Talk:Item response theory

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Novick's Statistical Theories of Mental Test Scores -- I am not sure how you could miss this and at the same time be concerned with issues that are fifty years old, such as comparing CTT and IRT. Another hisotorical point is that Lazarsfeld's models dealt with categorical latent variates and are typically discussed under the rubric of 'latent class analysis' (see e.g., Bartholemew and Knott, 1999). Arguably these are a very different kind of model than those found in IRT. I mean, if you are going to discuss Lazarsfeld's work in connection with IRT, you might as well also discuss Spearman's work on unidimensional factor analsyis as "pioneering work in IRT". The point is that these are not conventionally treated as the same classes of models. The class of models conventionally treated as IRT models are just those introduced by Birnbaum, which include the Rasch model as a special case.

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wikipedia entry does not serve that function. I am not sure who this entry is aimed at. It's not very useful to say that you have to be expert in the subject before you can understand the description here. As far as I can understand it, tests are graded using information (extracted from the test results as a whole) about 1) the difficulty of the question and 2) the ability of the student. It is not clear to me whether a student's grade is affected by his/her own performance. Does a stronger student get a better or worse score than a weaker student with the same test answers? If not, why use the students' ability as a parameter? Sorry, I just don't get it, and it is not explained here. I don't expect an answer on this talk page, but if anybody cares, they could edit the main article. Thanks

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addition to stating his (a past president of the psychometric society) own opinion, he also provides several references. That it is not decisively accepted by IRT practitioners at large is also attested by many of its staunchest proponents use of "objective", "Rasch" and "fundamental" as modifiers, and by the plethora of articles defending it (why defend what no one attacks?). If the giants in the field don't agree then it seems odd for the wiki to choose one side (as it does by use of the Andrich quote, as opposed to the Wright quote which has a modifier).

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that the definition of measurement in the natural sciences - physics, chemistry, etc. - is widely agreed. Indeed, it is implied by the definition of all SI units and the standard means of expressing magnitudes in physics (a number of units where the numbeer is a real). See Reese's quote in the psychometric article. Your edits seemed to me to suggest that Rasch and proponents have 'created' some mysterious definition of measurement, which is patently untrue. What has actually occurred is that various people have created definitions of measurement that are

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prevalent to use common item classical approaches. Use of IRT got a huge boost by New York State's "Truth in Testing" legislation that threatened to derail common item and equivalent form equating approaches. Almost all operational IRT work was done using mainframe computers until maybe the mid 80's. Desirability to reduce testing time by using adaptive testing models further boosted the use of IRT with work on the ASVAB and the the College Board's course placement tests (operational circa 1984).

2150:, posted for the use of all Wikipedians who have occasion to edit articles on human intelligence and related issues. I happen to have circulating access to a huge academic research library at a university with an active research program in these issues (and to another library that is one of the ten largest public library systems in the United States) and have been researching these issues since 1989. You are welcome to use these citations for your own research. You can help other Wikipedians by 1178:"Item response theory (IRT) is a body of related psychometric theory that provides a foundation for scaling persons and items based on responses to assessment items. The central feature of IRT models is that they relate item responses to characteristics of individual persons and assessment items. Expressed in somewhat more technical terms, IRT models are functions relating person and item parameters to the probability of a discrete outcome, such as a correct response to an item." 163: 142: 22: 173: 1058:

that are "completely different"--because "approach" could encompass so many things where Rasch is virtually identical to the 1PL, such as: having a one-parameter logistic function to describe responding; assuming a latent trait that explains responses; wanting "good" measurement; valuing what Rasch called

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This article is not appropriate for an encyclopeadia entry. I have a degree in psych and it is incomprehensible. It is jargon from beginning to end. I looked up the entry to find out what IRT meant. I haven't a clue. The people on the talk page are happy with it. They are evidently members of an

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both describe a sine function. For every solution to the characteristic curve that uses the fixed value of 1.0 for D, there exists an equivalent representation that uses the value 1.702. There is no mathematical way to way to distinguish the two. Can someone provide a reference to the significance of

