17 votes

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. ...
machow's user avatar
  • 291
12 votes
Accepted

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)...
Tom's user avatar
  • 606
11 votes
Accepted

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 ...
Ben Bolker's user avatar
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6 votes
Accepted

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
bdeonovic's user avatar
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6 votes
Accepted

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 ...
whuber's user avatar
  • 323k
6 votes

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 ...
philchalmers's user avatar
  • 3,063
6 votes
Accepted

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 ...
philchalmers's user avatar
  • 3,063
6 votes
Accepted

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 ...
Preston Botter's user avatar
6 votes
Accepted

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. ...
Jeremy Miles's user avatar
  • 17.9k
6 votes

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 $\theta$, $p_i({\theta})$...
Tim's user avatar
  • 138k
6 votes
Accepted

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 ...
Tom's user avatar
  • 606
5 votes

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 ...
Pier-Eric Chamberland's user avatar
5 votes

theta parameter in R's LTM package

It's the factor.scores function: WIRStheta <- ltm::factor.scores(two_pl)
Jeremy Miles's user avatar
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5 votes
Accepted

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 $\theta$ ...
Preston Botter's user avatar
5 votes

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-...
Preston Botter's user avatar
5 votes

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 (...
Preston Botter's user avatar
4 votes

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 ...
Preston Botter's user avatar
4 votes

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 $\alpha = 1$, $P(x = 1 | \theta, \alpha) \ne 0.5$....
philchalmers's user avatar
  • 3,063
4 votes
Accepted

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. ...
Weiwen Ng's user avatar
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4 votes
Accepted

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 ...
Preston Botter's user avatar
4 votes

$M_2$ 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 ...
Preston Botter's user avatar
4 votes
Accepted

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 ...
Tom's user avatar
  • 606
3 votes
Accepted

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 ...
philchalmers's user avatar
  • 3,063
3 votes
Accepted

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: <...
Sukaesi Marianti's user avatar
3 votes

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 ...
philchalmers's user avatar
  • 3,063
3 votes

How do you interpret/feedback IRT theta scores?

As @user136371 says, item response theory (IRT) theta scores estimates $\hat\theta$ can be interpreted as standardized z-scores when the latent variable mean $\mu_\theta$ and standard deviation $\...
Preston Botter's user avatar
3 votes

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

I agree that the accepted answer does not point towards specifically dedicated models. See for instance: Noel, Y. & Dauvier, B. (2007). A beta item response model for continuous bounded responses,...
George Klimmt's user avatar
3 votes
Accepted

Item information for 4PL under IRT

It's basically the same, but like the 3PL model you get progressively less information in the extreme ends of $\theta$ due to the upper/lower bound parameters. It has the form: $$I(\theta) = \frac{a^...
philchalmers's user avatar
  • 3,063
3 votes

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 ...
philchalmers's user avatar
  • 3,063
3 votes
Accepted

Guessing Factor in Item Response Theory

IRT can be used in many ways and there are many different models. First, many tests that use IRT are also computerized adaptive tests. In these, you don't have a choice of which questions to answer. ...
Peter Flom's user avatar
  • 120k

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