**ERIC Number:**EJ856069

**Record Type:**Journal

**Publication Date:**2009

**Pages:**5

**Abstractor:**ERIC

**Reference Count:**13

**ISBN:**N/A

**ISSN:**ISSN-1536-6367

On Interpreting the Parameters for Any Item Response Model

Thissen, David

Measurement: Interdisciplinary Research and Perspectives, v7 n2 p106-110 2009

Maris and Bechger's article is an exercise in technical virtuosity and provides much to be learned by students of psychometrics. In this commentary, the author begins with making two observations. The first is that the title, "On Interpreting the Model Parameters for the Three Parameter Logistic Model," belies the generality of parts of Maris and Bechger's essay. Its third section and discussion make points that are important for the understanding of "any" item response model based on continuous latent variables. The only relation of those sections with the three parameter logistic (3PL) model is that a version of the 3PL model is part of the illustration, and some of the algebraic techniques used in that section are introduced in the second section "Parameter Identifiability in the 3PL Model." The second observation is that, although the second section of the article, "Parameter Identifiability in the 3PL Model," contains algebra that shows that "a" 3PL model's parameters are not identified, it is not "the" 3PL model as that term is usually used. The demonstration is limited to a completely fixed-effects 3PL model. In modern item response theory (IRT), [theta] is usually considered a latent variable, as it is by Maris and Bechger in the article's third section and discussion. In any model in which [theta] is a latent variable, the population distribution, f([theta]) in Maris and Bechger's notation, is an essential part. The transformation of [theta] involved in the demonstration of the lack of identifiability in Maris and Bechger's second section would change the functional form of f([theta]), which is not permitted if the functional form for f([theta]) is part of the model. No lack of identifiability is shown for the latent-variable (or "marginal" [Bock & Lieberman, 1970; Bock & Aitkin, 1981]) form of the 3PL model that is in widespread use. While Maris and Bechger provide an interesting algebraic result for the fixed-effects form of the 3PL model, in this commentary the author talks about the more general final sections of the article.

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**Publication Type:**Journal Articles; Opinion Papers

**Education Level:**N/A

**Audience:**N/A

**Language:**English

**Sponsor:**N/A

**Authoring Institution:**N/A