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This article is not appropriate for an encyclopedia entry. I have a degree in psych and it is incomprehensible. It is jargon from beginning to end. I looked up the entry to find out what IRT meant. I haven't a clue. The people on this talk page are happy with it. They are evidently members of an

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I'll do some library diving when I get time to see what the authoritative sources in sufficiency's home field (mathematical statistics) say on the matter beyond the references I gave above, and get back to you. As far as Rasch measurement, I am hoping my feelings about Rasch measurement (pro and con)

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with the definition throughout the most established sciences (physics, etc.). I have no problem with you presenting alternative definitions, but be clear about them so the article can be written from that basis. There is no need to labour the definition of measurement implied by Rasch models, because

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There is a miscommunication here. Let me be as clear as possible. My whole point in inviting you to give an agreed upon definition of measurement in IRT is that it doesn't exist. Rasch explicitly showed the congruence of his models with measurement in physics in his 1960 book. What I actually said is

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The Rasch had already been covered, and there was no connection to newly introduced material. Also, the One Parameter Logistic Model (OPLM) is also a model referred to by Verhelst & Glas (1995) which potentially makes the statement quite confusing. The comments on Rasch were (as you stated) from

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What you guys seem to be arguing about is education at large, and are grinding your axe on a theory of educational testing that is probably one of the best things to happen to the regulation of educational testing in the US. I say this because if a test actually does what an IRT theory says it does,

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Thank you for the references to the use of the D constant. I now understand the issues better. The purpose of the constant is to make the item's charecteristic curve look like that of the CDF of the normal distribution by rescaling the ability scale. The entry in the article is still wrong, however.

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In the following copy of the first paragraph from the article, the last most technical paragraph is actually the most easy to understand. I would explain what "item" is because the term is too generic. I would replace scaling with rating if that is what is meant. In the first sentence alone, the use

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I happened to be investigating computer image processing and the links brought me to this page. The first paragraph is really incomprehensible to someone outside of the field. I initially thought that it was related to determination of the size of objects in an image. While it doesn't apply to me, I

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BTW, the worse sin of this section is that I am not sure, after studying it, how Rasch is "a completely different approach" as claimed in the article. In my edits, I have tried to emphasize the theoretical differences that would lead one to apply IRT or Rasch modeling--I think those are the aspects

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The problem with your citation was that it was entirely unclear what point was being made. Could you please just clarify the point in light of this discussion? Be bold in editing -- let's just have a discussion if you want to actually remove points that are being made, rather than add counterpoints.

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To see the relation between Rasch modeling and other domains of IRT, consider for example the case when items with response bias (DIF) are removed from a test. In principle, this is not any different than constructing a test to have items with uniform discrimination (which is all a Rasch model is).

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I came to this page because I was reading articles about standardized testing. IRT was mentioned, but not explained in the articles I found. I'm an educated professional, used to reading technical articles. I feel sure that somebody could describe IRT in a way that a lay person can understand. This

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if parameters are supposed to enter into a stochastic model (and any other model is clearly inferior as far as recovering the data is concerned, if that is the criterion). I'm not sure what you think Fischer and Molenaar "manage". It seems to me you think there is some problem with Rasch models and

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IRT has only two assumptions - local independence and form of the item response function. Local indepence subsumes unidimensionality in the case of unidimensional IRT models. Local independence is tanamount to saying the dimensionality of the data matches the dimensionality of the model. See Lord

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Birnbaum's work made IRT feasible on main frame computers by the early to mid 60's, but there was little reason to add the complexity of IRT to large-scale programs. The first large-scale program that used IRT was TOEFL around 1976-77, which had to use IRT equating methods because cheating was too

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Hi, I am not a frequent wiki user but I came accross this article and wanted to draw some things to your attention. Firstly I think you have forgotten to mention some important historical developments in IRT. In particular, the 2PL and 3PL models are attributable to Birnbaum's sections of Lord and

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That's the point, that is nothing more than a small rescaling to help the logistic function more closely approximate a cumulative normal function. Here's a good reference, though it's not available through ERIC: Camilli, G. (1994). Origin of the scaling constant "D" = 1.7 in item response theory.

