STRONG TRUE SCORE THEORY- IRT LECTURE 12 EPSY 625.

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STRONG TRUE SCORE THEORY- IRT LECTURE 12 EPSY 625

Strong True Score Theory Equivalent to g-theory: subject ability item difficulty Extension of true score theory Uses form of logistic regression: e Dag(  - bg ) Pr(1) = 1 + e Dag(  - bg )

Strong True Score Theory Equivalent to g-theory: subject ability item difficulty Extension of true score theory Uses form of logistic regression: e Dag(  - bg ) Pr(1) = 1 + e Dag(  - bg )

Pg()Pg()  ABILITY Difficulty b g Probability of Correct Answer Item Response Model Discrimination a g Difficulty: the ability score needed for a 50% probability of getting the item right Discrimination: slope of the IRT curve at the 50% probability intersection Assumptions:.local independence of items.single ability true score.logistic model for items: e Dag(  - bg ) Pr(1) = 1 + e Dag(  - bg )

MODELS One parameter model- only b g varies across items Two parameter model- both a g and b g vary across items

1-PARAMETER ESTIMATION MPLUS: TITLE:this is an example of a one –parameter logistic item response theory (IRT) model DATA:FILE IS ex5.5.dat; VARIABLE:NAMES ARE u1-u5; CATEGORICAL ARE u1-u5; ANALYSIS:ESTIMATOR = MLR; MODEL:f BY u1 (1) u2 (1) u3 (1) u4 (1) u5 (1); OUTPUT:TECH1 TECH8;

MPLUS 5.5 OUTPUT Thresholds Estimates S.E. Est./S.E. F BY U U U U U Thresholds U1$ U2$ U3$ U4$ U5$ Fixed slopes Item difficulties

2-PARAMETER ESTIMATION MPLUS: TITLE:this is an example of a two- parameter logistic item response theory (IRT) model DATA:FILE IS ex5.5.dat; VARIABLE:NAMES ARE u1-u20; CATEGORICAL ARE u1-u20; ANALYSIS:ESTIMATOR = MLR; MODEL:f BY u1-u20; OUTPUT:TECH1 TECH8;

MPLUS 5.5 OUTPUT MODEL RESULTS Estimates S.E. Est./S.E. F BY U U U U U U U U U U U U U U U U U U U U Thresholds U1$ U2$ U3$ U4$ U5$ U6$ U7$ U8$ U9$ U10$ U11$ U12$ U13$ U14$ U15$ U16$ U17$ U18$ U19$ U20$ Slopes (a parameters) difficulties (b parameters)

Three parameter model a g and b g vary across items parameter c g for guessing is added: Empirical studies indicate c g is usually lower than guessing rate Requires 5, ,000 cases for stable estimation (ETS, ACT or NAEP samples)

Pg()Pg()  ABILITY Probability of Correct Answer agag bgbg cgcg

Pg()Pg() 11.5 (1,2)(1,2) Pg()Pg() MULTIDIMENSIONAL IRT - CONCEPTS AND ISSUES - Difficulty in getting estimates - Inconsistent with factor model analysis