# Tag Info

### What is Item Response Theory (IRT) called for continuous response?

The accepted answer does not give models where the response is bounded between [0,1]. There are IRT models for exactly the case where the response variable is continuous, but bounded in this way. ...
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### Similarities and differences between IRT model and Logistic regression model

Have a look at Section 1.6 ("The linear regression perspective") in De Boeck and Wilson (2008) Explanatory Item Response Models (http://www.springer.com/de/book/9780387402758) and Formann, A. K. (2007)...
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### Analyzing a partially crossed design

As far as I can tell you are describing a partially crossed design. The good news is that this is one of Doug Bates's main development goals for lme4: efficiently ...
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### Item Response Theory vs Rasch Model

The Rasch model is a specific model under a very large umbrella term that is Item Response Theory. See for example the wiki on IRT which specifies the Rasch model as the 1 parameter IRT model
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### What is the probability that a student gets a better score than another on a test with randomly selected questions?

A dynamic program will make short work of this. Suppose we administer all questions to the students and then randomly select a subset $\mathcal{I}$ of $k=10$ out of all $n=100$ questions. Let's ...
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### Difference between empirical and marginal reliability of an IRT model

The functions mentioned provide two approaches to computing the so-called 'marginal' reliability of a test; one based on assuming the exact probability density function of the latent trait ...
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### What is the role of non-anchor items when equating scales across studies using IRT?

It is entirely possible to equate the test forms if the items common across all three forms contain no response bias (i.e., DIF). All that would be required is to estimate a multiple-group IRT model ...
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### Finding a Common Thread in Disparate Indicators

Have you considered the bifactor measurement model? From what I can glean from your question, it looks as though you are interested in a single social norms dimension with an item bank that could ...
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### Discrimination/Slope Item Response Theory Models

A steeper slope means a stronger relationship between ability and the question. It means that the item (and therefore the test) is more reliable - and reliability is the inverse of measurement error. ...
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### Discrimination/Slope Item Response Theory Models

Intuitions are useful, but it is worth understanding the math behind the model. We model the probability of answering correctly to $i$-th question by a person with the ability $\theta$, $p_i({\theta})$...
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### Predict person parameters in explanatory IRT with lme4

Trying to answer your question, I learnt several things; so you might excuse a lengthy answer. Also, there might be some shortcut I'm not aware of. However, at the moment I don't know of any standard ...
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### Item Response Theory vs Confirmatory Factor Analysis

I believe Yves Rosseel discusses it briefly in slides 91-93 of his 2014 workshop: http://www.personality-project.org/r/tutorials/summerschool.14/rosseel_sem_cat.pdf Taken from Rosseel (2014, link ...

### theta parameter in R's LTM package

It's the factor.scores function: WIRStheta <- ltm::factor.scores(two_pl)
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### Is it acceptable/common practice to report IRT theta scores as a percentile?

Yes, assuming your IRT model is estimated using marginal maximum likelihood (MML), which is typically when $\mu_\theta$ = 0 and $\sigma_\theta$ = 1 are used to identify the model, IRT $\theta$ ...
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### how do i transform irt discrimination parameters of a 2PL model into factor loadings

The formula you provided, $\lambda$ = $\frac{\alpha}{\sqrt{1+\alpha^2}}$, is the formula to transform Item Response Theory (IRT) slope/discrimination parameters of a normal ogive model (e.g., the 2-...
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### Weighing Questions within a Survey

Preamble It is possible to incorporate item-level weights (e.g., a correct response to item 1 is worth 2 points, a correct response to item 2 is worth 1 point, etc.) within an item response theory (...
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### Is Item Response Theory (IRT) a form of reinforcement learning?

Preamble As I am sure you are already aware, Item Response Theory (IRT) is an umbrella term for a family of statistical models used to model the relationship between a test-taker's latent ability and ...
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### In 1PL model, zero ability equals average ability, or change accuracy?

Assuming that your 1PL definition is $$P(x = 1 | \theta, \alpha) = \frac{1}{1 + \exp{[-1\cdot (\theta - \alpha)}]}$$ then no, when $\theta = 0$ and $\alpha = 1$, $P(x = 1 | \theta, \alpha) \ne 0.5$....
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### Difference between IRT and EFA to find factors

A better question might be: compare exploratory factor analysis (EFA) to confirmatory factor analysis (CFA). IRT, as I will explain later, can be thought of as a type of CFA. Exploratory vs. ...
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### How many parameters are estimated in a 2PL model?

Q1. which of the above is the canonical form of the 2PL model? (or if it is some other configuration not listed above.) The one-parameter logistic (1PL) model predicts the $i^{th}$ students response ...
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### $M_2$ Function in MIRT R Package

Are you trying to calculate the $M_2$ statistic (Maydeu-Olivares & Joe, 2006) or the $C_2$ statistic (Cai & Monroe, 2014)? I ask because it is possible to calculate the $M_2$ with your model ...
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### Weighing Questions within a Survey

I agree with @Preston Botter that this is an advanced application of IRT and support the advice that you might want to look for consultation. However, I am aware of a possible realization. The ...
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### IRT monotonicity

There are basically two approaches to doing this in the literature: semi-parametric modelling via flexible IRT models such as splines, and fully non-parametric IRT models with techniques such as ...
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### theta parameter in R's LTM package

Theta estimation according to the expected response pattern: Theta <- factor.scores(two_pl) Theta estimation according to the real data response pattern: <...

### Acceptable values for discrimination parameter - 2PL IRT Model

I think that the cut-off of 0.5 is related to the historical factor analysis tradition of requiring a standardized loading of |0.3| (where loadings can range from -1 to 1). To see this, first ...
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### What's the criteria of deleting item?

Your question is closely linked to the one found here relating to the magnitude of slopes in order to determine if an item contributes a meaningful amount of information (I assume you meant to say ...
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