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That the statistic (X1, X2, ... Xn) is sufficient, irregardless of whether it allows a reduction of the data or is a scalar, is in the mathematical statistics texts by Rohatgi (1976, pg. 339), Bickel and Doksum (1977, pg. 83) and Lehmann (1983, pg. 41), among others. Fischer and Molenaar (1995)

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As far as sufficient statistics, isn't the entire data set definitionally a sufficient statistic (albeit a not-very-useful one) for the model parameters in general, making the statement “has sufficient statistics” vacuous? (I would be interested in any references to mathematical statistics texts

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Some technical points: the article doesnt state _anything_ about estimation and the treatment of model fitting is very unsatisfactory -- these issues have been the core of IRT since the 1970s. I would recommend that if this article is to reflect the modern state of IRT it be largely re-written to

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Well, philosophers take little interest in IRT because philosophy is neither quantitative or scientific. Moreover, you are confusing psychometrics with psychological testing. Associating IRT with eugenics is like associating the physics of the internal combustion engine with drunk driving. And

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Incidentally, if you respond, I'll move the discussion to the bottom to keep things in chronological order, so please look for any responses at the bottom. If you don't respond, I'll move it after a few days. I'd also ask you to keep in mind constructive criticism and input is productive, whereas

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What works best for you in editing this part of the wiki? Should I post some proposed changes here in the discussion first for your modification, or would it be easier for if I scan-mailed you the two pages of Thissen and Wainer (if you don’t have a copy available) and let you take the first go?

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Person and item parameters have sufficient statistics (DATA only) in the Rasch model. There is no data reduction when the entire data set is called a statistic, and I would suggest you'd need to define the term statistic. So the answer is no, it is not at all vacuous to state that person and item

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In that case I would suggest starting a separate, later section of the IRT wiki dealing with the relationship between "Model building" based IRT and the philosophical underpinnings of Rasch measurement, instead of putting it in what is ostensibly the "Overview" section for IRT. It would make the

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feels that the second to last paragraph, where tests are described as imprecise and containing error, is too negative. I feel it is a statement of fact that is often misunderstood by non-psychometricians. I think it follows directly from the psychometric material here on Knowledge, particularly

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It is almost as if these mathematical insights fell straight from heaven, without any social or political contexts to guide their subsequent development. The inclusion of some related background on eugenics, educationism, and social progressivism, as it relates to IRT, would be helpful for those

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Did you use any quantitative methods in your degree? The reason I ask is that IRT is quite different from traditional quantitative methods taught in psych, and sometimes this makes it harder rather than easier to have some background. Whatever the case, though, I value your feedback. Some of the

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Fair enough. Keep in mind though that the concept of sufficiency is due to Sir Ronald Fisher and Rasch studied and worked with Fisher directly. Keep in mind also it ceases to be a purely mathematical matter where it comes to models used for empirical data. There is a quote from Rasch about this.

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There also seems to be a mis-characterization of the Rasch-IRT controversy, minimizing the differences. I have quotes by Andrich and others that I will try to incorporate. The main thrust seems to be that IRT essentially muddies the clarity of the Rasch separability theorem by adding extraneous

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for a brief account of the history of this definition. If you would like to propose a definition you think is widely accepted in IRT with a citation, be my guest. Please do not attempt to 'balance' by omitting a perspective. Balance on Knowledge should be achieved by considered presentation of

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As far as the definition of "measurement", it strikes me as patently untrue that it has a single agreed upon definition in psychometrics (regardless of what other wiki’s might say). The Thissen reference that you have removed twice deals with this from the IRT model building perspective. In

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alternative perspectives. There were some quite fundamental problems with previous edits. For example, the reference to "easily computed sufficient statistics" seemed to imply other models have sufficient statistics but they're just not easily computed. This was misleading to say the least.

