The paired comparison method for latent variables An Application of the Bradley Terry Model Almut Thomas Michaela Gareiß Regina Dittrich Reinhold Hatzinger nd Workshop on Psychometric Computing February th - February th LMU, Department for Statistics Thomas Gareiß Dittrich & Hatzinger The BTL for latent variables –
Introduction ❍ Instrument ❍ Example ❍ Standard Procedure ❍ Way out Analysing FIT with Paired Comparisons Methods Results Introduction Possible Refinement Results Comparison of Results Thomas Gareiß Dittrich & Hatzinger The BTL for latent variables –
Instrument Introduction Freizeit-Interessen-Test (FIT), Stangl ❍ Instrument based on Holland’s ( ) RIASEC-model . . . . ❍ Example ❍ Standard Procedure ❍ Way out Analysing FIT with Paired Comparisons Methods R ealistic : practical, physical Results Possible Refinement Results Comparison of Results Thomas Gareiß Dittrich & Hatzinger The BTL for latent variables –
Instrument Introduction Freizeit-Interessen-Test (FIT), Stangl ❍ Instrument based on Holland’s ( ) RIASEC-model . . . . ❍ Example ❍ Standard Procedure ❍ Way out Analysing FIT with Paired Comparisons Methods R ealistic : practical, physical Results Possible Refinement I nvestigative : intellectual, scientific Results Comparison of Results Thomas Gareiß Dittrich & Hatzinger The BTL for latent variables –
Instrument Introduction Freizeit-Interessen-Test (FIT), Stangl ❍ Instrument based on Holland’s ( ) RIASEC-model . . . . ❍ Example ❍ Standard Procedure ❍ Way out Analysing FIT with Paired Comparisons Methods R ealistic : practical, physical Results Possible Refinement I nvestigative : intellectual, scientific Results Comparison of Results A rtistic : creative, independent Thomas Gareiß Dittrich & Hatzinger The BTL for latent variables –
Instrument Introduction Freizeit-Interessen-Test (FIT), Stangl ❍ Instrument based on Holland’s ( ) RIASEC-model . . . . ❍ Example ❍ Standard Procedure ❍ Way out Analysing FIT with Paired Comparisons Methods R ealistic : practical, physical Results Possible Refinement I nvestigative : intellectual, scientific Results Comparison of Results A rtistic : creative, independent S ocial : supporting, helping Thomas Gareiß Dittrich & Hatzinger The BTL for latent variables –
Instrument Introduction Freizeit-Interessen-Test (FIT), Stangl ❍ Instrument based on Holland’s ( ) RIASEC-model . . . . ❍ Example ❍ Standard Procedure ❍ Way out Analysing FIT with Paired Comparisons Methods R ealistic : practical, physical Results Possible Refinement I nvestigative : intellectual, scientific Results Comparison of Results A rtistic : creative, independent S ocial : supporting, helping E nterprising : competitive, persuading Thomas Gareiß Dittrich & Hatzinger The BTL for latent variables –
Instrument Introduction Freizeit-Interessen-Test (FIT), Stangl ❍ Instrument based on Holland’s ( ) RIASEC-model . . . . ❍ Example ❍ Standard Procedure ❍ Way out Analysing FIT with Paired Comparisons Methods R ealistic : practical, physical Results Possible Refinement I nvestigative : intellectual, scientific Results Comparison of Results A rtistic : creative, independent S ocial : supporting, helping E nterprising : competitive, persuading C onventional : detail-oriented, organizing Thomas Gareiß Dittrich & Hatzinger The BTL for latent variables –
Example Introduction ❍ Instrument ❍ Example ❍ Standard Procedure ❍ Way out Which of the two alternatives would you prefer? Analysing FIT with Paired Comparisons Methods Results Possible Refinement Results Comparison of Results Thomas Gareiß Dittrich & Hatzinger The BTL for latent variables –
Example Introduction ❍ Instrument ❍ Example ❍ Standard Procedure ❍ Way out Which of the two alternatives would you prefer? Analysing FIT with Paired Comparisons Methods Results Build a greenhouse (R) grow and maintain ◦ ◦ Possible Refinement rare plants (I) Results in your own garden. Comparison of Results Thomas Gareiß Dittrich & Hatzinger The BTL for latent variables –
Example Introduction ❍ Instrument ❍ Example ❍ Standard Procedure ❍ Way out Which of the two alternatives would you prefer? Analysing FIT with Paired Comparisons Methods Results Build a greenhouse (R) grow and maintain ◦ ◦ Possible Refinement rare plants (I) Results in your own garden. Comparison of Results Play as a musician (A) ◦ ◦ be a conductor (E) in a folk group. Thomas Gareiß Dittrich & Hatzinger The BTL for latent variables –
