Test Information Function

RASCH MEASUREMENT
Transactions of the Rasch Measurement SIG American Educational Research Association
Vol. 25 No. 1 Summer 2011 ISSN 1051-0796

How Much Do Emotions Alter Our Measurements?
Do situational factors during measurement change measurement estimates (item difficulties, person abilities, standard errors, etc.)? Our research shows that item difficulties are different when one accounts for individual differences in positive affectivity during test administration. We calibrated the items of a Spelling Instrument ignoring, and then including, the influence of positive affectivity. A two-level Hierarchical Generalized Linear Model (HGLM) was used: Level-1 (Bernoulli) Rasch model for a test of i = 1,k dichotomous items: log ( pij / (1-pij) ) = β0j + β1jX1j + ... + βijXij + ... + β(k-1)jX(k-1)j where pij is the probability that person j will answer item i correctly. βoj is person ability relative to item k and is the intercept of the model. β1j is the easiness of the item 1 (relative to item k) for person j and the coefficient of dummy variable X1. For pij, all the dummy variables are 0, except for Xij = 1 which flags that this equation models a response to item i. Level-2 model expressing person and item estimates: β0j = γ00 + u0j β1j = γ10; ... ; βij = γi0; ... ; β(k-1)j = γ(k-1)0 γ00 is the mean of the person ability distribution relative to item k. u0j is the value of the random ability effect specific to person j. {u0j} are modeled to be normally distributed, N(0,τ), across the person sample. The item easinesses, {γi0} are modeled to be invariant across the sample. When this two-level model is applied to the response by person j to item i, the probability of a correct response becomes: log ( pij / (1-pij) ) = γ00 + γi0 + u0j In the analysis of our 7-item test of spelling ability, k = 7. In a second “adjusted” analysis, the Level-2 model was modified by adding the term γ01*PositiveAffect j to β0j in order to account for... [continues]

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