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Well, I didnt realise I had such a vested interest in this issue, but after reading some comments in this Missing Critique section, I think the following point should be made. The Rasch model, as with any other IRT model, is a theory of how tests _should be_ constructed -- it tells us what

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manage by saying what the particular sufficient statistic is (number correct score or sum score -- pages 10 and 16) or what other property is required for the given result (minimality and independence of some other statistic or from an exponential family -- pg. 25 and 222 respectively). --

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The basic idea is that and IRT model tells us what a test is _supposed to do_, and then tests are constructed (i.e., items are selected) so that they meet the assumptions of the model. The model is inherently normative, because educational evaluation is inherently normative.

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don't harm my attempts to add to this wiki any more than yours stop you. In my experience, most IRT researchers appreciate both the philosophical and statistical properties of the Rasch models as well as the need to deal with a wide variety of actual data sets. --

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complaining about relevant jargon by throwing in irrelevant jargon is hardly compelling. Lastly, why wouldn't response data be associated with its trait? We assume that the response to an algebra question is related to algebra knowledge; not exactly far-fetched.

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will not be close to the normal CDF no matter what value of D is picked. As support for my argument that the D constant does not belong in the 3PL equation, I point out that the Camilli reference given in the previous paragraph only talks about the 2PL model.

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article needs to be technical -- it is by definition a body of theory. However, the basic purpose and concepts can be made clearer, and I for one am open to suggestion and input. In order to begin somewhere, does the first sentence not make some sense for you?

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is analogous to chronbach's alpha (indeed it is typically very close in value) and so analogous to the traditional concept of reliability. The mean squared standard error can be used as the estimate of the variance of the error across persons. Take care ...

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I agree. The language is quite simple for someone with a quantitative background, which is necessary to understand IRT. Having a degree in psych won't help much. That's like saying a BA in Biology will help you understand meta-analysis of public health

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The Rasch section was ridiculously disproportionate and I have reduced it to a few short paragraphs that say THE SAME THING (IMHO). If anyone thinks I cut too much, I would suggest that you consider creating a new entry to house an in-depth discussion.

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IRT has been referred to as a body of related psychometric theory from early on, and I don't see good reason to say "it is not a theory per se". Doesn't this suggest the label is self-contradictory and so confused? I would also note that saying it is a

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Reliability vs information being introduced as a topic separately to information is to me inefficient (e.g. detail such as info fn being bell-shaped was repeated). Further, if we want to make this connection, it should be done properly. See below

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Also, to say that this article is written for statisticians is ridiculous -- its mathematical content is bare-bones. Really it seems that this article should be separated into two parts, one for social implications, one for statistical details.

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Do we really need two paragraphs distinguishing IRT from Rasch? I also prefer to have a more balanced set of references on the issue of distinguishing the two, and that the definition of measurement not be from a strictly Rasch perspective.

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I removed two external links to sites related to the Rasch model. Both links were "Objective Measurement" links, not general IRT links, and thus more appropriately belong on the Rasch model wiki (which I added to the "See also" section).

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then the ability estimates (i.e., people's test scores) based on that model are an accurate reflection of people's relative standing on the test. In terms of gate-keeping, this is better than, say, blatant upperclass chauvinism, right?

1936: 288:, I reverted the article, at least for now, becuase I don't believe that on balance, the changes enhanced it. Revert again if you wish -- prefer we work toward a better article in a considered way if possible. The issues were: 955:, which leads to sufficiency of total scores (or sometimes vectors as in Andersen, 1977). I can refer to various articles to make these points (most importantly Rasch, 1961), but I fear we'll just go around in circles all day. 1606:. For example, in a multiple choice exam question even random guessing will pick the correct answer. As I understand IRT, that is why the 3PL is used. In a typical exam with five choices, one would expect the fitted value of 2040: 1718:

The word "basis" in the introduction needs some explication -- why response-data would or could be correlated with "traits" or "ability" requires the acceptance of many assumptions, but this is not treated in the article.

