated in a 2PL model?

I'm familiar with 1PL IRT models, where you have some data matrix, and you model the latent factors, theta (the trait/ability) and (item) difficulty. ...
1 vote
1 answer
801 views

Overall goodness-of-fit/p-value for multiple items IRT model in R (ltm)

The data set which I am trying to analyse is Student Test Data. I have a data of responses (either 1/correct response or 0/incorrect response) on some questions of a set of students. I have fitted a "...
5 votes
2 answers
102 views

Finding a Common Thread in Disparate Indicators

All of the theory I know about factor analysis, scales, etc revolves around separating out indicators into groups that each have (ideally) one underlying dimension. I have a student for whom we'd ...
3 votes
1 answer
54 views

How to interpret factor analysis output here

I am using girth package which uses polychoric correlation and then applies factor analysis. I am using the example code given on above webpage under the subheading "Polychoric Correlation ...
1 vote
2 answers
248 views

Using Co-variates in Item Response Theory 3PL model?

I am using Item Response theory(IRT) using 3 Parameter Logistic Model(3PL) for Logic test. After training the model, I use the posterior means of the item parameters 𝛼, β and γ to estimate person ...
2 votes
2 answers
91 views

Appropriate Statistical Test to Determine Internal Cohesion of a Categorical Data

I have a dataset that is composed of mainly binary variables, each row represents a patient, and each column represents a symptom of a disease. The patient would tick 1 (if they experience the ...
2 votes
1 answer
57 views

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 ...
2 votes
2 answers
3k views

How do you interpret/feedback IRT theta scores?

In classical test theory (CTT), we would say something like: "Your score is higher than 80% of people in the normgroup." In item response theory (IRT), how do we interpret/feedback a theta ...
2 votes
1 answer
167 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 ...
26 votes
6 answers
20k views

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. ...
0 votes
0 answers
30 views

irt hybrid model predict latent estimate using bayesian method

I'm having some problem about irt prediction model. When i use irt hybrid model, it cannot predict the latent value even it has successfully converge during the irt model processed. It contain binary ...
1 vote
0 answers
41 views

Model test sensitivity to ability

I have a set of tests and a population of agents whose ability I want to assess. Each agent has taken some of the tests. The agents have no memory of the tests they have taken, so each time an agent ...
0 votes
0 answers
23 views

What do bad infit and outfit in dichotomous Rasch model signify?

I'm really a beginner with Psychometry. We've just started psychometry in our college and I've used software Jamovi for that purpose. Working with Dichotomous Rasch models to asses a Multiple choice ...
2 votes
1 answer
61 views

Repeating the same item with different offsets using the *mirt* package

Let's imagine that we want to develop an IRT model that describes the probability that a basketball player scores a basket when he shoots the ball from a certain distance. Distance is a continuous ...
8 votes
2 answers
7k views

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 vote
1 answer
64 views

Item response theory has "graded" models for Likert items. Is there an IRT model for if some items that are "Likert" and some that are "binary"?

Item Response Theory is most conventionally applied to binary data, but can also be applied to Likert data with "graded" models. But what if you have data that is a mixture of both Likert ...
0 votes
0 answers
27 views

Get random effect value from pattern of data

Rasch models are typically fit through an item response theory framework, but can also be estimated through a mixed effects model (e.g., see here). This is highly useful in my case because of some of ...
6 votes
1 answer
330 views

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 ...
4 votes
2 answers
2k views

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 (...
0 votes
0 answers
102 views

Longitudinal IRT model specification using MIRT bfactor function

I try to specify / calculate a longitudinal IRT latent growth model to compare learning gains between three school years in a large data set. The test were administered by a computer adaptive testing ...
0 votes
1 answer
49 views

Is ceiling effect mitigated by standardisation, renorming or combining with other indicators?

I have a psychological test that consist of a set of binary items. It has a noticeable ceiling effect in the sum scores (essentially, a majority of participants get most items correct). I also see ...
0 votes
0 answers
51 views

Python implementation of Marginal Maximum Likelihood estimate based 2-PL Dichotomous IRT

I am looking for implementations of simple Marginal Maximum Likelihood Estimate based 2-PL IRT Item estimation in Python. Any relevant Python libraries that do this (similar to snowIRT module in ...
3 votes
1 answer
1k views

IQ adaptive test items in 1pl, 2pl or 3pl IRT model?

Some adaptive test systems (e.g. school assessment tools) use the 1pl IRT model, while others use the 2pl or the 3pl. When developing an adaptive IQ test, is there a rule of thumb about which model ...
3 votes
1 answer
426 views

Item information in IRT with item covariates (linear logistic test model)

Short question: How does the calculation and interpretation of IRT item information and test information change in the presence of item properties? Long question: There's a variation on IRT called the ...
2 votes
0 answers
67 views

Implementing a 2-PL Dichotomous IRT Module in Python from scratch

I am trying to implement a 2-PL dichotomous IRT Model for my dataset from scratch in Python. Here is my code so far: ...
0 votes
0 answers
40 views

Development of an adaptive scale

I need your help with a problem that I noticed and I don't know the solution (I am not from statistics). In sum, I would like to create a measurement instrument that is adaptive in that respondents ...
0 votes
0 answers
28 views

What does MSE mean in the calculation of separation reliability for rasch model?

In the Rasch model, the reliability of separation can be calculated as 1 - (MSE / SD^2), where SD represents the standard deviation of person location measures on a logit scale, and MSE refers to the ...
0 votes
0 answers
17 views

When using different groups of examinees to answer the same set of items, whether the item parameter should be invariant?

I am now doing a project to estimate the item parameters from the pharmacotherapy exams. Two groups of students from the same university answer the same set of items. From my understanding, the item ...
0 votes
1 answer
100 views

How can I solve identifiability problems in my STAN estimation?

So I am trying to validate my STAN model before using real data and am having some trouble estimating parameters separately. My data structure contains count data with people on the rows, and test ...

1
2 3 4 5 6