Talk:Item response theory

message: Angela 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 Wikipedia, particularly classical test theory.
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?
Amead 19:09, 5 Jan 2004 (UTC)
replies: text: 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. Angela.
Amead, 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:
*The definition introduced did not properly define 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. probability theory) and efforts to make it so should not detract from the essential elements of a definition.  Having said this, some of the changes were great and I agree the definition needs to be improved.
*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 body of theory does not suggest it is a theory (i.e. particular theory).
*Extra spaces between 1st and 2nd para of overview look sloppy (minor point obviously)
*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 (**)
*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 an American perspective -- European, Asian, etc. perspectives also need to be considered.
BTW, you're right about link to discrimination, removed it.
(**)On reliability, let:
\hat{\theta} = \theta + \epsilon
Then \mbox{SE}({\theta}) is an estimate of the standard deviation of \epsilon for person with a given wighted score and
\frac{\mbox{VAR}[\theta]}{\mbox{VAR}[\hat{\theta}]}=\frac{\mbox{VAR}[\hat{\theta}]-\mbox{VAR}[\epsilon]}{\mbox{VAR}[\hat{\theta}]}
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 ... Stephenhumphry 03:22, 30 July 2005 (UTC)
thread_title: Negative language

message: Is the equation for the three parameter logistic equation correct? It contains four parameters if you include the D parameter. This parameter is not discussed in the article nor does it appear in Baker's online book discussing the three-parameter model.
Andrés (talk) 14:35, 17 April 2008 (UTC)
replies: text: D is not an estimated parameter.  It is a constant fixed to 1.0 or 1.702 to determine the scale.Iulus Ascanius (talk) 16:12, 17 April 2008 (UTC)

text: 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. 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, http://harvey.psyc.vt.edu/Documents/WagnerHarveySIOP2003.pdf, http://www2.hawaii.edu/~daniel/irtctt.pdf.  Any IRT book will explain it.
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. This rescaling is appropriate for the 2PL model but not for the 3PL model whenever c_i > 0. As stated latter in the article, the use of D=1.7 makes the characteristic curve of the 2PL differ by less than 0.1 from the that of the normal CDF. This bound is broken by any fitted value of c_i > 0. 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 c_i to be 0.2 or higher. For negative values of the responder's ability, any 3PL with c_i > 0 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. Andrés (talk) 14:32, 22 April 2008 (UTC)
thread_title: Equation

message: A definition of phi would be useful in the normal ogive equation.Gshouser (talk) 22:01, 2 September 2009 (UTC)
thread_title:  Normal Ogive Equation 

message: I've changed a passage in the article to read as follows:
: 
: An alternative formulation constructs IRFs based on the normal probability distribution; these are sometimes called normal ogive models.  For example, the formula for a two-parameter normal-ogive IRF is:
: 
:: 
p_i(\theta)= \Phi \left( \frac{\theta-b_i}{\sigma_i} \right)
: 
: where Φ is the cumulative distribution function (cdf) of the standard normal distribution.
: 
Nowhere earlier in the article did it say what Φ is, and yet it didn't say here either!  Why not??  Before my recent edits the article said
:  p_i(\theta)= \Phi \cdot \frac{\theta-b_i}{\sigma_i}
: 
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.
: 
Have I misunderstood this? Michael Hardy (talk) 05:15, 8 February 2010 (UTC)
thread_title:  My recent revision 

message: 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.
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.
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 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).
IRT entails three assumptions:
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). 
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 and Novick 16.3 page 361 in the brown hard-covered version).
NealKingston (talk) 22:12, 28 July 2010 (UTC)
thread_title:  Comments on the overview 

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thread_title:  Intelligence citations bibliography for updating this and other articles 

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thread_title: Assessment comment

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