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BTW, just to clarify a couple of things -- scaling items is not nonsensical if you understand the process of scaling (estimating scale locations from responses to items). Rating is most certainly not the same as scaling.

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Journal of Educational and Behavioral Statistics, 19(3), 293-295. If you need papers immediately available on the internet that mention but do'nt really explain, see www.fcsm.gov/05papers/Cyr_Davies_IIIC.pdf,

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I think a couple of paragraphs about IRT and Rasch is in order. The definition of measurement is not from a Rasch perspective. The definition of measurement throughout the natural sciences is quite clear. See

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statistical properties test items should have and then, on the basis that they have those properties, allows for the evaluation of individual's performance (relative to other individuals) on such items.

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That didn't appear to make sense. It looks like the kind of thing someone might write if they were dutifully copying the formula and misunderstood it, rather than explaining something they understood.

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In fact, as "Clarity" points out, it is difficult to understand what the IRT article is about. It is, quite simply, an article by statisticians for other statisticians, and not a general audience.

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IRT, rather it described (i) what it is used for and (ii) what it is not. While I agree a definition should be as non-technical as possible, this can only be so with reason (see for e.g.

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It's worth noting that I, the author, am a psychometrician (i.e., not likely to have a negative view of testing). Maybe someone can suggest a alternative wording that appears balanced?

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FYI in your recent revision of the normal ogive model, the parameter sigma_i is more often written as a_i = 1 /sigma_i and termed the 'discrimination parameter' of the item.

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Thanks for the comments, much appreciated. We'd better work on tightening up. It should be at least obvious what it is and what it is used for in the simplest possible terms.

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Cool. I'm trying to encourage a swath of IRT people I've worked with into contributing on their areas of specialization (MIRT, DIF, equating, unfolding models, etc...). --

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I think the Rasch-IRT "controversy" is already overemphasized. If anything, we need more info about how the Rasch method is self-serving, inadequate, and unscientific.

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A unidimensional trait denoted by θ ; Local independence of items; The response of a person to an item can be modeled by a mathematical item response function (IRF).

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Why is the history of the controversies and critiques of IRT missing? I'm sure philosophers have attacked the basic assumptions of IRT, but nowhere is this evident.

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Actually, I'm happy with the way it is now as it makes it clear you are talking about it in terms of standard error etc rather than sounding like someone's opinion.

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Would you mind e-mailing me using the wiki function? Couple of things I want to mention but don't want to congest the board. Thanks for the cooperative spirit.

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IRT did not become widely used until the late 1970s and 1980s, when personal computers gave many researchers access to the computing power necessary for IRT.

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Great, well I'll have a go if I get time also. Together, I'm sure we can improve. I think quite a few parts of the article could be improved personally.

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There is no connection between the rise of personal computers and the rise of IRT. Besides, pretty much no one had personal computers in the late 70s.

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I agree it is better placed in another section. Let's do that. I'm pretty flat out -- if you want to have a go, great, and I'll look at it when I can.

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of "items" twice with potentially different meanings is particularly confusing and scaling "items" based on their responses is a just nonsensical.

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references to discrimination and 2PL/3PL model make more sense. I think it would also be a better place for the "frame of reference" discussion.

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the epistemological case put forward for the models. As far as these models are concenred, the point is that the person and item parameters are

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just thought that I would provide some comment to highlight the confusion that a layman might encounter in trying to understand the content.

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parameter. This parameter is not discussed in the article nor does it appear in Baker's online book discussing the three-parameter model.

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When you have finished reviewing my changes, you may follow the instructions on the template below to fix any issues with the URLs.

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Baker, F. B. & Kim, S. (2004). Item Response Theory: Parameter Estimation Techniques(2nd ed.). New York: Marcel Dekker Inc.

