# 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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### 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 ...
42 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 ...
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### 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 ...
108 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 (&...
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### $M_2$ 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?
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### 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 ...
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### 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 ...
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### 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 ...
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1 vote
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### 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 ...
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### 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 ...
190 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 ...
62 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 ...
1 vote
66 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 ...
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### 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 ...
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### 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 ...
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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 ...
104 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 ...
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### 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 ...
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### 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 ...
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### 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: ...
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### 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 ...
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 ...
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### 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 ...
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### 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 vote
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### 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 ...
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1 vote
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### Must questionnaire questions have the same number of options for IRT models to work?

Given a questionnaire whose questions have different numbers of options available say having questions with ratings from 1-2 and 1-5. Could I use polytomous models such as a partial credit model to ...
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1 vote
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### Comparing scores on different dimensions in factor models

So I'm currently conducting some research where I'm using item response theory (IRT) to estimate the difficulty of school subjects in Norway. It turns out that a two-dimensional, simple-structure ...
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### Factor analysis (or similar) for data set with both continuous and dichotomous variables (+control for age?)

As you can tell from the title I'm in a bit of a fix. I have a data set with three continuous variables and one dichotomous one. Data collected from four groups. The data set is a developmental ...
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1 vote
432 views

### Fixing item parameters in MIRT

I am trying to estimate a multiple group model where I fix some of the item parameters and estimate the rest. I was expecting that this scenario would allow me to remove the restriction on the ...
154 views

### Estimating a higher-oder IRT model in R

Hi everyone, I am trying to estimate a higher-order model with the mirt package in R. I have already conducted an analysis using ...
38 views

### How can I run IRT-RSM on categorical items for measures of noncognitive skills if for some levels for some items there are 0 observations?

I am working on data with psychosocial scales in Stata. There are five measures of psychosocial ability used in the data, with between 4 to 9 items for each. All the items are measured on 4-pt Likert ...
1 vote
356 views

### How does an item intercept in CFA relate to the difficulty parameter in IRT?

I am having difficulty clarifying in my mind how item intercepts in Confirmatory Factor Analysis or SEM manifest, and how they are graphically represented in an IRT ICC plot. I understand that multi-...
118 views

### How is item response theory (IRT) with continuous responses related to factor analysis/SEM?

Nearly all of the papers and posts I've seen focus on the equivalence of confirmatory factor analysis (CFA) or structural equation modeling (SEM) with item response theory (IRT) models when the data ...
158 views

### How to interpret the Rasch reliability?

I am tasked to model a set of questionnaires in order to investigate about the food insecurity in the region where my project takes place. Using the Rasch model, I was able to conduct the protocol ...
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### Do you have to assess reliability for non-composite scores?

I feel like this is probably a really stupid question but I'm having issues finding the answer. When I think of reliability, normally I think of several items on a test that are compiled into some ...
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### 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 ...
1 vote
35 views

### Confirmatory factor analysis parameterization of the 2-PL item response model

For binary item response $i$ by person $j$, the 2-PL item response model is of the form: $$Response_{ij} \sim Bernoulli(p_{ij})$$ $$logit(p_{ij}) \sim \alpha_i(\theta_j - \eta_i)$$ Usually, $\alpha_i$ ...
1 vote
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### Item Factor Analysis, Item Response Theory and Exploratory IRT [duplicate]

I would be grateful if someone could explain the difference between Item Factor Analysis, Item Response Theory and Exploratory IRT. Any references especially for the exploratory IRT are welcome. Nikos
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### 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 ...
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1 vote
241 views

### Computing IRT score reliability across a range of ability in mirt

I am using mirt and would like to get reliability estimates across a range of ability for a 1-factor scale. Essentially, I would like to extract the data used to ...
366 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", ...
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### How do I calculate different reliabilty levels of theta when standard error of theta is known? (IRT-model) [duplicate]

I've recently seen a plot where the level of reliability is given for different SE values of theta estimates: I have also plotted the standard errors of theta as a function of theta but now I am ...
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1 vote
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### Calculation of reliability of scale scores in an IRT- model

While trying to compute the reliability of scale scores obtained from IRT models (bifactor models and unidimensional models) I was wondering why there are so many published papers who report omega ...
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### Methods for drawing population inferences from multiple sub-population datasets

What would be an appropriate model or method for making inferences about a broader population quantity from multiple quantities representing subsets of the population? Imagine, as an example, that I ...
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1 vote
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### Within item response theory, what is the $\theta$-grid?

Within item response theory, the latent trait (e.g., ability) is often depicted as $\theta$. Within item response theory, I have also come across the term $\theta$-grid. For example, the description ...
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### Discrimination/Slope Item Response Theory Models

In item response theory (IRT), 1-PL models, which include a slope parameter in addition to the intercept parameter, are better able to discriminate test-taker talent. Higher slopes translate to ...
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### Item Response Theory for Continuous-Unbounded Response

I would like to model a problem using IRT, but my response is continuous and possibly infinite (e.g. score of a game). I'm aware of Samejima's and Wang and Zeng's approach, but both attempts to bound ...
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### Rasch Analysis: comparison of the distribution person location estimates across independent samples

I hardly understand Rasch analysis (and this isn't my goal) but I need to clarify the following questions before delving deeper: Does it make any sense within the framework of Rasch analysis (and ...
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