Example Introduction ❍ Instrument ❍ Example ❍ Standard Procedure ❍ Way out Which of the two alternatives would you prefer? Analysing FIT with Paired Comparisons Methods Results Build a greenhouse (R) grow and maintain ◦ ◦ Possible Refinement rare plants (I) Results in your own garden. Comparison of Results Play as a musician (A) ◦ ◦ be a conductor (E) in a folk group. Produce (R) ◦ ◦ sale (E) christmas decoration. Thomas Gareiß Dittrich & Hatzinger The BTL for latent variables –
Standard Procedure Introduction ❍ Instrument ❍ Example ❍ Standard Procedure ❍ Way out Sum the selected items of each scale Analysing FIT with Paired Comparisons Methods Compare the means of the sub-scales Results Possible Refinement Results Comparison of Results Thomas Gareiß Dittrich & Hatzinger The BTL for latent variables –
Standard Procedure Introduction ❍ Instrument ❍ Example ❍ Standard Procedure ❍ Way out Sum the selected items of each scale Analysing FIT with Paired Comparisons Methods Compare the means of the sub-scales Results Possible Refinement Each item has a di ff erent attractivity Results Comparison of Results Thomas Gareiß Dittrich & Hatzinger The BTL for latent variables –
Standard Procedure Introduction ❍ Instrument ❍ Example ❍ Standard Procedure ❍ Way out Sum the selected items of each scale Analysing FIT with Paired Comparisons Methods Compare the means of the sub-scales Results Possible Refinement Each item has a di ff erent attractivity Results Comparison of Results The selection of an item depends on the o ff ered alternative Comparison of sub-scale means is not appropriate Thomas Gareiß Dittrich & Hatzinger The BTL for latent variables –
Way out Introduction ❍ Instrument Use of methods for Paired Comparisons ❍ Example ❍ Standard Procedure ❍ Way out Analysing FIT with Paired Comparisons Methods Results Possible Refinement Results Comparison of Results Thomas Gareiß Dittrich & Hatzinger The BTL for latent variables –
Way out Introduction ❍ Instrument Use of methods for Paired Comparisons ❍ Example ❍ Standard Procedure ❍ Way out Analysing FIT with Paired Comparisons Methods Results FIT: Possible Refinement Results di ff erent items Comparison of Results di ff erent items for each sub-scale comparisons e.g. R : I , I : A , Thomas Gareiß Dittrich & Hatzinger The BTL for latent variables –
Introduction Analysing FIT with Paired Comparisons Methods ❍ Problem ❍ Object Covariate ❍ Categorical Object Covariates ❍ Reparameterization Matrix Analysing FIT with Paired ❍ Including Subject Covariates ❍ Sample Comparisons Methods ❍ Solution Results Possible Refinement Results Comparison of Results Thomas Gareiß Dittrich & Hatzinger The BTL for latent variables –
Problem Introduction Analysing FIT with Paired Comparisons Methods ❍ Problem ❍ Object Covariate [R ] [I ] [I ] [A ] [A ] [S ] ... ❍ Categorical Object Covariates [R ] - ... ❍ Reparameterization Matrix [I ] - ❍ Including Subject Covariates [I ] - ❍ Sample [A ] - ❍ Solution Results [A ] - Possible Refinement [S ] - Results ... ... Comparison of Results Linear dependencies in the design matrix Thomas Gareiß Dittrich & Hatzinger The BTL for latent variables –
Object Covariate Introduction Analysing FIT with Paired Comparisons Methods ❍ Problem ❍ Object Covariate ❍ Categorical Object Covariates ❍ Reparameterization Matrix ❍ Including Subject Covariates ❍ Sample ❍ Solution Each sub-scale is treated as an object: R I A S E C Results Possible Refinement Results Comparison of Results Thomas Gareiß Dittrich & Hatzinger The BTL for latent variables –
Object Covariate Introduction Analysing FIT with Paired Comparisons Methods ❍ Problem ❍ Object Covariate ❍ Categorical Object Covariates ❍ Reparameterization Matrix ❍ Including Subject Covariates ❍ Sample ❍ Solution Each sub-scale is treated as an object: R I A S E C Results Possible Refinement Each item is assigned to a sub-scale Results Comparison of Results Thomas Gareiß Dittrich & Hatzinger The BTL for latent variables –
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