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through comments on that page. It will be extremely helpful for articles on human intelligence to edit them according to the

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Could some one explain why correlating "data" with "traits" and "abilities" (which are also social constructs) is "scaling"?

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which (IMO) is subsumed under the IRT assumptions of local item independence and subpopulation parameter invariance; etc.

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parameters designed to second guess test takers and item creators alike, making it Raschian separability impossible.

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To add to the above, I'm perplexed by your comments about articles "defending it". Defending what, exactly? By whom?

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An alternative formulation constructs IRFs based on the normal probability distribution; these are sometimes called

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Is the equation for the three parameter logistic equation correct? It contains four parameters if you include the

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the D parameter/constant? It still seems incorrect to me. A random selection of an article from the web, such as

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to delete these "External links modified" talk page sections if they want to de-clutter talk pages, but see the

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I had a problem with "scaling," since none of the other definitions seem to apply to the use given here. See:

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If you have discovered URLs which were erroneously considered dead by the bot, you can report them with

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iff the probability distribtion of the data conditional on the relevant statistic is not dependent on

569:{\displaystyle {\frac {{\mbox{VAR}}}{{\mbox{VAR}}}}={\frac {{\mbox{VAR}}-{\mbox{VAR}}}{{\mbox{VAR}}}}} 73: 52: 2222: 1723: 21: 1792: 1749: 1741: 1727: 1690: 1409: 1260: 1218: 1117: 580: 1364: 1041: 1017: 972: 758: 690: 652: 591: 194:

on Knowledge. If you would like to participate, please visit the project page, where you can join

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on Knowledge. If you would like to participate, please visit the project page, where you can join

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I should have time to do a little mucking around second week of October. ::crosses-fingers::: --

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before doing mass systematic removals. This message is updated dynamically through the template

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D is not an estimated parameter. It is a constant fixed to 1.0 or 1.702 to determine the scale.

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is, and yet it didn't say here either! Why not?? Before my recent edits the article said

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an American perspective -- European, Asian, etc. perspectives also need to be considered.

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Last edited at 06:27, 12 January 2007 (UTC). Substituted at 19:12, 29 April 2016 (UTC)

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You may find it helpful while reading or editing articles to look at a bibliography of

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If you found an error with any archives or the URLs themselves, you can fix them with

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https://web.archive.org/web/20041210140342/http://work.psych.uiuc.edu/irt/tutorial.asp

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parameter. In other words, it cannot change the class of the function. The functions

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Extra spaces between 1st and 2nd para of overview look sloppy (minor point obviously)

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esoteric circle. Talk plain English or give an example - or something. - Pepper

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This rescaling is appropriate for the 2PL model but not for the 3PL model whenever

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https://web.archive.org/web/20071211021313/http://assess.com/xcart/home.php?cat=37

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to be 0.2 or higher. For negative values of the responder's ability, any 3PL with

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https://web.archive.org/web/20060613221419/http://www.b-a-h.com/software/irt/icl/

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These seem valid points ... why not improve things? 11:16, 16 December 2009 (UTC)

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from the that of the normal CDF. This bound is broken by any fitted value of

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esoteric circle. Talk plain English or give an example - or something.

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Intelligence citations bibliography for updating this and other articles

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Comparison of Item-Fit Statistics for the Three-Parameter Logistic Model

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Knowledge standards for reliable sources for medicine-related articles

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emotive language tends to obstruct productive communication. Cheers.

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that restrict sufficient statistics from being the entire data set.)

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makes no difference. All one is doing is rescaling the value of the

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This previous comment makes no mathematical sense. Whether one uses

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A definition of phi would be useful in the normal ogive equation.

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makes the characteristic curve of the 2PL differ by less than

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and Novick 16.3 page 361 in the brown hard-covered version).

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Let's define a statistic as being sufficient for a parameter

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http://harvey.psyc.vt.edu/Documents/WagnerHarveySIOP2003.pdf

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for additional information. I made the following changes:

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I've changed a passage in the article to read as follows:

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does not suggest it is a theory (i.e. particular theory).

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parameters have sufficient statistics (total scores).

539: 521: 493: 459: 441: 381: 1971: 1862: 1640: 1612: 1577: 1556: 1530: 1495: 1412: 1367: 1340: 1307: 1280: 942:. If we were to condition on the entire data matrix, 907: 866: 820: 800: 780: 436: 414: 379: 336: 190:, a collaborative effort to improve the coverage of 85:, a collaborative effort to improve the coverage of 2285:using the archive tool instructions below. Editors 2034: 1930: 1659: 1625: 1596: 1562: 1542: 1514: 1446: 1398: 1353: 1326: 1293: 934: 893: 852: 806: 786: 568: 420: 400: 364:{\displaystyle {\hat {\theta }}=\theta +\epsilon } 363: 1027:I'm open to any alternatives for clarification. 2187:, and are posted here for posterity. Following 1958:Nowhere earlier in the article did it say what 600:Amount of distinguishing from Rasch Measurement 2271:This message was posted before February 2018. 1524:. As stated latter in the article, the use of 2181:The comment(s) below were originally left at 1459:, makes no mention of this scaling constant. 8: 716:of the congruence with the rest of science. 408:is an estimate of the standard deviation of 2243:http://work.psych.uiuc.edu/irt/tutorial.asp 948:according to that definition of sufficiency 292:The definition introduced did not properly 1952:(cdf) of the standard normal distribution. 428:for person with a given wighted score and 136: 47: 2221:I have just modified 3 external links on 2075:include the topics discussed in , e.g., 2024: 2013: 2000: 1976: 1970: 1916: 1905: 1892: 1867: 1861: 1645: 1639: 1617: 1611: 1582: 1576: 1555: 1529: 1500: 1494: 1481:http://www2.hawaii.edu/~daniel/irtctt.pdf 1429: 1411: 1381: 1366: 1345: 1339: 1318: 1306: 1285: 1279: 906: 865: 841: 825: 819: 799: 779: 549: 548: 538: 520: 503: 502: 492: 489: 469: 468: 458: 440: 437: 435: 413: 390: 380: 378: 338: 337: 335: 2263:http://assess.com/xcart/home.php?cat=37 138: 49: 19: 2253:http://www.b-a-h.com/software/irt/icl/ 401:{\displaystyle {\mbox{SE}}({\theta })} 7: 944:there is no probability distribution 184:This article is within the scope of 79:This article is within the scope of 38:It is of interest to the following 2373:Mid-importance psychology articles 2358:Low-importance Statistics articles 2184:Talk:Item response theory/Comments 1994: 1885: 853:{\displaystyle \beta _{ni}=x_{ni}} 14: 2225:. Please take a moment to review 2189:several discussions in past years 1950:cumulative distribution function 1748:) 04:37, 16 December 2009 (UTC) 1712:struggling with this article. 1483:. Any IRT book will explain it. 323:BTW, you're right about link to 204:Knowledge:WikiProject Psychology 171: 161: 140: 99:Knowledge:WikiProject Statistics 72: 51: 20: 2378:WikiProject Psychology articles 2363:WikiProject Statistics articles 1738:) 03:55, 16 December 2009 (UTC) 1215:http://en.wikipedia.org/Scaling 224:This article has been rated as 207:Template:WikiProject Psychology 119:This article has been rated as 102:Template:WikiProject Statistics 2115:IRT entails three assumptions: 1988: 1982: 1879: 1873: 1447:{\displaystyle \sin(Da_{i}*x)} 1441: 1419: 1393: 1374: 1248:) 14:35, 17 April 2008 (UTC) ( 1045:23:37, 26 September 2006 (UTC) 1032:03:31, 26 September 2006 (UTC) 1021:02:30, 26 September 2006 (UTC) 1002:05:17, 27 September 2006 (UTC) 976:03:39, 27 September 2006 (UTC) 762:23:37, 26 September 2006 (UTC) 748:03:31, 26 September 2006 (UTC) 732:05:38, 26 September 2006 (UTC) 721:03:31, 26 September 2006 (UTC) 694:03:39, 27 September 2006 (UTC) 673:01:20, 27 September 2006 (UTC) 656:23:37, 26 September 2006 (UTC) 643:03:31, 26 September 2006 (UTC) 628:00:58, 26 September 2006 (UTC) 613:21:00, 25 September 2006 (UTC) 560: 554: 545: 533: 527: 514: 508: 499: 480: 474: 465: 453: 447: 395: 387: 343: 1: 2339:02:23, 18 November 2017 (UTC) 2172:02:10, 2 September 2013 (UTC) 1801:16:55, 17 December 2009 (UTC) 1780:04:16, 17 December 2009 (UTC) 1758:04:38, 16 December 2009 (UTC) 1699:22:01, 2 September 2009 (UTC) 1399:{\displaystyle \sin(a_{i}*x)} 1227:04:03, 16 December 2009 (UTC) 1204:07:01, 28 February 2007 (UTC) 1194:12:55, 27 February 2007 (UTC) 1159:22:04, 24 February 2007 (UTC) 1144:22:55, 7 September 2014 (UTC) 1074:21:57, 23 November 2011 (UTC) 198:and see a list of open tasks. 93:and see a list of open tasks. 2203:06:27, 12 January 2007 (UTC) 2093:15:55, 9 February 2010 (UTC) 2065:05:15, 8 February 2010 (UTC) 1829:16:28, 9 February 2010 (UTC) 1107:10:57, 12 January 2007 (UTC) 1092:06:30, 12 January 2007 (UTC) 2368:B-Class psychology articles 2353:B-Class Statistics articles 2055:Have I misunderstood this? 2394: 2302:(last update: 5 June 2024) 2218:Hello fellow Wikipedians, 1680:14:32, 22 April 2008 (UTC) 1469:05:52, 21 April 2008 (UTC) 1269:16:12, 17 April 2008 (UTC) 1254:14:32, 17 April 2008 (UTC) 1126:16:12, 17 April 2008 (UTC) 595:20:27, 15 April 2006 (UTC) 230:project's importance scale 2196: 2137:22:12, 28 July 2010 (UTC) 1660:{\displaystyle c_{i}: --> 1597:{\displaystyle c_{i}: --> 1515:{\displaystyle c_{i}: --> 584:03:22, 30 July 2005 (UTC) 421:{\displaystyle \epsilon } 330:(**)On reliability, let: 223: 156: 118: 67: 46: 2098:Comments on the overview 935:{\displaystyle i=1,..,I} 894:{\displaystyle n=1,..,N} 271:19:09, 5 Jan 2004 (UTC) 2214:External links modified 1327:{\displaystyle D*a_{i}} 807:{\displaystyle \theta } 787:{\displaystyle \theta } 2152:suggesting new sources 2148:Intelligence Citations 2036: 1932: 1662: 1627: 1599: 1564: 1544: 1517: 1448: 1400: 1355: 1328: 1295: 936: 895: 854: 808: 788: 570: 422: 402: 365: 187:WikiProject Psychology 82:WikiProject Statistics 28:This article is rated 2037: 1933: 1685:Normal Ogive Equation 1663: 1628: 1626:{\displaystyle c_{i}} 1600: 1565: 1545: 1543:{\displaystyle D=1.7} 1518: 1449: 1401: 1356: 1354:{\displaystyle a_{i}} 1329: 1296: 1294:{\displaystyle a_{i}} 937: 896: 855: 809: 789: 571: 423: 403: 366: 260:classical test theory 2283:regular verification 2223:Item response theory 1969: 1860: 1638: 1610: 1575: 1554: 1528: 1493: 1410: 1365: 1338: 1305: 1278: 1060:specific objectivity 905: 864: 818: 798: 778: 434: 412: 377: 334: 2273:After February 2018 1563:{\displaystyle 0.1} 814:. 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